Integration of hyperplastic models in strain space

This paper presents a simple and flexible integration scheme designed to capture the elastic–plastic behaviour of materials directly from a free energy function, a dissipation function and kinematic constraints, typically formulated in strain space. As such, it eliminates the need to establish expressions for yield functions and/or plastic flow potentials. This is beneficial as analytical transformation of complex dissipation functions, particularly when combined with realistic kinematic constraints, often involves mathematical complexities. However, such a transformation is unnecessary as all essential information is already embedded within the various elements of the framework, that is the free energy potential, dissipation function and kinematic constraint expressions. Moreover, the scheme can be utilised to numerically visualise yield surfaces. The method is successfully applied to a family of sand and clay models featuring different dissipation functions, kinematic constraints (dilatancy rules) and friction mobilisation. These applications include showcasing models that lack analytical transformation, as well as models where analytical transformation to the yield and potential surfaces is possible, allowing for comparison. Through numerical simulation of several drained and undrained element tests, and the generation of yield surfaces, the efficacy of the proposed integration scheme is demonstrated. Furthermore, the proposed scheme is used to implement the Matsuoka–Nakai model in a finite-element programme to demonstrate its applicability to boundary value problems.