Alternative stress-integration schemes for large-deformation problems of solid mechanics

In solving nonlinear problems of solid mechanics by the finite-element method, stresses at integration points are usually obtained by integrating nonlinear constitutive equations, given known incremental strains. In a large-deformation analysis, stress–strain relationships must be frame independent such that any rigid-body motion does not induce strain within the material. This principle is generally satisfied by introducing an objective stress rate, such as the Jaumann or Truesdell stress rates, into the constitutive equations. This paper investigates three alternative algorithms for integrating stress–strain relationships in a large-deformation analysis. It is shown that the effect of rigid-body motion is equivalent to a stress transformation and this transformation can be introduced before, after or during integration of the stress–strain constitutive equations. Although there is no theoretical advantage, in terms of accuracy, for selecting one of these strategies over the others, in terms of efficiency of algorithms one is more advantageous than the others. Performance of the proposed algorithms is studied and compared by means of numerical examples. The results of this study can be used in the development of fast and robust algorithms for stress integration of constitutive equations in nonlinear finite-element analysis.