Gradient‐dependent plasticity: Formulation and algorithmic aspects

Abstract

Abstract A plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure (hardening parameter), but also on the Laplacian thereof. The consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity. To properly solve the set of non‐linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements. For appropriate boundary conditions this formulation can also be derived from a variational principle. Accordingly, the theory is complete. The addition of gradient terms becomes significant when modelling strain‐softening solids. Classical models then result in loss of ellipticity of the governing set of partial differential equations. The addition of the gradient terms preserves ellipticity after the strain‐softening regime has been entered. As a result, pathological mesh dependence as obtained in finite element computations with conventional continuum models is no longer encountered. This is demonstrated by some numerical simulations.