Critical softening in Cam-Clay plasticity: adaptive viscous regularization, dilated time and numerical integration across stress-strain jump discontinuities

Within the framework of continuum mechanics, the mechanical behaviour of geomaterials is often described through rate-independent elastoplasticity. In this field, the Cam-Clay models are considered as the paradigmatic example of hardening plasticity models exhibiting pressure dependence and dilation-related hardening/softening. Depending on the amount of softening exhibited by the material, the equations governing the elastoplastic evolution problem may become ill-posed, leading to either no solutions or two solution branches (critical and sub-critical softening). Recently, a method was proposed to handle subcritical softening in Cam-Clay plasticity through an adaptive viscoplastic regularization for the equations of the rate-independent evolution problem. In this work, an algorithm for the numerical integration of the Cam-Clay model with adaptive viscoplastic regularization is presented, allowing the numerical treatment of stress-strain jumps in the constitutive response of the material. The algorithm belongs to the class of implicit return mapping schemes, slightly rearranged to take into account the rate-dependent nature of inelastic deformations. Applications of the algorithm to standard axisymmetric compression tests are discussed.