Axisymmetric three‐ and four‐node finite elements for large strain elastoplasticity

Abstract

AbstractWithin the framework of the finite element method an application of the logarithmic strain space formulation of large strain elastoplasticity is illustrated for the examples of axisymmetric three‐node triangular and four‐node quadrilateral finite elements. The formulation of the large strain elastoplasticity is based on a strain space formulation in conjunction with logarithmic (or Hencky) strain tensors with respect to the reference configuration. It is therefore—from a material point of view—a full Lagrangian formulation. The use of logarithmic strains enables an additive split of finite dilatation and distortion, which are given by the logarithmic strain trace and deviator. As a consequence of the strain space formulation no stress tensors are involved in order to describe the plasticity. The stress which is work‐conjugate to the logarithmic strain follows from the stress‐strain relations and may be transformed to Cauchy stress. The desired finite element matrices are derived via the principle of virtual work applied to the Cauchy stress distribution of the current configuration. It should be noted that our considerations are not restricted to axisymmetry and that they remain valid for isoparametric, position‐ (displacement‐) based finite elements in general.