Crossed patch arrangements of linear triangular elements for upper bound finite-element analysis of plane strain deformation problems

In standard linear finite-element formulations, volumetric locking because of the incompressibility constraint that may occur in computational plasticity is often encountered. This study uses crossed patch arrangements of triangles to form quadrilateral elements in order to overcome the locking in the upper bound finite-element analysis of plane strain deformation problems. The velocity field is described in terms of linear triangular elements, while the incompressibility constraint is imposed by quadrilateral elements. Rigid, perfectly plastic materials, and strain hardening materials that form the von Mises model have been considered. The velocity formulation is presented and has been implemented in a finite-element code. Several examples, some benchmarks problems, are presented to illustrate the applicability of the approach for predicting the load, strain, and velocity field during the plastic deformation. Numerical results show that the crossed patch arrangements of linear triangular elements are free of volumetric locking and achieve well-defined limit loads. This study shows that the presented method can be used to simulate large plastic deformation under plane strain conditions.