Journal ArticleDOI
Aspects of the formulation and finite element implementation of large strain isotropic elasticity
TLDR
In this article, a formulation of isotropic large strain elasticity and computational aspects of its finite element implementation are discussed. But the authors focus on the finite element implementations of the model.Abstract:
The paper presents a formulation of isotropic large strain elasticity and addresses some computational aspects of its finite element implementation. On the theoretical side, an Eulerian setting of isotropic elasticity is discussed exclusively in terms of the Finger tensor as a strain measure. Noval aspects are a direct representation of the Eulerian elastic moduli in terms of the Finger tensor and their rigorous decomposition into decoupled volumetric and isochoric contributions based on a multiplicative split of the Finger tensor into spherical and unimodular parts. The isochoric stress response is formulated in terms of the eigenvalues of the unimodular part of the Finger tensor. A constitutive algorithm for the computation of the stresses and tangent moduli for plane problems is developed and applied to a model problem of rubber elasticity. On the computational side, the implementation of the constitutive model in three possible finite element formulations is discussed. After pointing out algorithmic techniques for the treatment of incompressible elasticity, several numerical simulations are presented which show the performance of the proposed constitutive algorithm and the convergence behaviour of the different finite element fomulations for compressible and incompressible elasticity.read more
Citations
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Journal ArticleDOI
Hyperelastic modelling of arterial layers with distributed collagen fibre orientations
TL;DR: A structural continuum framework that is able to represent the dispersion of the collagen fibre orientation is developed and allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls.
Book
Nonlinear Continuum Mechanics for Finite Element Analysis
Javier Bonet,Richard D. Wood +1 more
TL;DR: Bonet and Wood as discussed by the authors provide a complete, clear, and unified treatment of nonlinear continuum analysis and finite element techniques under one roof, providing an essential resource for postgraduates studying non-linear continuum mechanics and ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.
Journal ArticleDOI
A theory of finite viscoelasticity and numerical aspects
Stefanie Reese,Sanjay Govindjee +1 more
TL;DR: In this article, a nonlinear evolution law for finite deformation viscoelasticity was proposed, which is not restricted to states close to the thermodynamic equilibrium, and upon appropriate linearization, it can recover several established models of finite linear viscoels and linear velocities.
Journal ArticleDOI
Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials
TL;DR: In this paper, the deformation of a micro-structure is coupled with the local deformation at a typical material point of the macro-continuum by three alternative constraints of the microscopic fluctuation field.
Journal ArticleDOI
A micro-macro approach to rubber-like materials—Part I: the non-affine micro-sphere model of rubber elasticity
TL;DR: In this article, a micro-mechanically based network model for the description of the elastic response of rubbery polymers at large strains and details of its numerical implementation are presented.
References
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Book
The finite element method
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Journal ArticleDOI
On numerically accurate finite element solutions in the fully plastic range
TL;DR: In this paper, a general criterion for testing a mesh with topologically similar repeat units is given, and it is shown that only a few conventional element types and arrangements are suitable for computations in the fully plastic range.
Book
Finite Elements of Nonlinear Continua
TL;DR: The Methode des elements finis reference record was created on 2004-09-07, modified on 2016-08-08 as mentioned in this paper, and was used for the reference record.
Journal ArticleDOI
Geometrically non‐linear enhanced strain mixed methods and the method of incompatible modes
Juan C. Simo,Francisco Armero +1 more
TL;DR: In this paper, a class of assumed strain mixed finite element methods for fully nonlinear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case.