effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

theory and numerics of layered shells with variationally embedded interlaminar stresses abstract present paper deals with layered shells subjected to static loading the basic equations include besides the global equilibrium formulated in terms of stress resultants the local equilibrium in terms of stresses the geometric field equations the constitutive equations a constraint which enforces the correct shape of the superposed displacement field through the thickness and the boundary conditions thereby an interface to three dimensional material laws is created the weak form of the boundary value problem is derived and a finite element formulation for quadrilaterals is specified the mixed hybrid shell element possesses the usual 5 or 6 nodal degrees of freedom this allows standard geometrical boundary conditions and the elements are applicable also to shell intersection problems for linear elasticity the computed transverse shear stresses are automatically continuous at layer boundaries and zero at the outer surfaces in comparison to fully 3d computations present element formulation needs only a fractional amount of computing time

coupling of two and three dimensional composite shell elements in linear and non linear applications abstract a numerical model for the non linear analysis of laminates is presented the developed element is based on piecewise polynomial interpolation in thickness direction although the total number of degrees of freedom is comparable to a discretization with 3d brick elements this approach provides several advantages e g a simple mesh generation due to a 2d type data structure and a better bending behavior the developed isoparametric quadrilateral finite element allows prediction of the complete stress state furthermore a transition element is presented which is used to couple the developed element with 5 parameter shell elements several linear and non linear examples are presented to illustrate the performance of the developed numerical model

two scale analysis of heterogeneous elastic plastic materials with asymptotic homogenization and voronoi cell finite element model in this paper a multiple scale finite element model vcfem homo has been developed for elastic plastic analysis of heterogeneous porous and composite materials by combining asymptotic homogenization theory with the voronoi cell finite element model vcfem vcfem for microstructural modeling originates from dirichlet tessellation of representative material elements at sampling points in the structure structural modeling is done by the general purpose finite element code abaqus and interfacing with the microscale vcfem analysis is done through the user subroutine in abaqus for material constitutive relation umat asymptotic homogenization in umat generates macroscopic material parameters for abaqus following the macroscopic analysis a local vcfem analysis is invoked to depict the true evolution of microstructural state variables various numerical examples are executed for validating the effectiveness of vcfem homo and the effect of size shape and distribution of heterogeneities on local and global response is examined

a dual mixed approximation method for a three field model of a nonlinear generalized stokes problem in this work a dual mixed approximation of a nonlinear generalized stokes problem is studied the problem is analyzed in sobolev spaces which arise naturally in the problem formulation existence and uniqueness results are given and error estimates are derived it is shown that both lowest order and higher order mixed finite elements are suitable for the approximation method numerical experiments that support the theoretical results are presented

a robust non linear solid shell element based on a mixed variational formulation the paper is concerned with a geometrically non linear solid shell finite element formulation which is based on the hu washizu variational principle for the approximation of the independent displacement stress and strain fields the strain field is additively decomposed into two parts due to the fact that one part of the strain field is interpolated in the same manner as proposed by the enhanced assumed strain eas method it is denoted as eas field the other strain field is approximated with the same interpolation functions as the stress field in contrast to the eas concept the approximation spaces of the stresses and the enhanced assumed strains are not orthogonal consequently the stress field is not eliminated from the finite element equations for the displacements tri linear shape functions are considered shear locking and curvature thickness locking are treated using assumed natural strain interpolations a static condensation leads to a simple low order hexahedral solid shell element numerical tests show that the present model is very robust and allows larger load steps than an eas solid shell element

quasi norm error bounds for the finite element approximation of a non newtonian flow we consider the finite element approximation of a non newtonian flow where the viscosity obeys a general law including the carreau or power law for sufficiently regular solutions we prove energy type error bounds for the velocity and pressure these bounds improve on existing results in the literature a key step in the analysis is to prove abstract error bounds initially in a quasi norm which naturally arises in degenerate problems of this type

a posteriori estimators for mixed finite element approximations of a fluid obeying the power law we study a posteriori error estimation in the approximation by the finite element method of a fluid which obeys the power law 2 d u r 2d u p f u 0 1 r 2 abstract and calculable a posteriori estimators are given in two fields and in a three fields version of this problem furthermore we give some examples of fe spaces satisfying the inf sup condition which relates the discrete space of tensors and the discrete space of velocities needed for this formulation

a multi level computational model for multi scale damage analysis in composite and porous materials abstract an adaptive multi level methodology is developed in this paper to create a hierarchy of computational sub domains with varying resolution for multiple scale problems it is intended to concurrently predict evolution of variables at the structural and microstructural scales as well as to track the incidence and propagation of microstructural damage in composite and porous materials the microstructural analysis is conducted with the voronoi cell finite element model vcfem while a conventional displacement based fem code executes the macroscopic analysis the model introduces three levels in the computational domain which include macro macro micro and microscopic analysis it differentiates between non critical and critical regions and ranges from macroscopic computations using continuum constitutive relations to zooming in at hotspots for pure microscopic simulations coupling between the scales in regions of periodic microstructure is accomplished through asymptotic homogenization an adaptive process significantly increases the efficiency while retaining appropriate level of accuracy for each region numerical examples are conducted for composite and porous materials with a variety of microscopic architectures to demonstrate the potential of the model

an efficient and robust rotational formulation for isogeometric reissner mindlin shell elements abstract this work is concerned with the development of an efficient and robust isogeometric reissner mindlin shell formulation for the mechanical simulation of thin walled structures such structures are usually defined by non uniform rational b splines nurbs surfaces in industrial design software the usage of isogeometric shell elements can avoid costly conversions from nurbs surfaces to other surface or volume geometry descriptions the shell formulation presented in this contribution uses a continuous orthogonal rotation described by rodrigues tensor in every integration point to compute the current director vector the rotational state is updated in a multiplicative manner large deformations and finite rotations can be described accurately the proposed formulation is robust in terms of stable convergence behavior in the nonlinear equilibrium iteration for large load steps and geometries with large and arbitrary curvature and in terms of insensitivity to shell intersections with kinks under small angles three different integration schemes and their influence on accuracy and computational costs are assessed the efficiency and robustness of the proposed isogeometric shell formulation is shown with the help of several examples accuracy and efficiency is compared to an isogeometric shell formulation with the more common discrete rotational concept and to lagrange based finite element shell formulations the competitiveness of the proposed isogeometric shell formulation in terms of computational costs to attain a pre defined error level is shown

coupled generalized nonlinear stokes flow with flow through a porous medium in this article we analyze the flow of a fluid through a coupled stokes darcy domain the fluid in each domain is non newtonian modeled by the generalized nonlinear stokes equation in the free flow region and the generalized nonlinear darcy equation in the porous medium a flow rate is specified along the inflow portion of the free flow boundary we show existence and uniqueness of a variational solution to the problem we propose and analyze an approximation algorithm and establish a priori error estimates for the approximation

a class of general algorithms for multi scale analyses of heterogeneous media abstract a class of computational algorithms for multi scale analyses is developed in this paper the two scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements instead of the method of two scale asymptotic expansion the mathematical results on the generalized convergence are utilized in the two scale variational descriptions accordingly the global local type computational schemes can be unified in association with the homogenization procedure for general nonlinear problems after formulating the problem in linear elastostatics that with local contact condition and the elastoplastic problem we present representative numerical examples along with the computational algorithm consistent with our two scale modeling strategy as well as some direct approaches

quasi norm interpolation error estimates for the piecewise linear finite element approximation of p laplacian problems in this work new interpolation error estimates have been derived for some well known interpolators in the quasi norms the estimates are found to be essential to obtain the optimal a priori error bounds under the weakened regularity conditions for the piecewise linear finite element approximation of a class of degenerate equations in particular by using these estimates we can close the existing gap between the regularity required for deriving the optimal error bounds and the regularity achievable for the smooth data for the 2 d and 3 d p laplacian

residual a posteriori error estimator for a three field model of a non linear generalized stokes problem in this article we propose and analyze an a posteriori error estimator for a three field model of a generalized stokes problem the components of the a posteriori error estimator are defined via a non linear projection of the residues of the variational equations both upper and lower bounds for the approximation error are derived in terms of the components of the a posteriori error estimator the non linear projections do not need to be explicitly computed to construct the a posteriori error estimates

optimal control for quasi newtonian flows with defective boundary conditions we consider a generalized newtonian fluid with defective boundary conditions where only flow rates or mean pressures are prescribed on parts of boundary the defect boundary condition problem is formulated as an optimal control problem in which a neumann or dirichlet boundary control is used for matching given flow rates or mean pressures for the constrained optimization problem an optimality system is derived from which a solution of the problem is obtained computational algorithms are discussed and numerical results are also presented

eigendeformation based reduced order homogenization for failure analysis of heterogeneous materials the manuscript presents a novel model reduction approach for periodic heterogeneous media which combines the multiple scale asymptotic msa expansion method with the transformation field analysis tfa to reduce the computational cost of a direct homogenization approach without significantly compromising on solution accuracy the evolution of failure in micro phases and interfaces is modeled using eigendeformation adaptive model improvement strategy incorporating a hierarchical sequence of computational homogenization models is employed to control the accuracy of the model we present the model formulation and the computational details along with verification with respect to direct homogenization and validation with respect to physical experiments studies

a robust non linear mixed hybrid quadrilateral shell element in the paper a non linear quadrilateral shell element for the analysis of thin structures is presented the variational formulation is based on a hu washizu functional with independent displacement stress and strain fields the interpolation matrices for the mid surface displacements and rotations as well as for the stress resultants and strains are specified restrictions on the interpolation functions concerning fulfillment of the patch test and stability are derived the developed mixed hybrid shell element possesses the correct rank and fulfills the in plane and bending patch test using newton s method the finite element approximation of the stationary condition is iteratively solved our formulation can accommodate arbitrary non linear material models for finite deformations in the examples we present results for isotropic plasticity at finite rotations and small strains as well as bifurcation problems and post buckling response the essential feature of the new element is the robustness in the equilibrium iterations it allows very large load steps in comparison to other element formulations copyright 2005 john wiley sons ltd

analyse numerique des ecoulements quasi newtoniens dont la viscosite obeit a la loi puissance ou la loi de carreau we prove abstract error estimates for the approximation of the velocity and the pressure by a mixed fem of quasi newtonian flows whose viscosity obeys the power law or the carreau law these estimates are optimal in some cases they can be applied to most finite elements used for the solution of stokes s problem on prouve des estimations d erreur abstraites pour l approximation de la vitesse et la pression par une mef mixtes d ecoulements quasi newtoniens dont la viscosite obeit a la loi puissance ou la loi de carreau ces estimations sont optimales dans certains cas elles peuvent etre appliquees a la plupart des elements finis utilises pour la resolution du probleme de stokes

computational homogenization for heterogeneous thin sheets in this paper a computational homogenization technique for thin structured sheets is proposed based on the computational homogenization concepts for first and second order continua the actual three dimensional 3d heterogeneous sheet is represented by a homogenized shell continuum for which the constitutive response is obtained from the nested analysis of a microstructural representative volume element rve incorporating the full thickness of the sheet and an in plane representative cell of the macroscopic structure at an in plane integration point of the macroscopic shell the generalized strains i e the membrane deformation and the curvature are used to formulate the boundary conditions for the microscale rve problem at the rve scale all microstructural constituents are modeled as an ordinary 3d continuum described by the standard equilibrium and the constitutive equations upon proper averaging of the rve response the macroscopic generalized stress and the moment resultants are obtained in this way an in plane homogenization is directly combined with a through thickness stress integration from a macroscopic point of view a numerical generalized stress strain constitutive response at every macroscopic in plane integration point is obtained additionally the simultaneously resolved microscale rve local deformation and stress fields provide valuable information for assessing the reliability of a particular microstructural design

a coupled two scale shell model with applications to layered structures summary in this paper a coupled two scale shell model is presented a variational formulation and associated linearization for the coupled global local boundary value problem is derived for small strain problems various numerical solutions are computed within the so called fe 2 method the discretization of the shell is performed with quadrilaterals whereas the local boundary value problems at the integration points of the shell are discretized using 8 noded or 27 noded brick elements or so called solid shell elements at the bottom and top surface of the representative volume element stress boundary conditions are applied whereas at the lateral surfaces the in plane displacements are prescribed for the out of plane displacements link conditions are applied the coupled nonlinear boundary value problems are simultaneously solved within a newton iteration scheme with an important test the correct material matrix for the stress resultants assuming linear elasticity and a homogeneous continuum is verified copyright 2013 john wiley sons ltd

numerical analysis of a three fields model for a quasi newtonian flow abstract we study a finite element approximation of a non linear three fields version of stokes system for incompressible fluids such a problem arises when one considers a white metzner type model for a viscoelastic fluid flow and sets the relaxation time to zero the non linear aspect comes from the fact that a fraction of the viscosity of the fluid depends on the second invariant of the rate of deformation tensor we give existence and unicity results for the continuous problem and its approximation and we prove the error bound

noise constrained least mean squares algorithm we consider the design of an adaptive algorithm for finite impulse response channel estimation which incorporates partial knowledge of the channel specifically the additive noise variance although the noise variance is not required for the offline wiener solution there are potential benefits and limitations for the learning behavior of an adaptive solution in our approach a robbins monro algorithm is used to minimize the conventional mean square error criterion subject to a noise variance constraint and a penalty term necessary to guarantee uniqueness of the combined weight multiplier solution the resulting noise constrained lms nclms algorithm is a type of variable step size lms algorithm where the step size rule arises naturally from the constraints a convergence and performance analysis is carried out and extensive simulations are conducted that compare nclms with several adaptive algorithms this work also provides an appropriate framework for the derivation and analysis of other adaptive algorithms that incorporate partial knowledge of the channel

large strain two scale computational approach using c1 continuity finite element employing a second gradient theory a two scale computational algorithm employing second order computational homogenization under assumption of large strain is presented a micro macro transition has been proposed where the c1 continuity displacement based finite element is used for discretization at the macrolevel while the representative volume element at the microlevel is discretized by c0 continuity finite elements the performed finite element verifications show an advantage in comparison to available finite element formulations in order to improve numerical efficiency of the proposed computational procedures the algorithms are embedded into the finite element program abaqus the performance of the presented multiscale homogenization approach is demonstrated in numerical examples where the elastoplastic deformation responses are considered and compared with the small strain analysis