Numerical Techniques for the Finite Element Analysis of Elastic and Inelastic Material Nonlinearities

Summary

The objective of the paper is to unify nonlinear elastic and inelastic computations within the framework of the finite element method. Essentially two aspects are considered, (i) the step-by-step integration of the inelastic rate equations, and (ii) the solution of the underlying algebraic problem within each time step. In the first area stability and accuracy are of prime concern for the integration of the inelastic evolution laws with explicit or implicit time operators. In the second field direct forward approaches are contrasted with iterative strategies using both initial load and tangential gradient methods for advancing the solution within a given time interval. The overall computational schemes are illustrated at the viscoplastic example of a thick-walled cylinder subjected to internal pressure.