Solution of the elastic/visco-plastic constitutive equations: A finite volume approach

A novel two dimensional finite volume (FV) approach to the solution of elastic / visco-plastic solid mechanics problems is described. The numerical procedure is an extension of that developed by Fryer et al. for linear elastic materials and utilizes an unstructured mesh. The procedure is compared favorably with conventional finite element (FE) formulations with respect to both accuracy and CPU time. A number of test problems demonstrate the ability of the FV procedure to model a range of boundary constraints, in addition to mechanical and thermal loads. It might be argued from the work reported here that the FV approach shows the potential to be at least as effective as conventional FE formulations in representing nonlinear solid mechanics behavior.