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

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Abstract
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.

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