Parallel multilevel procedures for elastoplasticity computations in solid mechanics

A multigrid method is described that can solve history dependent, material nonlinear solid mechanics problems using the finite element method. Specifically, an incremental Newton-Raphson procedure is used to linearize the nonlinear equilibrium equations. The multigrid method is then used to solve the linear matrix equations at each Newton-Raphson iteration step. This algorithm uses a relaxation method to quickly eliminate the high frequency components of the error associated with a current approximation to the solution. A hierarchy of coarse meshes are then used to recursively compute this error. A small strain, von Mises elasto-plastic material model with both kinematic and isotropic hardening rules has been implemented. A simple interpolation procedure to determine the state variables for all the coarse meshes in the hierarchy is incorporated.The nonlinear multigrid method is applied to the solution of some two and three dimensional problems of importance in the field of Civil Engineering to examine its effectiveness. Extensive studies on the behavior of the algorithm are presented, and near optimum choices regarding the nonlinear multigrid parameters are proposed. Special emphasis is placed upon the effect of incompressibility on the behavior of the algorithm.The method is also implemented and executed on some shared memory parallel computers, namely a four processor Convex C240 and an eight processor Alliant FX/8. Some results demonstrating the vector and parallel performance of the code are presented.U of I OnlyETDs are only available to UIUC Users without author permissio