General steady creep analysis for various constitutive laws. Part 1: theory and formulation

Abstract

Generalized formulations of the finite element method with penalty multiplier for steady creep problems are proposed as being suitable for various constitutive relations. A simple expression is derived to obtain mean stress by identifying the physical quantity of the penalty multiplier. To solve the nonlinear problem, the Newton-Raphson or modified Newton-Raphson process with steepest descent technique is adopted. The detailed expressions of secant and tangential constitutive matrixes are deduced for Norton, Prandtl, Dorn and Garofalo creep laws. Some advice on numerical implementation is given.