Frame indifferent elastoplasticity of frictional materials at finite strain

Abstract

This paper puts forward a finite strain formulation based on the (i) thermodynamics of non-associated materials, (ii) logarithmic strain measures and corotational rates, and (iii) numerical procedures of gradient split and return mapping. Unlike most of the existing finite strain formulations which use classical strain measures and objective corotational rates, the current approach emphasises the logarithmic objective description as an alternative. This formulation overcomes the aberrant oscillations or hyperbolic responses which appear in shear zones when classical spins are used. The model combines this kinematic description with recent developments which extended the classical thermodynamics of generalized standard materials to non-associated materials. This thermodynamic framework allows deducing the constitutive relationships, yielding limits and flow rules directly from the energy functions instead of introducing them on ad hoc basis as commonly accepted in the classic theories of soil and rock mechanics.