Aspects of the formulation and finite element implementation of large strain isotropic elasticity
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. Novel 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 behavior of the different finite element formulations for compressible and incompressible elasticity.
- Publication:
-
International Journal for Numerical Methods in Engineering
- Pub Date:
- June 1994
- DOI:
- 10.1002/nme.1620371202
- Bibcode:
- 1994IJNME..37.1981M
- Keywords:
-
- Elastic Properties;
- Finite Element Method;
- Isotropy;
- Mathematical Models;
- Algorithms;
- Compressibility;
- Convergence;
- Eigenvalues;
- Modulus Of Elasticity;
- Tensors;
- Structural Mechanics