Finite Strain Analysis With the Dual Mesh Control Domain Method

Abstract

The Dual Mesh Control Domain Method (DMCDM), developed by Reddy (J.N. Reddy. “A dual mesh finite domain method for the numerical solution of differential equations.” Int J Comput Methods Eng Sci, 20(3):212–228, 2019), is an alternative to the classical weak-form Galerkin finite element method. An advantage of DMCDM is that it combines the interpolation capabilities of the finite element method with the direct use of an integral form of the balance laws. Furthermore, it is easily extensible to mixed formulations, resulting in simpler than traditional finite element formulations. In this work, we extend DMCDM to the fully finite strain case with plasticity. We introduce a new discretization algorithm for finite strain problems, which includes a mean-dilatation technique to solve the volumetric locking problem. Assessment is supported by five linear and five finite strain benchmark problems, one of them being 3D. Finite strain solutions were found to be stable, exempt from hourglassing, and also locking-free. Results are found to be competitive with classical F-bar and B-bar elements, with a simpler formulation.