Moving least-squares in finite strain analysis with tetrahedra support

A finite strain finite element (FE)-based approach to element-free Galerkin (EFG) discretization is introduced, based on a number of simplifications and specialized techniques in the context of a Lagrangian kernel. In terms of discretization, a quadratic polynomial basis is used, support is determined from the number of preassigned nodes for each quadrature point and quadrature points coincide with the centroids of tetrahedra. Diffuse derivatives are adopted, which allow for the use of convenient non-differentiable weight functions which approximate the Dirac-Delta distribution. Due to the use of a Lagrangian kernel, recent finite strain elasto-plastic constitutive developments based on the Mandel stress are adopted in a direct form. These recent developments are especially convenient from the implementation perspective, as EFG formulations for finite strain plasticity have been limited by the previous requirement of updating the kernel. We also note that, although tetrahedra are only adopted for integration in the undeformed configuration, mesh deformation is of no consequence for the results. Four 3D benchmark tests are successfully solved.

Automated summary

This paper introduces a finite element-based approach to element-free Galerkin discretization for finite strain, which uses simplifications and specialized techniques based on a Lagrangian kernel. A quadratic polynomial basis is used for discretization, and support is determined based on the number of preassigned nodes for each quadrature point. Quadrature points coincide with the centroids of tetrahedra. The use of a Lagrangian kernel allows for the adoption of recent developments in finite strain elasto-plastic constitutive modeling. Four 3D benchmark tests were successfully solved.