A two-dimensional linear assumed strain triangular element for finite deformations analysis

FLORES FERNANDO G.

JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME

ASME

Año: 2005 vol. 73 p. 970 - 976

0021-8936

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then non-conforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. An hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong non-linearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.