On the integration of stresses in large deformations plasticity

Abstract

Discusses an alternative formulation for the incremental determination of stresses in strain measures that can be used to replace the stress rates currently employed. The formulation is based on Doyle‐Hill generalized definition of strain, the corresponding conjugate stresses and an isotropic hyperelastic constitutive equation. When used to analyze the simple shear deformation, the proposed formulation avoids the pathologies usually observed (oscillations, pressure build up, path dependence). The origin and importance of these pathologies is then discussed in relation to different materials behavior. It is shown that the incremental procedure used together with the logarithmic definition of strain is the most convenient, but that other approximations may be used in well defined particular situations. The numerical algorithms proposed are detailed in an Appendix.

Citation

Marcon, A.F., Bittencourt, E. and Creus, G.J. (1999), "On the integration of stresses in large deformations plasticity", Engineering Computations, Vol. 16 No. 1, pp. 49-69. https://doi.org/10.1108/02644409910251229