An Assumed strain triangular element for finite deformations analysis in two-dimensions

Abstract

In this paper a linear assumed strain approach for a triangular elementable to handle finite deformations problems is presented. The element geometry is defined by three nodes with two degrees of freedom per node only. The element is based on a total Lagrangian formulation. The strains are computed from the rigth Cauchy Green tensor interpolated linearly from values obtained at the middle of the element sides. In this approach the gradient at each side of the triangle is evaluated resorting to the geometry of the adjacent element. Then a non-conforming approach over a four element patch is defined, nevertheless the element pass the patch test.To deal with plasticity at finite deformations an additive decomposition of elastic and plastic strains is adopted, in terms of the logarithmic stress-strain pair. For the elastic part a linear stress-strain relation (an hyper-elastic model) is considered while an anisotropic quadratic yield function (Hill) for the plastic part is used. Two finite element codes have been used to test the element: an implicit static/dynamic program for moderately non-linear problems and a explicit dynamic code for problems with strong non-linearities. Several examples are shown to assess the behaviour of present element in linear plane stress states and non-linear plane strain and axil-symmetric problems.