inverse elastostatic stress analysis in pre deformed biological structures demonstration using abdominal aortic aneurysms in stress analysis of membrane like biological structures the geometry constructed from in vivo image which often corresponds to a deformed state is routinely taken as the initial stress free geometry in this paper we show that this limitation can be completely removed using an inverse elastostatic approach namely a method for finding the initial geometry of an elastic body from a given deformed state we demonstrate the utility of the inverse approach using a patient specific abdominal aortic aneurysm model and identify the scope of error in stress estimation in the conventional approach within a realistic range of material parameter variations

computational method of inverse elastostatics for anisotropic hyperelastic solids the paper presents a computational method for predicting the initial geometry of a finitely deforming anisotropic elastic body from a given deformed state the method is imperative for a class of problem in stress analysis particularly in biomechanical applications while the basic idea has been established elsewhere comput methods appl mech eng 1996 136 47 57 int j numer meth engng 1998 43 821 838 the implementation in general anisotropic solids is not a trivial exercise but comes after a systematic development of eulerian representations of constitutive equations in this paper we discuss the general representation in the context of fibrous hyperelastic solids and provide explicit stress functions for some commonly used soft tissue models including the fung model and the holzapfel model a three field mixed formulation is introduced to enforce quasi incompressibility constraints the practical utility of this method is demonstrated using an example of aneurysm stress analysis copyright 2006 john wiley sons ltd

computational methods for inverse finite elastostatics abstract in the inverse motion problem in finite hyper elasticity the classical formulation relies on conservation laws based on eshelby s energy momentum tensor this formulation is shown to be lacking in several regards for a particular class of inverse motion problems where the deformed configuration and cauchy traction are given and the undeformed configuration must be calculated it is shown that for finite element calculations a simple re examination of the equilibrium equations provides a more suitable finite element formulation this formulation is also shown to involve only minor changes to existing elements designed for forward motion calculations examples illustrating the method in simple and complex situations involving a neo hookean material are presented

complete identification methods for the causal hierarchy we consider a hierarchy of queries about causal relationships in graphical models where each level in the hierarchy requires more detailed information than the one below the hierarchy consists of three levels associative relationships derived from a joint distribution over the observable variables cause effect relationships derived from distributions resulting from external interventions and counterfactuals derived from distributions that span multiple parallel worlds and resulting from simultaneous possibly conflicting observations and interventions we completely characterize cases where a given causal query can be computed from information lower in the hierarchy and provide algorithms that accomplish this computation specifically we show when effects of interventions can be computed from observational studies and when probabilities of counterfactuals can be computed from experimental studies we also provide a graphical characterization of those queries which cannot be computed by any method from queries at a lower layer of the hierarchy

inverse formulation for geometrically exact stress resultant shells the inverse elastostatics method tackles a class of problems in which the deformed geometry and the applied load are known while the initial geometry and the stress in the deformed state are to be determined the method is imperative for many biomechanics applications particularly for image based stress analysis of living organs as the geometry captured by imaging often correspond to a pre deformed configuration 3 4 the computational aspects of inverse elastostatics i e the inverse formulations have been established for general elastic solids 1 2 3 in this work the inverse formulation of thin walled structures modeled as geometrically exact stress resultant shell 5 is presented the inverse formulation builds on a fundamental assumption of the elastic media that the stress depends on local relative motion of the body if either the reference or the deformed configuration is given the other can be found from the elastostatic equilibrium the shell formulation follows the same logic albeit involving shell kinematics and kinetics regardless of the additional assumptions introduced in the shell theory the fundamental premise underlying inverse analysis remains the same in the proposed formulation the inverse problem is solved by using the standard week form of shell balance equations which are yet parameterized and linearized in terms of the inverse motion to facilitate an effective numerical computation an invariant approached is used to formulate the constitutive equations a consistent reduction from 3d energy function is also introduced numerical examples involving both isotopic and anisotropic materials are provided for validating the formulation applications to several biological thin walled structures demonstrate the practical utility of the method

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

causal diagrams for empirical research summary the primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject matter information in particular the paper develops a principled nonparametric framework for causal inference in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data if so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions otherwise the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained

mixed stabilized finite element methods in nonlinear solid mechanics part i formulation abstract this paper exploits the concept of stabilized finite element methods to formulate stable mixed stress displacement and strain displacement finite elements for the solution of nonlinear solid mechanics problems the different assumptions and approximations used to derive the methods are exposed the proposed procedure is very general applicable to 2d and 3d problems implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation

a uniform nodal strain tetrahedron with isochoric stabilization a stabilized node based uniform strain tetrahedral element is presented and analyzed for finite deformation elasticity the element is based on linear interpolation of a classical displacement based tetrahedral element formulation but applies nodal averaging of the deformation gradient to improve mechanical behavior especially in the regime of near incompressibility where classical linear tetrahedral elements perform very poorly this uniform strain approach adopted here exhibits spurious modes as has been previously reported in the literature we present a new type of stabilization exploiting the circumstance that the instability in the formulation is related to the isochoric strain energy contribution only and we therefore present a stabilization based on a isochoric volumetric splitting of the stress tensor we demonstrate that by stabilizing the isochoric energy contributions only reintroduction of volumetric locking through the stabilization can be avoided the isochoric volumetric splitting can be applied for all types of materials with only minor restrictions and leads to a formulation that demonstrates impressive performance in examples provided

a computational method to assess the in vivo stresses and unloaded configuration of patient specific blood vessels in the modelling process of cardiovascular diseases one often comes across the numerical simulation of the blood vessel wall when the vessel geometry is patient specific and is obtained in vivo via medical imaging the stress distribution throughout the vessel wall is unknown however simulating the full physiological pressure load inside the blood vessel without incorporating the in vivo stresses will result in an inaccurate stress distribution and an incorrect deformation of the vessel wall in this work a computational method is formulated to restore the zero pressure geometry of patient specific blood vessels and to recover the in vivo stress field of the loaded structures at the moment of imaging the proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations as only an update of the mesh is required the formulation of this method allows for a straightforward implementation in combination with existing structural solvers even if the structural solver is a black box

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

a numerical framework for material characterisation of inhomogeneous hyperelastic membranes by inverse analysis an inverse method for estimating the distributions of the elastic properties of hyperelastic inhomogeneous membranes is proposed the material description of the membrane is based on a versatile constitutive model in which two stiffness parameters govern the nonlinear elastic behaviour of the material the estimation procedure includes a finite element framework the two stiffness parameters in the constitutive law are assumed to vary continuously over the inhomogeneous membrane and in the finite element framework the distributions of the two parameters are approximated using standard linear shape functions experimental results are assumed to exist in terms of nodal displacements from a test with known geometry and boundary conditions the experimental membrane is modelled in the finite element framework and the deformation of it is predicted an error function quantifying the discrepancy between the experimentally obtained deformation pattern and the numerically predicted pattern is then minimised with respect to the nodal values of the two interpolated parameters in a number of numerical examples the proposed procedure is assessed by attempting to reproduce the given random reference distributions of material properties the proposed estimation method is fully able to reproduce the reference distributions of the two material parameters with excellent accuracy

a framework for residual based stabilization of incompressible finite elasticity stabilized formulations and f methods for linear triangles and tetrahedra abstract a new variational multiscale framework for finite strain incompressible elasticity is presented significant contributions in this work are i a systematic derivation of multiscale formulations that include the classical f method as a particular subclass ii an error estimation procedure for nonlinear elasticity that emanates naturally from within the present multiscale framework and iii robust performance of linear triangular and tetrahedral elements for modeling nearly incompressible materials in the finite strain range when viewed from the variational multiscale perspective the classical f method is shown to include only a volumetric or diagonal fine scale deformation gradient while the proposed formulation includes the full spectrum of inter scale coupling effects also the error estimation procedure readily carries over from developments conducted for small strain linear problems the formulation is presented first in the context of displacement based methods and then extended to more general mixed methods accommodating arbitrary combinations of displacement pressure interpolations an extensive set of benchmark problems is investigated to show the performance of the method for a variety of hyperelastic materials exhibiting incompressible response

methods for analysing spatial processes of several types of points two approaches are described to the analysis of spatial patterns consisting of several types of points the first approach uses a method of asymptotically unbiased estimation of the second moment distribution the second uses methods based on regions of empty space in the patterns some distributional results are given in each case and a method of monte carlo testing conditional on the marginal structure is described the methods are illustrated by being applied to some physiological data

assumed deformation gradient finite elements with nodal integration for nearly incompressible large deformation analysis an assumed strain finite element technique for non linear finite deformation is presented the weighted residual method enforces weakly the balance equation with the natural boundary condition and also the kinematic equation that links the elementwise and the assumed deformation gradient assumed gradient operators are derived via nodal integration from the kinematic weighted residual a variety of finite element shapes fits the derived framework four node tetrahedra eight 27 and 64 node hexahedra are presented here since the assumed deformation gradients are expressed entirely in terms of the nodal displacements the degrees of freedom are only the primitive variables displacements at the nodes the formulation allows for general anisotropic materials and no volumetric deviatoric split is required the consistent tangent operator is inexpensive and symmetric furthermore the material update and the tangent moduli computation are carried out exactly as for classical displacement based models the only deviation is the consistent use of the assumed deformation gradient in place of the displacement derived deformation gradient examples illustrate the performance with respect to the ability of the present technique to resist volumetric locking a constraint count can partially explain the insensitivity of the resulting finite element models to locking in the incompressible limit copyright 2008 john wiley sons ltd

a new framework for large strain electromechanics based on convex multi variable strain energies finite element discretisation and computational implementation abstract in gil and ortigosa 2016 gil and ortigosa introduced a new convex multi variable framework for the numerical simulation of electro active polymers eaps in the presence of extreme deformations and electric fields this extends the concept of polyconvexity to strain energies which depend on non strain based variables the consideration of the new concept of multi variable convexity guarantees the well posedness of generalised gibbs energy density functionals and hence opens up the possibility of a new family of mixed variational principles the aim of this paper is to present as an example the finite element implementation of two of these mixed variational principles these types of enhanced methodologies are known to be necessary in scenarios in which the simpler displacement potential based formulation yields non physical results such as volumetric locking bending and shear locking pressure oscillations and electro mechanical locking to name but a few crucially the use of interpolation spaces in which some of the unknown fields are described as piecewise discontinuous across elements can be used in order to efficiently condense these fields out this results in mixed formulations with a computational cost comparable to that of the displacement potential based approach yet far more accurate finally a series of very challenging numerical examples are presented in order to demonstrate the accuracy robustness and efficiency of the proposed methodology

inferring interventions in product based possibilistic causal networks many algorithms deal with non experimental data in possibilistic networks most of them are direct adaptations of the probabilistic approaches in this paper we propose to represent another kind of data which is experimental data caused by external interventions in possibilistic networks in particular we present different and equivalent graphical interpretations of such manipulations using an adaptation of the do operator to a possibilistic framework we then propose an efficient algorithm to evaluate effects of non simultaneous sequences of both experimental and non experimental data the main advantage of our algorithm is that it unifies treatments of the two kinds of data through the conditioning process with only a small extra cost

topology optimization utilizing inverse motion based form finding topology optimization at finite strain setting using the concept of inverse motion based form finding is introduced this novel procedure allows boundary conditions and shape of the structure in the operating deformed state to be prescribed the outcome of the optimization algorithm will be the shape of the undeformed structure i e the state in which the structure should be manufactured the objective of the optimization considered is to find the stiffest structure for a given amount of material the problem is regularized using a helmholtz filter which is formulated in the deformed configuration both the elastic boundary value problem and the partial differential equation associated with the helmholtz filter are solved using the finite element method the optimization problem is solved using a sequence of convex separable approximations the paper is closed by 2d as well as 3d numerical examples that clearly illustrates that the method is able to find optimal solutions for inverse motion finite strain topology optimization problems

an augmented iterative method for identifying a stress free reference configuration in image based biomechanical modeling continued advances in computational power and methods have enabled image based biomechanical modeling to become an important tool in basic science diagnostic and therapeutic medicine and medical device design one of the many challenges of this approach however is identification of a stress free reference configuration based on in vivo images of loaded and often prestrained or residually stressed soft tissues and organs fortunately iterative methods have been proposed to solve this inverse problem among them sellier s method this method is particularly appealing because it is easy to implement convergences reasonably fast and can be coupled to nearly any finite element package by means of several practical examples however we demonstrate that in its original formulation sellier s method is not optimally fast and may not converge for problems with large deformations fortunately we can also show that a simple inexpensive augmentation of sellier s method based on aitken s delta squared process can not only ensure convergence but also significantly accelerate the method

mixed enhanced formulation for geometrically linear axisymmetric problems a four noded quadrilateral axisymmetric formulation in the context of a mixed enhanced method is presented the strain field is represented by two sets of element parameters which results in enhanced performance and coarse mesh accuracy in bending dominated problems and locking free response in the near incompressible limit the mixed fields presented are such that variational stress recovery is permissible in addition the formulation is cast such that the mixed parameters are obtained explicitly yielding finite element arrays with the proper rank using standard order quadrature in this paper our attention is restricted to the area of geometrically linear problems in solid mechanics representative simulations show favourable performance of the formulation copyright 2002 john wiley sons ltd

facilitating score and causal inference trees for large observational studies assessing treatment effects in observational studies is a multifaceted problem that not only involves heterogeneous mechanisms of how the treatment or cause is exposed to subjects known as propensity but also differential causal effects across sub populations we introduce a concept termed the facilitating score to account for both the confounding and interacting impacts of covariates on the treatment effect several approaches for estimating the facilitating score are discussed in particular we put forward a machine learning method called causal inference tree cit to provide a piecewise constant approximation of the facilitating score with interpretable rules cit splits data in such a way that both the propensity and the treatment effect become more homogeneous within each resultant partition causal inference at different levels can be made on the basis of cit together with an aggregated grouping procedure cit stratifies data into strata where causal effects can be conveniently assessed within each besides a feasible way of predicting individual causal effects ice is made available by aggregating ensemble cit models both the stratified results and the estimated ice provide an assessment of heterogeneity of causal effects and can be integrated for estimating the average causal effect ace mean square consistency of cit is also established we evaluate the performance of proposed methods with simulations and illustrate their use with the nsw data in dehejia and wahba 1999 where the objective is to assess the impact of a labor training program the national supportedwork nsw demonstration on post intervention earnings

implicit finite incompressible elastodynamics with linear finite elements a stabilized method in rate form abstract we propose a stabilization method for linear tetrahedral finite elements suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics in particular we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models in this sense the presented development can be considered an important extension and complement to the stabilization approach proposed by the authors in previous work which was instead focused on explicit time integration and simple neo hookean models for nearly incompressible elasticity with the goal of computational efficiency we also present a two step block gauss seidel strategy for the time update of displacements velocities and pressures specifically a mixed system of equations for the velocity and pressure is updated implicitly in a first stage and the displacements are updated explicitly in a second stage the proposed mixed formulation is then embedded in newton type strategies for the nonlinear solution of the equations of motion various implicit time integration strategies are considered and particularly we focus on high frequency dissipation time integrators which are preferable in transient mechanics applications an extensive set of numerical computations with linear tetrahedral elements is presented to demonstrate the performance of the proposed approach

a stabilized nodally integrated tetrahedral a stabilized nodally integrated linear tetrahedral is formulated and analysed it is well known that linear tetrahedral elements perform poorly in problems with plasticity nearly incompressible materials and acute bending for a variety of reasons low order tetrahedral elements are preferable to quadratic tetrahedral elements particularly for nonlinear problems but the severe locking problems of tetrahedrals have forced analysts to employ hexahedral formulations for most nonlinear problems on the other hand automatic mesh generation is often not feasible for building many 3d hexahedral meshes a stabilized nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity nearly incompressible materials and acute bending the formulation is analytically and numerically shown to be stable and optimally convergent for the compressible case provided sufficient smoothness of the exact solution u c2 h1 3 future work may extend the formulation to the incompressible regime and relax the regularity requirements nonetheless the results demonstrate that the method is not susceptible to locking and performs quite well in several standard linear and nonlinear benchmarks published in 2006 by john wiley sons ltd

an arc length method including line searches and accelerations this paper describes a method for introducing line searches into the arc length solution procedure such line searches may be used at each iteration to calculate an optimum scalar step length which scales the normal iterative vector in practice a loose tolerance is provided so that on many iterations the line searches are avoided however on difficult iterations the line searches are shown to lead to a substantial improvement in the convergence characteristics a simple single parameter acceleration is also developed using line search concepts the new arc length method is applied to both the geometrically nonlinear analysis of shallow shells and the materially nonlinear analysis of reinforced concrete beams and slabs significant improvements are demonstrated in relation to the standard arc length method

bivariate cox processes some models for bivariate spatial point patterns summary from certain points of view the range of probability models currently available for describing the joint behaviour of two point processes is rather limited in this paper we explore the structure of some further models and apply our results to the statistical analysis of bivariate spatial point patterns in many branches of science there is interest in the study and description of data which represent the locations of objects as points in an essentially planar region in the present paper we assume that the objects are of two qualitatively distinguishable types and refer to the data as a bivariate spatial point pattern a statistical analysis of such data should seek to provide some meaningful summary descriptions of the separate point patterns for each of the two types of object and of any possible inter relationship between these two patterns for example fig 1 shows the locations of 173 newly emergent and 155 1 year old bramnble 0 a a tv t to 0 x t

mixed linear linear simplicial elements for incompressible elasticity and plasticity this paper exploits the concept of orthogonal sub grid scales to stabilize the behaviour of mixed linear linear simplicial elements triangles and tetrahedra in incompressible or nearly incompressible situations both incompressible elastic and j2 plastic constitutive behaviours have been considered the different assumptions and approximations used to derive the method are exposed implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the elements derived are free of volumetric locking and spurious oscillations of the pressure and that the results obtained compare favourably with those obtained with the q1p0 quadrilateral

computational methods for inverse deformations in quasi incompressible finite elasticity this paper presents a formulation for incorporating quasi incompressibility in inverse design problems for finite elastostatics where deformed configurations and cauchy tractions are known in the recent paper of govindjee and mihalic 1996 comput methods appl mech engng 136 47 57 a method for solving this class of inverse problems was presented for compressible materials here we extend this work to the important case of nearly incompressible materials a displacement pressure mixed formulation is combined with a penalty method to enforce the quasi incompressible constraint without locking numerical examples are presented and compared to known solutions further examples present practical applications of this research to active problems in elastomeric component design 1998 john wiley sons ltd

a mixed enhanced formulation tetrahedral finite elements this paper considers the solution of problems in three dimensional solid mechanics using tetrahedral finite elements a formulation based on a mixed enhanced treatment involving displacement pressure and volume effects is presented the displacement and pressure are used as nodal quantities while volume effects and enhanced modes belong to individual elements both small and finite deformation problems are addressed and sample solutions are given to illustrate the performance of the formulation copyright 2000 john wiley sons ltd

introduction to causal inference the goal of many sciences is to understand the mechanisms by which variables came to take on the values they have that is to find a generative model and to predict what the values of those variables would be if the naturally occurring mechanisms were subject to outside manipulations the past 30 years has seen a number of conceptual developments that are partial solutions to the problem of causal inference from observational sample data or a mixture of observational sample and experimental data particularly in the area of graphical causal modeling however in many domains problems such as the large numbers of variables small samples sizes and possible presence of unmeasured causes remain serious impediments to practical applications of these developments the articles in the special topic on causality address these and other problems in applying graphical causal modeling algorithms this introduction to the special topic on causality provides a brief introduction to graphical causal modeling places the articles in a broader context and describes the differences between causal inference and ordinary machine learning classification and prediction problems

variational gradient plasticity at finite strains part ii local global updates and mixed finite elements for additive plasticity in the logarithmic strain space the second part of our work on variational inelasticity with long range effects outlines the formulation and finite element implementation of additive finite gradient plasticity in the logarithmic strain space it is considered to be the most simple approach to finite plasticity suitable for the purely phenomenological description of polycrystalline metals or amorphous materials if structures of the geometrically linear theories are defined in the lagrangian logarithmic strain space we start from a mixed saddle point principle for metric type additive plasticity which is specified for the important model problem of isochoric von mises plasticity with gradient extended hardening softening response the mixed variational structure includes the hardening softening variable itself as well as its dual driving force the numerical implementation exploits the underlying variational structure yielding a canonical symmetric structure of the monolithic problem it results in a novel finite element design of the coupled problem incorporating a long range hardening softening parameter and its dual driving force this allows a straightforward local definition of plastic loading unloading driven by the long range fields providing very robust finite element implementations of gradient plasticity it includes a rational method for the definition of elastic plastic boundaries epbs in gradient plasticity along with a postprocessor that defines the plastic variables in the elastic range we discuss alternative mixed finite element designs of the coupled problem including a local global solution strategy of short and long range fields all methods are derived in a rigorous format from variational principles numerical benchmarks demonstrated the excellent performance of the proposed mixed variational approach to gradient plasticity in the logarithmic strain space

on configurational forces in multiplicative elastoplasticity abstract the main goal of this work consists in the elaboration of the material or rather configurational mechanics in the context of multiplicative elastoplasticity this nowadays well established approach which is inherently related to the concept of a material isomorphism or in other words to a local rearrangement is adopted as a paradigm for the general modelling of finite inelasticity the overall motion in space is throughout assumed to be compatible and sufficiently smooth according to the underlying configurations namely the material and the spatial configuration as well as what we call the intermediate configuration different representations of balance of linear momentum are set up for the static case the underlying flux terms are thereby identified as stress tensors of piola and cauchy type and are assumed to derive from a free energy density function thus taking hyperelastic formats moreover the incorporated source terms namely the configurational volume forces are identified by comparison arguments these quantities include gradients of distortions as well as dislocation density tensors in particular those dislocation density tensors related to the elastic or plastic distortion do not vanish due to the general incompatibility of the intermediate configuration as a result configurational volume forces which are settled in the intermediate configuration embody non vanishing dislocation density tensors while their material counterparts directly incorporate non vanishing gradients of distortions this fundamental property enables us to recover the celebrated peach koehler force for finite inelasticity acting on a single dislocation from the intermediate configuration volume forces

mixed enhanced formulation for finite deformation axisymmetric torsion the development and implementation of a four noded quadrilateral element for the analysis of the axisymmetric torsion problem is presented in the context of the mixed enhanced method the deformation gradient is developed from two sets of element interpolants of which one may be explicitly obtained resulting in only two undetermined enhanced parameters needed for the satisfaction of the near incompressible limit the resulting element arrays yield proper rank with standard 2 2 quadrature the introduction of a three field variation statement for the problem along with the interpolations for the stress and deformation gradient render a variational stress recovery permissible several numerical examples are explored in the setting of finite kinematics with physically non linear material properties to further induce coupling between the radial and axial displacement and the longitudinal rotation copyright 2004 john wiley sons ltd

a new framework for large strain electromechanics based on convex multi variable strain energies variational formulation and material characterisation abstract following the recent work of bonet et al 2015 this paper postulates a new convex multi variable variational framework for the analysis of electro active polymers eaps in the context of reversible nonlinear electro elasticity this extends the concept of polyconvexity ball 1976 to strain energies which depend on non strain based variables introducing other physical measures such as the electric displacement six key novelties are incorporated in this work first a new definition of the electro mechanical internal energy is introduced expressed as a convex multi variable function of a new extended set of electromechanical arguments crucially this new definition of the internal energy enables the most accepted constitutive inequality namely ellipticity to be extended to the entire range of deformations and electric fields and in addition to incorporate the electro mechanical energy of the vacuum and hence that for ideal dielectric elastomers as a degenerate case second a new extended set of variables work conjugate to those characterising the new definition of multi variable convexity is introduced in this paper third both new sets of variables enable the definition of novel extended hu washizu type of mixed variational principles which are presented in this paper for the first time in the context of nonlinear electro elasticity fourth some simple strategies to create appropriate convex multi variable energy functionals in terms of convex multi variable invariants by incorporating minor modifications to a priori non convex multi variable functionals are also presented fifth a tensor cross product operation de boer 1982 used in bonet et al 2015 to facilitate the algebra associated with the adjoint of the deformation gradient tensor is incorporated in the proposed variational electro mechanical framework leading to insightful representations of otherwise complex algebraic expressions finally under a characteristic experimental setup in dielectric elastomers the behaviour of a convex multi variable constitutive model capturing some intrinsic nonlinear effects such as electrostriction is numerically studied

causality conditional independence and graphical separation in settable systems we study the connections between causal relations and conditional independence within the settable systems extension of the pearl causal model pcm our analysis clearly distinguishes between causal notions and probabilistic notions and it does not formally rely on graphical representations as a foundation we provide definitions in terms of suitable functional dependence for direct causality and for indirect and total causality via and exclusive of a set of variables based on these foundations we provide causal and stochastic conditions formally characterizing conditional dependence among random vectors of interest in structural systems by stating and proving the conditional reichenbach principle of common cause obtaining the classical reichenbach principle as a corollary we apply the conditional reichenbach principle to show that the useful tools of d separation and d separation can be employed to establish conditional independence within suitably restricted settable systems analogous to markovian pcms

coupled fluid structure interaction hemodynamics in a zero pressure state corrected arterial geometry abstract hemodynamic conditions in large arteries are significantly affected by the interaction of the pulsatile blood flow with the distensible arterial wall a numerical procedure for solving the fluid structure interaction problem encountered in cardiovascular flows is presented we consider a patient specific carotid bifurcation geometry obtained from 3d reconstruction of in vivo acquired tomography images which yields a geometrical representation of the artery corresponding to its pressurized state to recover the geometry of the artery in its zero pressure state which is required for a fluid structure interaction simulation we utilize inverse finite elastostatics time dependent flow simulations with in vivo measured inflow volume flow rate in the 3d undeformed artery are performed through the finite element method the coupled momentum method for fluid structure interaction is adopted to incorporate the influence of wall compliance in the numerical computation of the time varying flow domain to demonstrate the importance in recovering the zero pressure state of the artery in hemodynamic simulations we compute the time varying flow field with compliant walls for the original and the zero pressure state corrected geometric configurations of the carotid bifurcation the most important resulting effects in the hemodynamic environment are evaluated our results show a significant change in the wall shear stress distribution and the spatiotemporal extent of the recirculation regions

determining the finite elasticity reference state from a loaded configuration there are a number of situations where the deformed configuration of a body is known and it is necessary to determine the reference state previous methods developed to calculate the reference state involve the formulation of the finite elasticity equations in terms of the deformed configuration this paper demonstrates that the undeformed reference state can be accurately determined from a deformed configuration and the associated loading conditions by using conventional finite elasticity balance equations together with a solution procedure that treats the reference configuration as the unknowns the mathematical theory behind the solution method is described validated with an analytical solution and verified using experimental studies on gel phantoms the practical utility of this method is then demonstrated in the field of breast biomechanics copyright 2007 john wiley sons ltd

finite element modelling of inverse design problems in large deformations anisotropic hyperelasticity this paper introduces a finite element model for the inverse design of pieces with large displacements in the elastic range the problem consists in determining the initial shape of the piece such that it attains the designed shape under the effect of service loads the model is particularly focused on the design of parts with a markedly anisotropic behavior like laminated turbine blades although the formulation expresses equilibrium on the distorted configuration it uses a standard constitutive equations library that is expressed as usual for measures attached to the undistorted configuration in this way the modifications to a standard finite elements code are limited to the routines for the computation of the finite element internal forces and tangent matrix two examples are given the first one for validation purposes while the second is an application which has industrial interest for the design of turbine blades copyright 2007 john wiley sons ltd

improved versions of assumed enhanced strain tri linear elements for 3d finite deformation problems abstract improved three dimensional tri linear elements for finite deformation problems are developed based on an assumed enhanced strain methodology which in the linear regime incorporates the classical method of incompatible modes as a particular case three crucial modifications of a recently proposed element which reduces to wilson s brick in the linear regime are introduced to prevent locking response in distorted configurations and to maintain proper rank while preserving excellent performance in bending dominated and localization problems i a modified quadrature rule ii an additional enhancement of the divergence term and iii a modification of the isoparametric shape function derivatives for the three dimensional problem moreover these modified shape function derivatives are shown to improve the performance of the standard tri linear brick in distorted configurations in addition a strategy is described to circumvent the memory storage requirements in the static condensation procedure of the enhanced strain parameters the excellent performance of the improved methodology is illustrated in representative numerical simulations

a mixed tetrahedral element with nodal rotations for large displacement analysis of inelastic structures summary a novel mixed four node tetrahedral finite element equipped with nodal rotational degrees of freedom is presented its formulation is based on a hu washizu type functional suitable to the treatment of material nonlinearities rotation and skew symmetric stress fields are assumed as independent variables the latter entering the functional to impose rotational compatibility and suppress spurious modes exploiting the choice of equal interpolation for strain and symmetric stress fields a robust element state determination procedure requiring no element level iteration is proposed the mixed element stability is assessed by means of an original and effective numerical test the extension of the present formulation to geometric nonlinear problems is achieved through a polar decomposition based corotational framework after validation in both material and geometric nonlinear context the element performances are investigated in demanding simulations involving complex shape memory alloy structures supported by the comparison with available linear and quadratic tetrahedrons and hexahedrons the numerical results prove accuracy robustness and effectiveness of the proposed formulation copyright 2016 john wiley sons ltd

mediation analysis with time varying exposures and mediators in this paper we consider causal mediation analysis when exposures and mediators vary over time we give non parametric identification results discuss parametric implementation and also provide a weighting approach to direct and indirect effects based on combining the results of two marginal structural models we also discuss how our results give rise to a causal interpretation of the effect estimates produced from longitudinal structural equation models when there are time varying confounders affected by prior exposure and mediator natural direct and indirect effects are not identified however we define a randomized interventional analogue of natural direct and indirect effects that are identified in this setting the formula that identifies these effects we refer to as the mediational g formula when there is no mediation the mediational g formula reduces to robins regular g formula for longitudinal data when there are no time varying confounders affected by prior exposure and mediator values then the mediational g formula reduces to a longitudinal version of pearl s mediation formula however the mediational g formula itself can accommodate both mediation and time varying confounders and constitutes a general approach to mediation analysis with time varying exposures and mediators

a first order hyperbolic framework for large strain computational solid dynamics part i total lagrangian isothermal elasticity abstract this paper introduces a new computational framework for the analysis of large strain fast solid dynamics the paper builds upon previous work published by the authors gil et al 2014 48 where a first order system of hyperbolic equations is introduced for the simulation of isothermal elastic materials in terms of the linear momentum the deformation gradient and its jacobian as unknown variables in this work the formulation is further enhanced with four key novelties first the use of a new geometric conservation law for the co factor of the deformation leads to an enhanced mixed formulation advantageous in those scenarios where the co factor plays a dominant role second the use of polyconvex strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes for solid dynamics problems moreover the introduction of suitable conjugate entropy variables enables the derivation of a symmetric system of hyperbolic equations dual of that expressed in terms of conservation variables third the new use of a tensor cross product 61 greatly facilitates the algebraic manipulations of expressions involving the co factor of the deformation fourth the development of a stabilised petrov galerkin framework is presented for both systems of hyperbolic equations that is when expressed in terms of either conservation or entropy variables as an example a polyconvex mooney rivlin material is used and for completeness the eigen structure of the resulting system of equations is studied to guarantee the existence of real wave speeds finally a series of numerical examples is presented in order to assess the robustness and accuracy of the new mixed methodology benchmarking it against an ample spectrum of alternative numerical strategies including implicit multi field fraeijs de veubeke hu washizu variational type approaches and explicit cell and vertex centred finite volume schemes

numerical simulation of ductile fracture with the rousselier constitutive law this contribution aims at developing robust and reliable tools dedicated to predictive numerical simulation of ductile fracture description of damage mechanisms relies here on the rousselier constitutive law to achieve robustness and objectivity several points need then to be addressed reduction of the set of internal variables so as to recast the model into the framework of generalised standard materials proper expression of the normal plastic flow rule at the vertex of the yield surface finite strain formulation based on a multiplicative split of the deformation gradient fully implicit integration of the constitutive equations leading to a single scalar equation that admits a unique root use of mixed finite elements to avoid volumetric locking strain gradient based nonlocal model to control strain localisation and remedy spurious mesh dependency the capabilities of the resulting numerical formulation are demonstrated through simulating the cup cone fracture of a notched tensile specimen

inverse motion based form finding for quasi incompressible finite electroelasticity this work deals with inverse motion based form finding for electroelasticity the inverse motion problem is formulated for the electroelastic case and the resulting equations are implemented within a finite element framework a four field variational approach is adopted taking into consideration the typically incompressible behavior of the elastomer materials commonly used in electromechanical applications by means of numerical simulations the inverse motion based form finding makes it possible to design the referential configuration so that a given set of loads and boundary conditions results in a prespecified deformed configuration the computational finite element framework established in this work allows for such numerical simulations and testing and thereby the possibility to improve the design and accuracy in electroelastic applications such as grippers sensors and seals less

on referential and spatial formulations of inverse elastostatic analysis abstract there are two families of element formulation for inverse elastostatic analysis in the literature they employ different computation procedures at the element and material levels it has been suggested that one of them can preserve material library while the other requires redeveloping the material functions in this article we show that these two formulations are completely equivalent under certain conditions both can preserve the material library while under other conditions neither can we show that the modification of material functions is caused by the need of updating material symmetry in the inverse solution process several theoretical results were obtained while establishing the equivalence including an identity relating the inverse and forward tangent tensors for isotropic materials a comprehensive documentation of these two formulations is provided

reformulation of nodally integrated continuum elements to attain insensitivity to distortion summary the nodally integrated continuum element nice formulation is an assumed strain finite element technique derived from a weighted residual statement that weakly enforces both the balance equation and the kinematic equation the original nice formulation has a number of desirable attributes e g resistance to volumetric locking but similar to classical finite elements it is sensitive to a geometrical distortion of the finite element mesh the present work analyzes the nice technique from this viewpoint the source of the sensitivity to the shape of the element is identified and an improvement of the nice formulation is proposed we illustrate the performance of the revised nice formulation on extremely distorted meshes the tetrahedral meshes contain zero volume or negative volume elements including slivers and the new nice formulation is shown to have the condition number of the stiffness matrix under control even in the presence of slivers furthermore insensitivity to distortions is demonstrated for quadratic and cubic hexahedral elements the proposed improvement confers robustness to all element shapes treated by the nice formulation the approximation properties of the original nice formulation are preserved in particular the improved version is also locking free and at the same time the need for stabilization also carries over copyright 2011 john wiley sons ltd

a finite element method for a three field formulation of linear elasticity based on biorthogonal systems abstract we consider a mixed finite element method based on simplicial triangulations for a three field formulation of linear elasticity the three field formulation is based on three unknowns displacement stress and strain in order to obtain an efficient discretization scheme we use a pair of finite element bases forming a biorthogonal system for the strain and stress the biorthogonality relation allows us to statically condense out the strain and stress from the saddle point system leading to a symmetric and positive definite system the strain and stress can be recovered in a post processing step simply by inverting a diagonal matrix moreover we show a uniform convergence of the finite element approximation in the incompressible limit numerical experiments are presented to support the theoretical results

elastic properties of anisotropic vascular membranes examined by inverse analysis an inverse method for estimating the distributions of the nonlinear elastic properties of inhomogeneous and anisotropic vascular membranes such as cerebral aneurysms is proposed the material description of the membrane is based on a versatile structural model able to represent multiple collagen layers and the passive response of the vascular wall each individual layer is assumed to behave transversely isotropic following exponential stiffening with increasing loading the model includes four parameters to be explainable physically two initial stiffnesses of the collagen fabric a parameter related to the nonlinearity of the collagen fabric angle between the principal directions of the collagen fabric and a reference coordinate system for this finite deformation problem a finite element framework for membranous structures considering pressure boundary loading is outlined i e the principle of virtual work its linearisation and the related spatial discretisation the estimation procedure consists of the following three steps i in vivo or in vitro approaches record the mechanical responses of membranous structures whose properties are to be determined ii define a corresponding finite element model iii minimise an error function regarding the unknown parameters that quantifies the deviation of the numerical prediction from the recorded data to achieve a robust parameter estimation an element partition method is employed the outcome of the procedure is affected by the number of nodes defined on the membrane surface and the number of load steps in a numerical example the proposed procedure is assessed by reestablishing given reference distributions in a reference membrane the deviations of the estimated material parameter distributions from the related reference fields are within just a few percent in most of the investigated cases the standard deviation for the resulting maximum principal stress was even below 1 which is accurate enough for rupture risk assessment of vascular membranes

on the dependence structure of bivariate recurrent event processes inference and estimation bivariate or multivariate recurrent event processes are often encountered in longitudinal studies in which more than one type of event is of interest there has been much research on regression analysis for such data but little has been done to measure the dependence between recurrent event processes we propose a time dependent measure termed the rate ratio to assess the local dependence between two types of recurrent event processes we model the rate ratio as a parametric function of time and leave unspecified all other aspects of the distribution we develop a composite likelihood procedure for model fitting and parameter estimation we show that the proposed estimator is consistent and asymptotically normal its finite sample performance is evaluated by simulation and illustrated by an application to a soft tissue sarcoma study

shear band localization via local j2 continuum damage mechanics this paper describes a novel formulation for the solution of problems involving shear band localization using a local isotropic j2 continuum damage model and mixed linear simplex triangles and tetrahedra stabilization methods are used to ensure existence and uniqueness of the solution attaining global and local stability of the corresponding discrete finite element formulation consistent residual viscosity is used to enhance robustness and convergence of the formulation implementation and computational aspects are also discussed a simple isotropic local j2 damage constitutive model is considered either with linear or exponential softening the softening modulus is regularized according to the material mode ii fracture energy and the element size numerical examples show that the formulation derived is fully stable and remarkably robust totally free of volumetric locking and spurious oscillations of the pressure as a consequence the results obtained do not suffer from spurious mesh size or mesh bias dependence comparing very favourably with those obtained with the ill posed standard approaches 2004 elsevier b v all rights reserved

triangles and tetrahedra in explicit dynamic codes for solids explicit dynamic codes which are used currently for the study of plastic deformations in impact or with some modification for metal forming suffer two serious limitations first only quadrilateral or hexahedral linear elements can be used thus limiting the possibilities of adaptive refinement and adaptive meshing second even with the use of such elements special devices such as reduced integration must be introduced to avoid locking and reduce costs these necessitate complex hour glass control mending type procedures the main difficulties are those due to the need of treatment of almost incompressible deformation modes recently similar difficulties have been overcome in the context of fluid dynamics soil dynamics and we show here how the processes introduced there can be adopted effectively to the present problem thus allowing an almost unrestricted choice of element interpolations 1998 john wiley sons ltd

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis