Explicit Integration of a Thermodynamics-Based Constitutive Model with Internal Variables

Advanced soil constitutive models are essential for reliable finite element analyses of geotechnical boundary value problems. Over the last two decades, many soil constitutive models have been developed within the paradigm of Thermodynamics with Internal Variables (TIV). Within this theoretical framework, the mechanical behaviour is described by the free energy and the rate of dissipation functions. However, the dependence of the free energy function on the adopted internal variables naturally produces a coupled response between the reversible and dissipative behaviours. This leads to a rather complex elasto-plastic formulation in terms of Cauchy stress, making its numerical integration challenging. This paper presents the integration of a TIV-based Cam-Clay-type constitutive model in the generalised stress space, rather than in the commonly used Cauchy stress space, taking advantage of a more straightforward formulation. Moreover, the implementation of a new driver for the integration in the generalised stress space is provided. The effectiveness of the integration strategy is demonstrated through a series of ideal simulations on the single-element, paving the way to the integration of more complex TIV-based constitutive models.