Finite element analysis of diffuse instability using an implicitly integrated pressure–density dependent elastoplastic model

A very important characteristic of geomaterials is that they display a rich variety of failure modes arising from the instability of otherwise uniform states. This so-called material instability results from the interaction of particles with their neighbours at the microscale and has its origins in the strong dependence of material behaviour on stress, density and plastic strain softening. Thus, the proper understanding of material behaviour is essential to the formulation of realistic constitutive models and to the capturing of various failure patterns and instabilities in geomaterials. The main objective of this paper is to study diffuse instability in geomaterials using Hill's second-order work criterion within the finite element setting. A novel constitutive model that incorporates pressure and density dependencies is briefly presented and an implicit Euler backward return-mapping algorithm is formulated for the stress integration of the model. We use the spectral decomposition of the stress tensor so as to reduce the problem dimensions by working in the principal stress space, and as such increase the efficiency of numerical simulation. The hypoelastic behaviour of the model is accounted for via a secant bulk modulus. At the end, to confirm the algorithm performance at the boundary-value problem scale, we simulate a conventional triaxial compression test on a cylindrical sand specimen with a heterogeneous density field. Our analyses revealed that diffuse instability was properly captured in our FE-based simulations through Hill's criterion.