Elasto-Plastic Analysis Using a Stress-Based Finite Element Method and an Endochronic Theory of Plasticity

Abstract

A stress-based finite element methodology that uses the endochronic theory to model elasto-plastic structural behavior is presented. xhe methodology is implemented through a “tangent” stiffness formulation using a discretization of four-fields consisting of: 1) stress, 2) displacement, 3) magnitude of plastic strain, and 4) hydrostatic stress. The four-field approach allows elastically incompressible materials and materials that become incompressible due to plastic flow to be modeled. The stress-based element has been demonstrated to give more accurate solutions for displacements and stresses than conventional displacement models [1]. The more accurate stress solution obtained with stress-based formulations allow fewer elements to be used. In addition, the more accurate stress solution combined with a reduced number of elements usually leads to faster convergence rates. The magnitude of plastic strain is included as an unknown variable to treat the case of perfect or near perfect plasticity. The hydrostatic stress is retained as a global field variable to ensure that the incompressibi1ity constraint associated with fully plastic flows or with elastically incompressible materials does not “lock” the element.