Gradient Plasticity Modeling of Geomaterials in a Meshfree Environment

Deformation and strength behavior of geomaterials in the preand post-failure regimes are of significant interest in various geomechanics applications. To address the need for development of a realistic constitutive framework, which allows for an accurate simulation of pre-failure response as well as an objective and meaningful post-failure response, a strain gradient plasticity model is formulated by incorporating the gradients of volumetric and deviatoric plastic strains on the evolution of damage in geomaterials. The resulting constitutive equations along with the balance of linear momentum for the continuum are cast into a coupled system of equations, with displacements and plastic multiplier appearing as the primary unknowns in the final governing integral equations. A finite element discretization of the governing equations requires the use of C-1 continuous elements, which are undesirable from an implementation point of view. This issue is naturally resolved when a meshfree discretization is used. Hence the developed model is formulated within the framework of a meshfree environment. The new constitutive model allows a thorough analysis of grain size effects on strength and dilatancy of rocks. The role and effectiveness of the new gradient terms on regularizing the underlying boundary value problems of geomechanics beyond the initiation of strain localization can also be assessed.