Nonlocal strain regularisation for critical state models with volumetric hardening

Abstract

The finite element (FE) method may suffer from numerical instability and mesh dependency when modelling the formation of shear bands using strain-softening constitutive models. Nonlocal methods have been shown to be capable of avoiding these numerical issues effectively. This paper proposes a novel generic algorithm for incorporating existing nonlocal methods into the FE formulation of elasto-plastic constitutive models with volumetric hardening laws. Using the example of the modified Cam Clay (MCC) model this paper shows that instabilities are inevitable if the nonlocal plastic volumetric strains are directly used to update the hardening parameter. The paper further proposes a robust regularisation algorithm to overcome this issue. This algorithm has been implemented into a bespoke FE code and its capability in significantly reducing mesh dependency while maintaining numerical stability is verified through a series of numerical analyses of biaxial compression tests for highly overconsolidated clays. The performance of various existing nonlocal methods is also critically assessed.