NUMERICAL METHODS FOR MINIMIZERS AND MICROSTRUCTURES IN NONLINEAR ELASTICITY

Numerical Methods for Minimizers and Microstructures in Nonlinear Elasticity

A standard finite element method and a finite element truncation method are applied to solve the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff materials. Finite element solutions are proved to exist and to be in the form of minimizers in appropriate sets of admissible finite element functions for both methods...

Existence of Minimizers and Microstructure in Nonlinear Elasticity

In this paper, the existence of a solution in the form of a minimizer or microstructure is established for the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff type materials. Necessary and sufficient conditions for minimizing sequences of the potential energy to converge to a minimizer or to microstructure are ...

Discontinuous Galerkin methods for nonlinear elasticity

An Efficient Numerical Method for Cavitation in Nonlinear Elasticity

This paper is concerned with the numerical computation of cavitation in nonlinear elasticity. The Crouzeix-Raviart nonconforming finite element method is shown to prevent the degeneration of the mesh provoked by the conventional finite element approximation of this problem. Upon the addition of a suitable stabilizing term to the elastic energy, the method is used to solve cavitation problems in...

The Convergence of Regularized Minimizers for Cavitation Problems in Nonlinear Elasticity

Abstract. Consider a nonlinearly elastic body which occupies the region Ω ⊂ Rm (m = 2, 3) in its reference state and which is held in tension under prescribed boundary displacements on ∂Ω. Let x0 ∈ Ω be any fixed point in the body. It is known from variational arguments that, for sufficiently large boundary displacements, there may exist discontinuous weak solutions of the equilibrium equations...