A path-following method for elasto-plastic solids and structures based on control of plastic dissipation and plastic work

A path-following method that is based on controlling plastic dissipation or plastic work in an inelastic solid or structure is presented. It can be effective for highly nonlinear materially and geometrically problems. In particular, it can be applied for elasto-plastic problems where the standard arc-length methods fail, or to avoid artificial and undesirable elastic unloading of a complete solid or structure during the computation. The essential ingredients, the plastic dissipation and the plastic work based constraint equations, are derived by using either explicit or implicit pseudo-time step integration. These constraint equations are valid for geometrically nonlinear small strain elasto-plasticity with hardening. Their implementation in the framework of the path-following method is described. Several numerical examples are presented in order to illustrate very satisfying performance of the derived path-following method. It performed very well for some challenging shell problems.