Large-deformation triangular and tetrahedral element formulations for unstructured meshes

摘要

The increasing use of automatic mesh generators and remeshers has spurred the need for accurate and efficient triangular and tetrahedral elements in unstructured meshes. In large-deformation analysis of solids, accuracy and efficiency require the treatment of volumetric locking and element distortions, respectively. In this paper, a mixed formulation is proposed to treat these issues, and applied to triangular and tetrahedral elements. The formulation enforces, in the weak sense, the expression for the volumetric strain in terms of the deformation gradient. The mixed formulation is combined with an irreducible formulation to provide a balance between the treatment of volumetric locking and the maintenance of an adequate critical timestep. Three techniques are proposed to determine such a balance at the local (element) level. Example computations in two and three dimensions of an iron cylinder impacting a rigid surface are used to demonstrate the formulations, and to compare them to the irreducible displacement-based formulation.