The ‘effective‐stress‐function’ algorithm for thermo‐elasto‐plasticity and creep

An algorithm for stable and accurate computations of stresses in finite element thermo-elastic-plastic and creep analysis of metals is presented. The effective-stress-function algorithm solves the governing equations of the inelastic constitutive behaviour by calculating the zero of the appropriate effective-stress-function: a functional relationship which involves as unknown only the effective stress. The derivation of the effective-stress-function for thermo-elasto-plasticity conditions, including creep, for 2-D and 3-D analysis is presented, and the algorithmic steps of the stress solution are discussed. For use in the stiffness matrix a tangent material stress-strain relationship is evaluated consistent with the effective-stress-function algorithm. The solution of some demonstrative problems shows the effectiveness of the solution procedure.