A triangular finite element with local remeshing for the large strain analysis of axisymmetric solids

Abstract

In this work a three-node triangular finite element with two degrees of freedom per node for the large strain elasto-plastic analysis of axisymmetric solids is presented. The formulation resorts to the adjacent elements to obtain a quadratic interpolation of the geometry over a patch of four elements from which an average deformation gradient is defined. Thus the element formulation falls within the framework of assumed strain elements or more precisely of F-bar type formulations. The in-plane behavior of the element is similar to the linear strain triangle, but without the drawbacks of the quadratic triangle, e.g. contact or distortion sensitivity. The element does not suffer of volumetric locking in problems with isochoric plastic flow and the implementation is simple. It has been implemented in a finite element code with explicit time integration of the momentum equations and tools that allow the simulation of industrial processes. The widely accepted multiplicative decomposition of the deformation gradient in elastic and plastic components is adopted here. An isotropic material with non-linear isotropic hardening has been considered. Two versions of the element have been implemented based on a Total and an Updated Lagrangian Formulation respectively. Some approximations have been considered in the latter formulation aimed to reduce the number of operations in order to increase numerical efficiency. To consider bulk forming, with large geometric changes, an automatic local remeshing strategy has been developed. Several examples are considered to assess the element performance with and without remeshing.