mesh adaptive finite element formulation for moisture transfer in materials with a critical moisture content wetting or drying of most open porous building materials is characterized by a sharp moving waterfront due to the high moisture gradients at the waterfront an accurate finite element simulation requires a very fine mesh to reduce computational costs a mesh adaptive method based on the arbitrary lagrangian eulerian ale technique is proposed to continuously relocate the nodes on the computational domain a remesh indicator is equally distributed in problems of water imbibition or drying of open porous building materials specific attention has been paid to the zone of critical moisture content to this extent the traditional jump based indicator quantifying the jump of a selected state variable has been modified into an area based remesh indicator an error analysis of an academic example shows that the area based indicator is superior to the jump based one to illustrate the capabilities of the remeshing method based on an area based indicator one and two dimensional examples of water imbibition of ceramic brick and drying of cellulose fibre cement are included copyright 1999 john wiley sons ltd

generalized fictitious methods for fluid structure interactions analysis and simulations we present a new fictitious pressure method for fluid structure interaction fsi problems in incompressible flow by generalizing the fictitious mass and damping methods we published previously in 1 the fictitious pressure method involves modification of the fluid solver whereas the fictitious mass and damping methods modify the structure solver we analyze all fictitious methods for simplified problems and obtain explicit expressions for the optimal reduction factor convergence rate index at the fsi interface 2 this analysis also demonstrates an apparent similarity of fictitious methods to the fsi approach based on robin boundary conditions which have been found to be very effective in fsi problems we implement all methods including the semi implicit robin based coupling method in the context of spectral element discretization which is more sensitive to temporal instabilities than low order methods however the methods we present here are simple and general and hence applicable to fsi based on any other spatial discretization in numerical tests we verify the selection of optimal values for the fictitious parameters for simplified problems and for vortex induced vibrations viv even at zero mass ratio for ever resonance we also develop an empirical a posteriori analysis for complex geometries and apply it to 3d patient specific flexible brain arteries with aneurysms for very large deformations we demonstrate that the fictitious pressure method enhances stability and convergence and is comparable or better in most cases to the robin approach or the other fictitious methods

variational r adaption in elastodynamics we develop a variational r adaptive finite element framework for solid dynamic applications and explore its conceptual links with the theory of dynamic configurational forces the central idea underlying the proposed approach is to allow hamilton s principle of stationary action to determine jointly the evolution of the displacement field and the discretization of the reference configuration of the body this is accomplished by rendering the action stationary with respect to the material and spatial nodal coordinates simultaneously however we find that a naive consistent galerkin discretization of the action leads to intrinsically unstable solutions remarkably we also find that this unstable behavior is eliminated when a mixed multifield version of hamilton s principle is adopted additional features of the proposed numerical implementation include the use of uncoupled space and time discretizations the use of independent space interpolations for velocities and deformations the application of these interpolations over a continuously varying adaptive mesh and the application of mixed variational integrators with independent time interpolations for velocities and nodal parameters the accuracy robustness and versatility of the approach are assessed and demonstrated by way of convergence tests and selected examples

adaptive computations using material forces and residual based error estimators on quadtree meshes quadtree is a hierarchical data structure that is well suited for h adaptive mesh refinement due to the presence of hanging nodes classical shape functions are non conforming on quadtree meshes in this paper we use natural neighbor basis functions to construct conforming interpolants on quadtree meshes to this end the recently proposed construction of polygonal basis functions is adapted to quadtree elements a fast technique for calculating stiffness matrix on quadtree meshes is introduced residual based error estimators and material force technique are used to estimate the error on quadtree meshes the performance of the adaptive technique is demonstrated through the solution of linear and nonlinear boundary value problems

the equilibrium of material forces in a 1d phase transition problem this paper aims at the use of material forces in estimating the interface location in an elastic one dimensional two phase problem a variational formulation based on variations of both the dependent and the independent variables results in the weak form of the momentum and the canonical momentum equations thus providing an appropriate framework for the use of the finite element method using this one can compute apart from the finite element solution to the equilibrium equation for the physical forces the corresponding one to the equilibrium equation for the material forces which provides the location of the interface in this way the total energy is minimized with respect to the deformations as well as to the interface location our theoretical expectations are confirmed by a numerical example concerning a one dimensional deformation induced phase transition problem with known analytical solution

stable and accurate pressure approximation for unsteady incompressible viscous flow how to properly specify boundary conditions for pressure is a longstanding problem for the incompressible navier stokes equations with no slip boundary conditions an analytical resolution of this issue stems from a recently developed formula for the pressure in terms of the commutator of the laplacian and leray projection operators here we make use of this formula to a improve the accuracy of computing pressure in two kinds of existing time discrete projection methods implicit in viscosity only and b devise new higher order accurate time discrete projection methods that extend a slip correction idea behind the well known finite difference scheme of kim and moin we test these schemes for stability and accuracy using various combinations of c 0 finite elements for all three kinds of time discretization one can obtain third order accuracy for both pressure and velocity without a time step stability restriction of diffusive type furthermore two kinds of projection methods are found stable using piecewise linear elements for both velocity and pressure

the stationary arrival process of independent diffusers from a continuum to an absorbing boundary is poissonian we consider the arrival process of infinitely many identical independent diffusion processes from an infinite bath to an absorbing boundary previous results on this problem were confined to independent brownian particles arriving at an absorbing sphere the present paper extends these results to general diffusion processes without any symmetries and without resorting to explicit expressions for solutions to the relevant equations it is shown that for general absorbing boundaries and force fields the steady stream of arrivals is poissonian with rate equal to the total flux on the absorbing boundary as calculated from the continuum theory of diffusion with transport the considered arrival problem arises in the theory of langevin simulations of ions in electrolytic solutions in a langevin simulation ions enter and exit the simulation region and it is necessary to compute the probability laws for their entrance times into the simulation while the simulated ions inside the small simulation region inte

on deformational and configurational mechanics of micromorphic hyperelasticity theory and computation abstract a micromorphic continuum formulation is presented in the context of both the spatial and the material motion problem for both approaches the kinematics as well as the balance relations together with the various representations of the occurring stress fields are derived the relations between the spatial motion problem and the material motion problem quantities are examined in detail upon a hyperelastic constitutive assumption a finite element approximation is derived and the material force method which is especially suited for defect mechanics problems is successfully applied to the present micromorphic continuum theory

a semi local spectral hp element solver for linear elasticity problems summary we develop an efficient semi local method for speeding up the solution of linear systems arising in spectral hp element discretization of the linear elasticity equations the main idea is to approximate the element wise residual distribution with a localization operator we introduce in this paper and subsequently solve the local linear system additionally we decouple the three directions of displacement in the localization operator hence enabling the use of an efficient low energy preconditioner for the conjugate gradient solver this approach is effective for both nodal and modal bases in the spectral hp element method but here we focus on the modal hierarchical basis in numerical tests we verify that there is no loss of accuracy in the semi local method and we obtain good parallel scalability and substantial speed up compared to the original formulation in particular our tests include both structure only and fluid structure interaction problems with the latter modeling a 3d patient specific brain aneurysm copyright 2014 john wiley sons ltd

on the numerical modelling of quasi static crack growth in linear elastic fracture mechanics in this paper we present a strategy for the simulation of a propagating crack under mixed mode linear elastic conditions using a discontinuous finite element method a key issue is to accurately compute the incremental change in the kink angle of the propagating crack during subsequent steps we have chosen to work with a domain formulation of the material force vector as a criteria for the propagation direction we describe the theoretical background together with the numerical implementation in detail and show some results for different loading conditions copyright 2005 john wiley sons ltd

a coupled momentum method for modeling blood flow in three dimensional deformable arteries abstract blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel moreover wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid however computational methods for simulating blood flow in three dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries computing blood flow in deformable domains using standard techniques like the ale method remains a formidable problem for large realistic anatomic and physiologic models of the cardiovascular system we have developed a new method to simulate blood flow in three dimensional deformable models of arteries the method couples the equations of the deformation of the vessel wall at the variational level as a boundary condition for the fluid domain we consider a strong coupling of the degrees of freedom of the fluid and the solid domains and a linear membrane model enhanced with transverse shear for the vessel wall the effect of the vessel wall boundary is therefore added in a monolithic way to the fluid equations resulting in a remarkably robust scheme we present here the mathematical formulation of the method and discuss issues related to the fluid solid coupling membrane formulation time integration method and boundary and initial conditions implementation is discussed and results with simple geometries as well as large subject specific models are presented

scalable parallel methods for monolithic coupling in fluid structure interaction with application to blood flow modeling we introduce and study numerically a scalable parallel finite element solver for the simulation of blood flow in compliant arteries the incompressible navier stokes equations are used to model the fluid and coupled to an incompressible linear elastic model for the blood vessel walls our method features an unstructured dynamic mesh capable of modeling complicated geometries an arbitrary lagrangian eulerian framework that allows for large displacements of the moving fluid domain monolithic coupling between the fluid and structure equations and fully implicit time discretization simulations based on blood vessel geometries derived from patient specific clinical data are performed on large supercomputers using scalable newton krylov algorithms preconditioned with an overlapping restricted additive schwarz method that preconditions the entire fluid structure system together the algorithm is shown to be robust and scalable for a variety of physical parameters scaling to hundreds of processors and millions of unknowns

on a solution strategy for energy based mesh optimization in finite hyperelastostatics the objective of this work is the development of a numerical solution strategy for energy based mesh optimization in finite hyperelastostatics in finite element computations that rely on the principle of minimum potential energy the variational principle itself provides the basis for r adaptive methods the numerical solution can be improved by further minimizing the discrete potential energy with respect to the material node point positions in this paper we regard the mesh optimization as a nonlinear minimization problem with equality and inequality constraints the equality constraints correspond to the spatial equilibrium condition whereas the inequality constraints are given by the natural restriction that material elements with a negative volume jacobian are inadmissible based on this interpretation we develop a stable numerical solution strategy in which two approaches of nonlinear programming are combined applying a barrier method the minimization problem is transformed into a sequence of problems without inequality constraints each problem of the sequence is solved by means of a newton scheme that operates on the constrained surface given by the spatial equilibrium condition

a quasi static discontinuous galerkin configurational force crack propagation method for brittle materials summary this paper presents a framework for r adaptive quasi static configurational force cf brittle crack propagation cast within a discontinuous galerkin dg symmetric interior penalty sipg finite element scheme cracks are propagated in discrete steps with a staggered algorithm along element interfaces which align themselves with the predicted crack propagation direction the key novelty of the work is the exploitation of the dg face stiffness terms existing along element interfaces to propagate a crack in a mesh independent r adaptive quasi static fashion driven by the cf at the crack tip this adds no new degrees of freedom to the data structure additionally as dg methods have element specific degrees of freedom a geometry driven p adaptive algorithm is also easily included allowing for more accurate solutions of the cf on a moving crack front further for non determinant systems we introduce an average boundary condition that restrains rigid body motion leading to a determinant system to the authors knowledge this is first time such a boundary condition has been described the proposed formulation is validated against single and multiple crack problems with single and mixed mode cracks demonstrating the predictive capabilities of the method this article is protected by copyright all rights reserved

a phase field ale method for simulating fluid structure interactions in two phase flow abstract we present a phase field ale method for simulating fluid structure interactions fsi in two phase flow we solve the navier stokes equation coupled with the cahn hilliard equation and the structure equation in an arbitrary lagrangian eulerian ale framework for the fluid solver a spectral hp element method is employed for spatial discretization and backward differentiation for time discretization for the structure solver a galerkin method is used in lagrangian coordinates for spatial discretization and the newmark scheme for time discretization the mesh is updated from the initial configuration by a harmonic mapping constructed from the velocity of the interface between the fluid and the structure subdomains to test the accuracy of the phase field approach of this multi physics method we first simulate two phase co annular laminar flow in a stationary pipe and compare the results with the analytical solution to test the accuracy of the fsi solver we simulate a pipe conveying single phase flow and compare the results with an existing validated code newman and karniadakis 1997 finally we present two numerical simulations of fsi in two phase flow specifically in a flexible pipe conveying two fluids that induce self sustained oscillations and in external cross flow past a circular cylinder that modifies the classical vortex street due to a kelvin helmholtz instability these three dimensional simulations demonstrate the capability of the method in dealing with fsi problems in two phase flow with moving grids as well as its robustness and efficiency in handling different fluids with large contrast in physical properties

application of material forces to hyperelastostatic fracture mechanics i continuum mechanical setting the concern of this work is a consequent exploitation of the notion of material forces for the application within hyperelastostatic fracture mechanics contrary to physical forces material forces act on the material manifold thus essentially representing the tendency of defects like cracks or inclusions to move relative to the ambient material based on the formulation of the appropriate quasi static balance laws in the material space we aim at a fresh look onto classical aspects of hyperelastostatic fracture mechanics operating throughout within the geometrically nonlinear setting we emphasize on the one hand the duality of the direct and the inverse motion description and on the other hand we re establish the classical path integrals from elementary equilibrium considerations in the material space

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

generalized robin neumann explicit coupling schemes for incompressible fluid structure interaction stability analysis and numerics we introduce a new class of explicit coupling schemes for the numerical solution of fluid structure interaction problems involving a viscous incompressible fluid and an elastic structure these methods generalize the arguments reported in 13 10 to the case of the coupling with thick walled structures the basic idea lies in the derivation of an intrinsic interface robin consistency at the space semi discrete level using a lumped mass approximation in the structure the fluid solid splitting is then performed through appropriate extrapolations of the solid velocity and stress on the interface based on these methods a new parameter free robin neumann iterative procedure is also proposed for the partitioned solution of implicit coupling a priori energy estimates guaranteeing the added mass free stability of the schemes and the convergence of the iterative procedure are established the accuracy and robustness of the methods are illustrated in several numerical examples

an integrated approach to shape optimization and mesh adaptivity based on material residual forces abstract this contribution is concerned with the coupling of finite element based shape optimization to methods of mesh adaptivity therein the nodal points of a finite element mesh serve as design variables in an optimization problem that aims to minimize a cost functional with respect to different constraints in order to avoid the occurrence of oscillating boundaries in the optimal design trials we generate the respective design updates through solving a series of fictitious boundary value problems on an updated lagrangian configuration the design update process is accompanied by adaptive mesh refinement to obtain more accurate results for the structural analysis and the design sensitivity analysis for the mesh adaptation process we consider r adaptive node relocation h adaptive mesh refinement and a combination of both approaches in each case the derivations rest upon the notion of material residual forces induced by finite element discretization and the coupling of shape optimization and mesh adaptivity is of intermittent type i e mesh adaptivity is invoked once a certain number of design updates has been generated we examine the benefits of the proposed method on the basis of some numerical examples in comparison to the same shape optimization method not involving adaptive mesh refinement where we evaluate the corresponding numerical costs the gain in accuracy and the effects on the optimal shapes being obtained

curvilinear immersed boundary method for simulating fluid structure interaction with complex 3d rigid bodies the sharp interface curvib approach of ge and sotiropoulos l ge f sotiropoulos a numerical method for solving the 3d unsteady incompressible navier stokes equations in curvilinear domains with complex immersed boundaries journal of computational physics 225 2007 1782 1809 is extended to simulate fluid structure interaction fsi problems involving complex 3d rigid bodies undergoing large structural displacements the fsi solver adopts the partitioned fsi solution approach and both loose and strong coupling strategies are implemented the interfaces between immersed bodies and the fluid are discretized with a lagrangian grid and tracked with an explicit front tracking approach an efficient ray tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies numerical experiments are carried out for two fsi problems vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions for both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements the numerical experiments suggest that both the properties of the structure mass geometry and the local flow conditions can play an important role in determining the stability of the fsi algorithm under certain conditions the fsi algorithm is unconditionally unstable even when strong coupling fsi is employed for such cases however combining the strong coupling iteration with under relaxation in conjunction with the aitken s acceleration technique is shown to effectively resolve the stability problems a theoretical analysis is presented to explain the findings of the numerical experiments it is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the fsi algorithm the stabilizing role of under relaxation is also clarified and the upper bound of the under relaxation coefficient required for stability is derived

an arbitrary lagrangian eulerian finite element method for finite strain plasticity this paper presents a new arbitrary lagrangian eulerian ale finite element formulation for finite strain plasticity in non linear solid mechanics we consider the models of finite strain plasticity defined by the multiplicative decomposition of the deformation gradient in an elastic and a plastic part f fefp with the stresses given by a hyperelastic relation in contrast with more classical ale approaches based on plastic models of the hypoelastic type the ale formulation presented herein considers the direct interpolation of the motion of the material with respect to the reference mesh together with the motion of the spatial mesh with respect to this same reference mesh this aspect is shown to be crucial for a simple treatment of the advection of the plastic internal variables and dynamic variables in fact this advection is carried out exactly through a particle tracking in the reference mesh a calculation that can be accomplished very efficiently with the use of the connectivity graph of the fixed reference mesh a staggered scheme defined by three steps the smoothing the advection and the lagrangian steps leads to an efficient method for the solution of the resulting equations we present several representative numerical simulations that illustrate the performance of the newly proposed methods both quasi static and dynamic conditions are considered in these model examples copyright 2003 john wiley sons ltd

bdf like methods for nonlinear dynamic analysis we present several time integration algorithms of second order accuracy that are numerically simple and effective for nonlinear elastodynamic problems these algorithms are based on a general four step scheme that has a resemblance to the backward differentiation formulas we also present an extension to the composite strategy of the bathe method appropriate values for the algorithmic parameters are determined based on considerations of stability and dissipativity and less dissipative members of each algorithm have been identified we demonstrate the convergence characteristics of the proposed algorithms with a nonlinear dynamic problem having analytic solutions and test these algorithms with several three dimensional nonlinear elastodynamic problems involving large deformations and rotations employing st venant kirchhoff and compressible neo hookean hyperelastic material models these tests show that stable computations are obtained with the proposed algorithms in nonlinear situations where the trapezoidal rule encounters a well known instability

multiscale models and stochastic simulation methods for computing rare but key binding events in cell biology abstract the main difficulty in simulating diffusion processes at a molecular level in cell microdomains is due to the multiple scales involving nano to micrometers few to many particles have to be simulated and simultaneously tracked while there are exploring a large portion of the space for binding small targets such as buffers or active sites bridging the small and large spatial scales is achieved by rare events representing brownian particles finding small targets and characterized by long time distribution these rare events are the bottleneck of numerical simulations a naive stochastic simulation requires running many brownian particles together which is computationally greedy and inefficient solving the associated partial differential equations is also difficult due to the time dependent boundary conditions narrow passages and mixed boundary conditions at small windows we present here two reduced modeling approaches for a fast computation of diffusing fluxes in microdomains the first approach is based on a markov mass action law equations coupled to a markov chain the second is a gillespie s method based on the narrow escape theory for coarse graining the geometry of the domain into poissonian rates the main application concerns diffusion in cellular biology where we compute as an example the distribution of arrival times of calcium ions to small hidden targets to trigger vesicular release

strong localized perturbations of eigenvalue problems this paper considers the effect of three types of perturbations of large magnitude but small extent on a class of linear eigenvalue problems for elliptic partial differential equations in bounded o

a stable fluid structure interaction solver for low density rigid bodies using the immersed boundary projection method dispersion of low density rigid particles with complex geometries is ubiquitous in both natural and industrial environments we show that while explicit methods for coupling the incompressible navier stokes equations and newton s equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios for more complex particles such as a body with a protrusion they become unstable we present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method similarly to previous work on this method the resulting matrix equation in the present approach is solved using a block lu decomposition each step of the block lu decomposition is modified to incorporate the rigid body dynamics we show that our method achieves second order accuracy in space and first order in time third order for practical settings only with a small additional computational cost to the original method our implicit coupling yields stable solution for density ratios as low as 10 4 we also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method

geometry update driven by material forces for simulation of brittle crack growth in functionally graded materials functionally graded materials fgms are advanced materials that possess continuously graded properties such that the growth of cracks is strongly dependent on the gradation of the material in this work a thermodynamic consistent framework for crack propagation in fgms is presented by applying a dissipation inequality to a time dependent migrating control volume the direction of crack growth is obtained in terms of material forces as a result of the principle of maximum dissipation in the numerical implementation a staggered algorithm deformation update for fixed geometry followed by geometry update for fixed deformation is employed within each time increment the geometry update is a result of the incremental crack propagation which is driven by material forces the corresponding mesh is generated by combining delaunay triangulation with local mesh refinement furthermore a newton algorithm is proposed taking into account mesh transfer of displacements for crack propagation in incremental elasticity in two numerical examples brittle crack propagation in fgms is investigated for various directions of strength gradation within the structures copyright 2008 john wiley sons ltd

stabilization of explicit coupling in fluid structure interaction involving fluid incompressibility abstract in this work we propose a stabilized explicit coupling scheme for fluid structure interaction problems involving a viscous incompressible fluid the coupled discrete formulation is based on nitsche s method with a time penalty term giving l 2 control on the fluid pressure variations at the interface for a linear model problem we prove that the scheme is stable in the energy norm irrespectively of the so called added mass effect namely the fluid structure density ratio and the geometry of the domain numerical experiments in the linear and non linear case show that optimal time accuracy can be obtained by performing one defect correction iteration

a computational framework of three dimensional configurational force driven brittle crack propagation abstract we consider a variational formulation of quasi static brittle fracture and develop a new finite element based computational framework for propagation of cracks in three dimensional bodies we outline a consistent thermodynamical framework for crack propagation in elastic solids and show that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global clausius planck inequality in the sense of coleman s method consequently the crack propagation direction associated with the classical griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front the variational formulation is realized numerically by a standard spatial discretization with finite elements which yields a discrete formulation of the global dissipation in terms configurational nodal forces therefore the constitutive setting of crack propagation in the space discretized finite element context is naturally related to discrete nodes of a typical finite element mesh in a consistent way with the node based setting the discretization of the evolving crack discontinuity is performed by the doubling of critical nodes and interface facets of the mesh the crucial step for the success of this procedure is its embedding into an r adaptive crack facet reorientation procedure based on configurational force based indicators in conjunction with crack front constraints we propose a staggered solution procedure that results in a sequence of positive definite discrete subproblems with successively decreasing overall stiffness providing a robust algorithmic setting in the postcritical range the predictive capabilitiy of the proposed formulation is demonstrated by means of representative numerical simulations

on configurational forces in the context of the finite element method the theory of configurational forces is briefly recast together with the underlying balance laws it is shown that in the case of a homogeneous body without body forces the additional balance laws are identically satisfied if the standard force balance holds in approximate solutions for example obtained by finite elements the equilibrium is not satisfied exactly thus configurational forces occur on discretization nodes an implementation of the configurational force balance into the finite element scheme is presented the use of configurational forces is discussed with three main aspects it is demonstrated how configurational forces can be used to check and to improve the finite element solution examples from fracture mechanics and problems with material inhomogeneities are discussed copyright 2001 john wiley sons ltd

mass and volume specific views on thermodynamics for open systems a general framework for the thermodynamics of open systems is presented the theory is fundamentally based on the generalized balance of mass which is enhanced by additional surface flux and volume source terms the presentation highlights the influence of the enhanced mass balance on the remaining balance equations to clarify the impact of the variable reference density we introduce the notions of volume specific and mass specific formats particular attention is drawn to the fact that the mass specific balance equations are free from explicit open system contributions they resemble the classical balance equations and can thus be evaluated in complete analogy to the closed system case restrictions for the constitutive equations follow from the second law of thermodynamics as illustrated for the particular model problem of thermo hyperelasticity

enrichment of enhanced assumed strain approximations for representing strong discontinuities addressing volumetric incompressibility and the discontinuous patch test summary we present a geometrically nonlinear assumed strain method that allows for the presence of arbitrary intra finite element discontinuities in the deformation map special attention is placed on the coarsemesh accuracy of these methods and their ability to avoid mesh locking in the incompressible limit given an underlying mesh and an arbitrary failure surface we first construct an enriched approximation for the deformation map with the nonlinear analogue of the extended finite element method x fem with regard to the richer space of functions spanned by the gradient of the enriched approximation we then adopt a broader interpretation of variational consistency for the construction of the enhanced strain in particular in those elements intersected by the failure surface we construct enhanced strain approximations which are orthogonal to piecewise constant stress fields contrast is drawn with existing strong discontinuity approaches where the enhanced strain variations in localized elements were constructed to be orthogonal to constant nominal stress fields importantly the present formulation gives rise to a symmetric tangent stiffness matrix even in localized elements the present modification also allows for the satisfaction of a discontinuous patch test wherein two different constant stress fields on each side of the failure surface lie in the solution space we demonstrate how the proposed modifications eliminate spurious stress oscillations along the failure surface particularly for nearly incompressible material response additional numerical examples are provided to illustrate the efficacy of the modified method for problems in hyperelastic fracture mechanics copyright c 2000 john wiley sons ltd

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

an ale formulation based on spatial and material settings of continuum mechanics part 1 generic hyperelastic formulation abstract the present contribution deals with the derivation of a generic hyperelastic arbitrary lagrangian eulerian formulation on the basis of a consistent variational framework the governing equations follow straightforwardly from the dirichlet principle for conservative mechanical systems thereby the key idea is the reformulation of the total variation of the potential energy at fixed referential coordinates in terms of its variation at fixed material and at fixed spatial coordinates the corresponding euler lagrange equations define the spatial and the material motion version of the balance of linear momentum i e the balance of spatial and material forces in a consistent dual format in the discretised setting the governing equations are solved simultaneously rendering the spatial and the material configuration which minimise the overall potential energy of the system the remeshing strategy of the ale formulation is thus no longer user defined but objective in the sense of energy minimisation if the governing equations are derived from a potential i e either from an incremental potential or from a total potential as in the present case they are inherently symmetric both in the continuous case and in the discrete case this symmetry property is particularly appealing since it ensures symmetric system matrices upon discretisation

application of material forces to hyperelastostatic fracture mechanics ii computational setting the concern of this work is a novel algorithmic treatment of hyperelastostatic fracture mechanics problems consistent to the notion of material forces within the geometrically nonlinear setting of continuum mechanics to this end we consider the continuum mechanics of material forces as outlined in part i of this work p steinmann int j solid struct 37 7371 7391 which act contrary to the common physical forces on the material manifold or rather in the material space in the sequel it is proposed to discretize the corresponding quasi static balance of pseudo momentum by a standard galerkin finite element procedure as a result we obtain global discrete node point quantities the material node point forces which prove to be of the same qualitative and quantitative importance for the assessment of fracture mechanics problems as the classical j integral

on existence and completeness of conservation laws associated with elementary beam theory abstract from a variational principle with varying boundaries conservation laws in the context of elementary beam theory are derived necessary and sufficient conditions are given for transformations leading to conservation laws the formulas obtained are applied to several examples

a posteriori error estimation for standard finite element analysis a new residual type estimator based on projections of the error on subspaces of locally supported functions is presented the estimator is defined by a standard element by element refinement first an approximation of the energy norm of the error is obtained solving local problems with homogeneous dirichlet boundary conditions a later enrichment of the estimation is performed by adding the contributions of projections on a new family of subspaces this estimate is a lower bound of the measure of the actual error the estimator does not need to approximate local boundary conditions for the error equation therefore computation of flux jumps is not necessary moreover the estimator can be applied in mixed meshes containing elements of different shapes and its implementation in a standard finite element code is straightforward the presented results show the effectiveness of the estimator approximating both the distribution and the global measure of the error as well as its usefulness in adaptive procedures

diffusion escape through a cluster of small absorbing windows we study the first eigenvalue of the laplace equation in a bounded domain in r d d 2 3 with mixed neumann dirichlet zaremba boundary conditions the neumann condition is imposed on most of the boundary and the dirichlet boundary consists of a cluster of small windows when the windows are well separated the first eigenvalue is asymptotically the sum of eigenvalues of mixed problems with a single dirichlet window however when two or more dirichlet windows cluster tightly together they interact nonlinearly we compare our asymptotic approximation of the eigenvalue to the escape rate of simulated brownian particles through the small windows

a convergence study of a new partitioned fluid structure interaction algorithm based on fictitious mass and damping we develop analyze and validate a new method for simulating fluid structure interactions fsis which is based on fictitious mass and fictitious damping in the structure equation we employ a partitioned method for the fluid and structure motions in conjunction with sub iteration and aitken relaxation in particular the use of such fictitious parameters requires sub iterations in order to reduce the induced error in addition to the local temporal truncation error to this end proper levels of tolerance for terminating the sub iteration procedure have been obtained in order to recover the formal order of temporal accuracy for the coupled fsi problem these fictitious terms have a significant effect leading to better convergence rate and hence substantially smaller number of sub iterations through analysis we identify the proper range of these parameters which we then verify by corresponding numerical tests we implement the method in the context of spectral element discretization which is more sensitive than low order methods to numerical instabilities arising in the explicit fsi coupling however the method we present here is simple and general and hence applicable to fsi based on any other discretization we demonstrate the effectiveness of the method in applications involving 2d vortex induced vibrations viv and in 3d flexible arteries with structural density close to blood density we also present 3d results for a patient specific aneurysmal flow under pulsatile flow conditions examining in particular the sensitivity of the results on different values of the fictitious parameters

an analysis of a new stable partitioned algorithm for fsi problems part i incompressible flow and elastic solids stable partitioned algorithms for fluid structure interaction fsi problems are developed and analyzed in this two part paper part i describes an algorithm for incompressible flow coupled with compressible elastic solids while part ii discusses an algorithm for incompressible flow coupled with structural shells importantly these new added mass partitioned amp schemes are stable and retain full accuracy with no sub iterations per time step even in the presence of strong added mass effects e g for light solids the numerical approach described here for bulk compressible solids extends the scheme of banks et al 1 2 for inviscid compressible flow and uses robin mixed boundary conditions with the fluid and solid solvers at the interface the basic amp robin conditions involving a linear combination of velocity and stress are determined from the outgoing solid characteristic relation normal to the fluid solid interface combined with the matching conditions on the velocity and traction two alternative forms of the amp conditions are then derived depending on whether the fluid equations are advanced with a fractional step method or not the stability and accuracy of the amp algorithm is evaluated for linearized fsi model problems the full nonlinear case being left for future consideration a normal mode analysis is performed to show that the new amp algorithm is stable for any ratio of the solid and fluid densities including the case of very light solids when added mass effects are large in contrast it is shown that a traditional partitioned algorithm involving a dirichlet neumann coupling for the same fsi problem is formally unconditionally unstable for any ratio of densities exact traveling wave solutions are derived for the fsi model problems and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the amp algorithm for the cases of light medium and heavy solids

adaptive strategies and error control for computing material forces in fracture mechanics the concept of material forces pertains to a variation of the inverse motion map while the placement field is kept fixed from the weak formulation of the self equilibrating eshelby material stress tensor it turns out that the classical j integral formulations in fracture mechanics are just special cases due to the choice of particular weight functions in this contribution we discuss a posteriori error control of the material forces as part of an adaptive strategy to reduce the discretization error to an acceptable level the data of the dual problem involves the quite non conventional tangent stiffness of the material eshelby stress tensor with respect to a variation of the physical strain field the suggested strategy is applied to the common fracture mechanics problem of a single edged crack whereby different strategies for computing the j integral are compared we also consider the case in which the crack edges are not parallel i e a notch

an ale formulation based on spatial and material settings of continuum mechanics part 2 classification and applications abstract in the second paper of this two part contribution a specialisation towards neo hookean material will be made of the generic hyperelastic arbitrary lagrangian eulerian ale formulation derived in part 1 first for the sake of comparison and classification several existing ale solution schemes are discussed including total and updated approaches as well as monolithic and staggered algorithms then implementational details are provided for the newly proposed ale strategy the versality and the limitations of the present formulation are shown by means of a set of one dimensional and multi dimensional numerical examples in particular it is shown that with the proposed ale formulation potential energies can be obtained that are minimum for the considered topology

computer modeling of cardiovascular fluid structure interactions with the deforming spatial domain stabilized space time formulation hemodynamic factors such as the wall shear stress are believed to affect a number of cardiovascular diseases including atherosclerosis and aneurysm since resolving phenomena in a living human body is currently beyond the capabilities of in vivo measurement techniques computer modeling is expected to play an important role in gaining a better understanding of the relationship between the cardiovascular diseases and the hemodynamic factors we have developed a computer modeling technique for cardiovascular hemodynamic simulations with this modeling technique patient specific 3d geometry of an artery can be analyzed we take into account some of the important factors in human body for the purpose of demonstrating in vivo situations in a virtual world the interaction between the blood flow and the deformation of the arterial walls is a factor that we are specifically focusing on for such fluid structure interactions we have developed a computer modeling tool based on the deforming spatial domain stabilized space time dsd sst formulation this simulation tool is applied to a patient specific model under pulsatile blood flow conditions the simulations show that the flow behavior with compliant arterial walls is different from what we see with rigid arterial walls consequently the distribution of the wall shear stress on the compliant arterial walls is significantly different from that on the rigid arterial walls we deduce that the compliance of the arterial walls needs to be taken into account in cardiovascular hemodynamic simulations and the computer modeling tool we have developed can be effective in investigation of cardiovascular diseases

accurate stable and efficient navier stokes solvers based on explicit treatment of the pressure term we present numerical schemes for the incompressible navier stokes equations based on a primitive variable formulation in which the incompressibility constraint has been replaced by a pressure poisson equation the pressure is treated explicitly in time completely decoupling the computation of the momentum and kinematic equations the result is a class of extremely efficient navier stokes solvers full time accuracy is achieved for all flow variables the key to the schemes is a neumann boundary condition for the pressure poisson equation which enforces the incompressibility condition for the velocity field irrespective of explicit or implicit time discretization of the viscous term in the momentum equation the explicit time discretization of the pressure term does not affect the time step constraint indeed we prove unconditional stability of the new formulation for the stokes equation with explicit treatment of the pressure term and first or second order implicit treatment of the viscous term systematic numerical experiments for the full navier stokes equations indicate that a second order implicit time discretization of the viscous term with the pressure and convective terms treated explicitly is stable under the standard cfl condition additionally various numerical examples are presented including both implicit and explicit time discretizations using spectral and finite difference spatial discretizations demonstrating the accuracy flexibility and efficiency of this class of schemes in particular a galerkin formulation is presented requiring only c0 elements to implement

theory and numerics for finite deformation fracture modelling using strong discontinuities a general finite element approach for the modelling of fracture is presented for the geometrically non linear case the kinematical representation is based on a strong discontinuity formulation in line with the concept of partition of unity for finite elements thus the deformation map is defined in terms of one continuous and one discontinuous portion considered as mutually independent giving rise to a weak formulation of the equilibrium consisting of two coupled equations in addition two different fracture criteria are considered firstly a principle stress criterion in terms of the material mandel stress in conjunction with a material cohesive zone law relating the cohesive mandel traction to a material displacement jump associated with the direct discontinuity secondly a criterion of griffith type is formulated in terms of the material crack driving force mcdf with the crack propagation direction determined by the direction of the force corresponding to the direction of maximum energy release apart from the material modelling the numerical treatment and aspects of computational implementation of the proposed approach is also thoroughly discussed and the paper is concluded with a few numerical examples illustrating the capabilities of the proposed approach and the connection between the two fracture criteria copyright 2005 john wiley sons ltd

a numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains we present a new numerical methodology for simulating fluid structure interaction fsi problems involving thin flexible bodies in an incompressible fluid the fsi algorithm uses the dirichlet neumann partitioning technique the curvilinear immersed boundary method curvib is coupled with a rotation free finite element fe model for thin shells enabling the efficient simulation of fsi problems with arbitrarily large deformation turbulent flow problems are handled using large eddy simulation with the dynamic smagorinsky model in conjunction with a wall model to reconstruct boundary conditions near immersed boundaries the curvib and fe solvers are coupled together on the flexible solid fluid interfaces where the structural nodal positions displacements velocities and loads are calculated and exchanged between the two solvers loose and strong coupling fsi schemes are employed enhanced by the aitken acceleration technique to ensure robust coupling and fast convergence especially for low mass ratio problems the coupled curvib fe fsi method is validated by applying it to simulate two fsi problems involving thin flexible structures 1 vortex induced vibrations of a cantilever mounted in the wake of a square cylinder at different mass ratios and at low reynolds number and 2 the more challenging high reynolds number problem involving the oscillation of an inverted elastic flag for both cases the computed results are in excellent agreement with previous numerical simulations and or experiential measurements grid convergence tests studies are carried out for both the cantilever and inverted flag problems which show that the curvib fe fsi method provides their convergence finally the capability of the new methodology in simulations of complex cardiovascular flows is demonstrated by applying it to simulate the fsi of a tri leaflet prosthetic heart valve in an anatomic aorta and under physiologic pulsatile conditions

sub iteration leads to accuracy and stability enhancements of semi implicit schemes for the navier stokes equations we present an iterative semi implicit scheme for the incompressible navier stokes equations which is stable at cfl numbers well above the nominal limit we have implemented this scheme in conjunction with spectral discretizations which suffer from serious time step limitations at very high resolution however the approach we present is general and can be adopted with finite element and finite difference discretizations as well specifically at each time level the nonlinear convective term and the pressure boundary condition both of which are treated explicitly in time are updated using fixed point iteration and aitken relaxation eigenvalue analysis shows that this scheme is unconditionally stable for stokes flows while numerical results suggest that the same is true for steady navier stokes flows as well this finding is also supported by error analysis that leads to the proper value of the relaxation parameter as a function of the flow parameters in unsteady flows second and third order temporal accuracy is obtained for the velocity field at cfl number 5 14 using analytical solutions systematic accuracy stability and cost comparisons are presented against the standard semi implicit method and a recently proposed fully implicit scheme that does not require newton s iterations in addition to its enhanced accuracy and stability the proposed method requires the solution of symmetric only linear systems for which very effective preconditioners exist unlike the fully implicit schemes

arbitrary lagrangian eulerian ale formulation for hyperelastoplasticity summary the arbitrary lagrangian eulerian ale description in nonlinear solid mechanics is nowadays standard for hypoelastic plastic models an extension to hyperelastic plastic models is presented here a fractional step method a common choice in ale analysis is employed for time marching every time step is split into a lagrangian phase which accounts for material effects and a convection phase where the relative motion between the material and the finite element mesh is considered in contrast to previous ale formulations of hyperelasticity or hyperelastoplasticity the deformed configuration at the beginning ofthe time step not the initial undef ormed configuration is chosen as the reference configuration as a consequence convecting variables is required in the description ofthe elastic response this is not the case in previous f were only the plastic response contains convection terms in exchange for the extra convective terms however the proposed ale approach has a major advantage only the quality ofthe mesh in the spatial domain must be ensured by the ale remeshing strategy in previous formulations it is also necessary to keep the distortion ofthe mesh in the material domain under control thus the f potential ofthe ale description as an adaptive technique can be exploited here these aspects are illustrated in detail by means ofthree numerical examples a necking test a coining test and a powder compaction test copyright c 2000 john wiley sons ltd

diffusion on a sphere with localized traps mean first passage time eigenvalue asymptotics and fekete points a common scenario in cellular signal transduction is that a diffusing surface bound molecule must arrive at a localized signaling region on the cell membrane before the signaling cascade can be completed the question then arises of how quickly such signaling molecules can arrive at newly formed signaling regions here we attack this problem by calculating asymptotic results for the mean first passage time for a diffusing particle confined to the surface of a sphere in the presence of n partially absorbing traps of small radii the rate at which the small diffusing molecule becomes captured by one of the traps is determined by asymptotically calculating the principal eigenvalue for the laplace operator on the sphere with small localized traps the asymptotic analysis relies on the method of matched asymptotic expansions together with detailed properties of the green s function for the laplacian and the helmholtz operators on the surface of the unit sphere the asymptotic results compare favorably with

a framework for fracture modelling based on the material forces concept with xfem kinematics a theoretical and computational framework which covers both linear and non linear fracture behaviour is presented as a basis for the formulation we use the material forces concept due to the close relation between on one hand the eshelby energy momentum tensor and on the other hand material defects like cracks and material inhomogeneities by separating the discontinuous displacement from the continuous counterpart in line with the extended finite element method xfem we are able to formulate the weak equilibrium in two coupled problems representing the total deformation however in contrast to standard xfem where the direct motion discontinuity is used to model the crack we rather formulate an inverse motion discontinuity to model crack development the resulting formulation thus couples the continuous direct motion to the inverse discontinuous motion which may be used to simulate linear as well as non linear fracture in one and the same formulation in fact the linear fracture formulation can be retrieved from the non linear cohesive zone formulation simply by confining the cohesive zone to the crack tip these features are clarified in the two numerical examples which conclude the paper copyright 2005 john wiley sons ltd

fluid structure interaction problems with strong added mass effect in this paper the so called added mass effect is investigated from a different point of view of previous publications the monolithic fluid structure problem is partitioned using a static condensation of the velocity terms following this procedure the classical stabilized projection method for incompressible fluid flows is introduced the procedure allows obtaining a new pressure segregated scheme for fluid structure interaction problems which has good convergent characteristics even for biomechanical application where the added mass effect is strong the procedure reveals its power when it is shown that the same projection technique must be implemented in staggered fsi methods copyright 2009 john wiley sons ltd

an u ale formulation of 3 d unsteady viscoelastic flow the arbitrary lagrange euler ale formulation is applied to the analysis of unsteady viscoelastic flow of an upper convected maxwell ucm medium it is shown how the requirement of incremental objectivity affects the stress updating scheme the current implementation of the ale formulation uses the time discontinuous galerkin least squares td gls method to handle the advective parts of the equations further the ale formulation is compared with an updated ale formulation that is shown to give comparable results but is much more cost effective the technique presented is particularly effective for free surface flows three applications are given

a numerical strategy for investigating the kinetic response of stimulus responsive hydrogels we present a strategy for obtaining numerical solutions to a system of non linear coupled evolution equations describing volume transitions in stimulus responsive hydrogels srhs the theory underlying our sharp interface model of phase transitions in srhs is provided along with the assumptions leading to the specialized formulation that is the starting point for the numerical method the discrete formulation is then developed with a hybrid extended finite element level set method xfe lsm domain integral methodologies are used consistently to extract interfacial quantities such as the mechanical driving traction the jump in the normal component of the solute flux and requisite geometric information several benchmark studies are provided to demonstrate the accuracy and robustness of the numerical strategy we then investigate various features of srh kinetics including the regimes of unstable and stable phase transitions surface pattern formation and bulk phase separation

regular article a discontinuous galerkin ale method for compressible viscous flows in moving domains we present a matrix free discontinuous galerkin method for simulating compressible viscous flows in two and three dimensional moving domains to this end we solve the navier stokes equations in an arbitrary lagrangian eulerian ale framework spatial discretization is based on standard structured and unstructured grids but using an orthogonal hierarchical spectral basis the method is third order accurate in time and converges exponentially fast in space for smooth solutions a novelty of the method is the use of a force directed algorithm from graph theory that requires no matrix inversion to efficiently update the grid while minimizing distortions we present several simulations using the new method including validation with published results from a pitching airfoil and new results for flow past a three dimensional wing subject to large flapping insect like motion

validation of subject specific automated p fe analysis of the proximal femur abstract background the use of subject specific finite element fe models in clinical practice requires a high level of automation and validation in yosibash et al 2007a reliable simulations of the human proximal femur by high order finite element analysis validated by experimental observations j biomechanics 40 3688 3699 a novel method for generating high order finite element p fe models from ct scans was presented and validated by experimental observations on two fresh frozen femurs harvested from a 30 year old male and 21 year old female herein we substantiate the validation process by enlarging the experimental database 54 year old female femur improving the method and examine its robustness under different ct scan conditions approach a fresh frozen femur of a 54 year old female was scanned under two different environments in air and immersed in water dry and wet ct thereafter the proximal femur was quasi statically loaded in vitro by a 1000 n load the two qct scans were manipulated to generate p fe models that mimic the experimental conditions we compared p fe displacements and strains of the wet ct model to the dry ct model and to the experimental results in addition the material assignment strategy was reinvestigated the inhomogeneous young s modulus was represented in the fe model using two different methods directly extracted from the ct data and using continuous spatial functions as in yosibash et al 2007a reliable simulations of the human proximal femur by high order finite element analysis validated by experimental observations j biomechanics 40 3688 3699 results excellent agreement between dry and wet fe models was found for both displacements and strains i e the method is insensitive to ct conditions and may be used in vivo good agreement was also found between fe results and experimental observations the spatial functions representing young s modulus are local and do not influence strains and displacements prediction finally the p fe results of all three fresh frozen human femurs compare very well to experimental observations exemplifying that the presented method may be in a mature stage to be used in clinical computer aided decision making

artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows this note investigates the so called arti cial added mass e ect which is responsible for devastating instabilities within sequentially staggered fluid structure interaction fsi simulations where incompressible fluids are considered a discrete representation of the added mass operatorma is given and instability conditions are evaluated for different temporal discretisation schemes it is proven that for every sequentially staggered scheme and given spatial discretisation of a problem a mass ratio between fluid and structural mass density can be found at which the coupled system becomes unstable the analysis is quite general and does not depend upon the particular spatial discretisation schemes used however here special attention is put on stabilised finite elements employed on the fluid partition numerical investigations further highlight the results

goal oriented a posteriori error estimates in linear elastic fracture mechanics goal oriented a posteriori error estimators are presented in this paper for the error obtained while approximately evaluating the j integral in linear elastic fracture mechanics using the finite element method the j integral provides a criterion for crack propagation of a pre existing crack therefore its reliable and accurate evaluation is of considerable importance in engineering applications to prevent failure of structures this can be achieved by goal oriented adaptive finite element methods based on the well established strategy of solving an auxiliary dual problem in order to control the error of a non linear functional here the j integral in this paper two principally different goal oriented adaptive strategies are presented the first strategy rests upon equilibrated residual error estimators based on local neumann problems whereas the second one makes use of averaging techniques the paper is concluded by a numerical example that illustrates our theoretical results

comparison of artificial dissipation and limited flux schemes in arbitrary lagrangian eulerian finite element formulations a comparison is made between arbitrary lagrangian eulerian ale finite element formulations for simulation of forming processes based on an artificial dissipation scheme and a limited flux scheme the first ale algorithm is based on an averaging procedure used in post processing of finite element calculations the second ale algorithm stems from a finite difference method for compressible fluid dynamics both approaches have complementary characteristics with respect to accuracy and implementation

the narrow escape problem the narrow escape problem in diffusion theory is to calculate the mean first passage time of a diffusion process to a small target on the reflecting boundary of a bounded domain the problem is equivalent to solving the mixed dirichlet neumann boundary value problem for the poisson equation with small dirichlet and large neumann parts the mixed boundary value problem which goes back to lord rayleigh originates in the theory of sound and is closely connected to the eigenvalue problem for the mixed problem and for the neumann problem in domains with bottlenecks we review here recent developments in the non standard asymptotics of the problem which are based on several ingredients a better resolution of the singularity of neumann s function resolution of the boundary layer near the small target by conformal mappings of domains with bottlenecks and the breakup of composite domains into simpler components the new methodology applies to two and higher dimensional problems selected applications are r

added mass and damping in fluid structure interaction abstract this paper is concerned with the added mass matrix for a mechanical structure vibrating in an incompressible liquid it is shown in particular that this matrix does not depend on viscosity and from this fact can be calculated as if the fluid is perfect the viscous effect on the mechanical system can then be represented by a damping term of type time convolution the presence of a flowing fluid around the structure leads to additional damping terms proportional to the fluid density

tetrahedral composite finite elements we develop and analyse a composite ct3d tetrahedral element consisting of an ensemble of 12 four node linear tetrahedral elements coupled to a linear assumed deformation defined over the entire domain of the composite element the element is designed to have well defined lumped masses and contact tractions in dynamic contact problems while at the same time minimizing the number of volume constraints per element the relation between displacements and deformations is enforced weakly by recourse to the hu washizu principle the element arrays are formulated in accordance with the assumed strain prescription the formulation of the element accounts for fully non linear kinematics integrals over the domain of the element are computed by a five point quadrature rule the element passes the patch test in arbitrarily distorted configurations our numerical tests demonstrate that ct element has been found to possess a convergence rate comparable to those of linear simplicial elements and that these convergence rates are maintained as the near incompressible limit is approached we have also verified that the element satisfies the babuska brezzi condition for a regular mesh configuration these tests suggest that the ct3d element can indeed be used reliably in calculations involving near incompressible behaviour which arises e g in the presence of unconfined plastic flow

truly monolithic algebraic multigrid for fluid structure interaction the coupling of flexible structures to incompressible fluids draws a lot attention during the last decade many different solution schemes have been proposed in this contribution we concentrate on strong coupling fluid structure interaction by means of monolithic solution schemes therein a newton krylov method is applied to the monolithic set of nonlinear equations such schemes require good preconditioning to be efficient we propose two preconditioners that apply algebraic multigrid techniques to the entire fluid structure interaction system of equations the first is based on a standard block gauss seidel approach where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem the second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields the resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance

a projection semi implicit scheme for the coupling of an elastic structure with an incompressible fluid we address the numerical simulation of fluid structure systems involving an incompressible viscous fluid this issue is particularly difficult to face when the fluid added mass acting on the structure is strong as it happens in hemodynamics for example indeed several works have shown that in such situations implicit coupling seems to be necessary in order to avoid numerical instabilities although significant improvements have been achieved during the last years solving implicit coupling often exhibits a prohibitive computational cost in this work we introduce a semi implicit coupling scheme which remains stable for a reasonable range of the discretization parameters the first idea consists in treating implicitly the added mass effect whereas the other contributions geometrical non linearities viscous and convective effects are treated explicitly the second idea relies on the fact that this kind of explicit implicit splitting can be naturally performed using a chorin temam projection scheme in the fluid we prove conditional stability of the scheme for a fully discrete formulation several numerical experiments point out the efficiency of the present scheme compared to several implicit approaches

arbitrary lagrangian eulerian finite element analysis of strain localization in transient problems non local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint the non locality prevents strain localization with zero global dissipation of energy and consequently finite element calculations converge upon mesh refinements to non zero width localization zones one of the major drawbacks of these models is that the element size needed in order to capture the localization zone must be smaller than the internal length hence the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity this paper deals with the application of the arbitrary lagrangian eulerian ale formulation well known in hydrodynamics and fluid structure interaction problems to transient strain localization in a non local damageable material it is shown that the ale formulation which is employed in large boundary motion problems can also be well suited for non linear transient analysis of softening materials where localization bands appear the remeshing strategy is based on the equidistribution of an indicator that quantifies the interelement jump of a selected state variable two well known one dimensional examples illustrate the capabilities of this technique the first one deals with localization due to a propagating wave in a bar and the second one studies the wave propagation in a hollow sphere

on the comparison of two approaches to compute material forces for inelastic materials application to single slip crystal plasticity abstract the main goal of this contribution is the application of the material force method to dissipative materials whereby special emphasis is placed on the application to crystal plasticity balance equations on the material manifold as e g the material motion balance of momentum generally necessitate the computation of the spatial gradient of additional internal degrees of freedom or rather internal variables we therefore focus in this work on the comparison of two different numerical approaches to compute these gradient fields within a finite element setting namely a node point based and an integration point based formulation several numerical examples underline that the latter framework which is the convenient numerically comparatively cheap and well established approach in computational inelasticity turns out to be sufficiently accurate for the problem at hand

goal oriented r adaptivity based on variational arguments in the physical and material spaces abstract the error in a local quantity of interest depends on the error in the corresponding dual solution or generalized green s function this fact is used in dual weighted based goal oriented error estimation techniques and h or p adaptive algorithms this contribution is concerned with a novel approach for goal oriented r adaptivity based on energy minimization principles for the primal and the dual problems the minimization of the energy of the primal problem as well as the minimization of the energy of the dual problem with respect to a design function lead to the primal and dual material residuals respectively these residuals are error indicators for the discretization error on the current mesh we propose a goal oriented mesh optimization algorithm which ends in an optimized mesh with respect to a chosen quantity of interest by means of selected computational examples we demonstrate the capability of the proposed framework

material forces in open system mechanics the basic concern of the present work is the exploitation of the notion of material forces in the theoretical and computational analysis of open systems with particular application to biomechanical problems based on a completely dual framework for the spatial and the material motion problem we introduce the balance equations for open system thermodynamics in combination with the appropriate constitutive equations they constitute the basis of the finite element formulation derived thereafter for the spatial motion problem the solution of the governing equations basically the balance of mass and momentum renders the discrete nodal values of the density and the deformation as primary unknowns for the material motion problem the computational analysis of the balance of momentum yields the discrete material node point forces which can be interpreted as driving forces for the local rearrangement of material inhomogeneities once the spatial motion problem has been solved the material force method is nothing but a mere post processing step from an algorithmic point of view as a convincing benefit of the proposed strategy the computation of the material forces is extremely cheap and requires no additional finite element data structure in the context of biomechanics material forces give further insight into complex biomechanically induced processes such as functional adaption morphogenesis healing or growth for example material forces on the boundary can be considered as a measure of shape sensitivity and thus indicate morphological changes while material forces in the interior indicate the tendency to create new mass locally or to equilibrate local density inhomogeneities

robin based semi implicit coupling in fluid structure interaction stability analysis and numerics in this paper we propose a semi implicit coupling scheme for the numerical simulation of fluid structure interaction systems involving a viscous incompressible fluid the scheme is stable irrespective of the so called added mass effect and allows for conservative time stepping within the structure the efficiency of the scheme is based on the explicit splitting of the viscous effects and geometrical convective nonlinearities through the use of the chorin temam projection scheme within the fluid stability comes from the implicit pressure solid coupling and a specific robin treatment of the explicit viscous solid coupling derived from nitsche s method

fully decoupled time marching schemes for incompressible fluid thin walled structure interaction in this paper we introduce a class of fully decoupled time marching schemes velocity pressure displacement splitting for the coupling of an incompressible fluid with a thin walled elastic or viscoelastic structure the time splitting combines a projection method in the fluid with a specific robin neumann treatment of the interface coupling a priori energy estimates guaranteeing unconditional stability are established for some of the schemes the accuracy and performance of the methods proposed are illustrated by a thorough numerical study

on the configurational force balance in thermomechanics the aim of this paper is a new formulation of the configurational force balance in the general framework of thermomechanics to this end invariance requirements of the configurational working are used following an approach proposed by gurtin to define the notion of working in a more general framework the ideas of green and naghdi concerning the basic postulates of thermomechanics are invoked and used consistently the main results are that the configurational forces balance in the general setting of thermomechanics without the invocation of constitutive relations and the pseudo momentum equation for classical and dissipationless thermoelasticity finally we give an application to fracture theory we show that in classical thermoelasticity the derived pseudo momentum balance provides a crack driving force consistent with the well known expression of the energy release rate

robin robin preconditioned krylov methods for fluid structure interaction problems in this work we propose a robin robin preconditioner combined with krylov iterations for the solution of the interface system arising in fluid structure interaction fsi problems it can be seen as a partitioned fsi procedure and in this respect it generalizes the ideas introduced in s badia f nobile c vergara j comput phys 227 2008 7027 7051 we analyze the convergence of gmres iterations with the robin robin preconditioner on a model problem and compare its efficiency with some existing algorithms the method is shown to be very efficient for many challenging fluid structure interaction problems such as those characterized by a large added mass effect or by enclosed fluids in particular the possibility to solve balloon type problems without any special treatment makes this algorithm very appealing compared to the computationally intensive existing approaches c 2009 elsevier b v all rights reserved

robust and direct evaluation of j2 in linear elastic fracture mechanics with the x fem numerical simulation of fracture mechanics is of major importance in the design of structures such as planes or dams for such complex structures robustness and accuracy of the simulations are necessary the finite element method is classically considered for the simulation of such problems however the crack must be explicitly meshed in order to incorporate the discontinuity of the displacement field across crack faces this process has to be handled at each step of propagation the main drawback of this approach is the computational and human cost of remeshing the x fem method was proposed as a response to this issue 1 2 it uses the concept of partition of unity 3 in two ways first to take into account the displacement jump across crack faces far away from the crack tip and also to enrich the approximation close to the tip with some analytical asymptotic fields another important issue in fracture mechanics is the prediction of crack growth direction several criteria have been proposed one can cite for example the maximum hoop stress criterion 4 the maximum tangential stress criterion or the symmetry principle 5 the maximum energy release rate criterion 6 also called vectorial j integral criterion 7 is an alternative which was initially proposed by hellen and blackburn 7 the main difference in evaluating this criterion with respect to the classical j integral rely on the difficulties in the evaluation of the second component j2 of the energy release rate vector j it is well known that j1 which is basically the j integral is path independent concerning j2 herrmann and herrmann 8 have shown that it is path independent only in a modified manner i e by adding an extra contribution on the crack faces however this new contribution requires an accurate determination of the mechanical fields near the crack tip it is well known that the quality of these fields near a singularity is not ensured in the finite element context this is why some authors proposed specific strategies to avoid the integration near the tip for an accurate numerical evaluation of j2 9 10 for enriched finite