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.

► We focus on time instabilities in Cam-Clay plasticity related to critical softening.
► An adaptive viscoplastic regularization is adopted.
► The solution exists and is unique in the whole space of admissible stress states.
► We propose an algorithm for the integration of the regularized viscoplastic equations.
► The performance of the algorithm is evaluated by means of single-element tests.