Ordinary state-based peridynamic plastic model with Drucker-Prager criterion considering geometric nonlinearity

Abstract

In this paper, an ordinary state-based peridynamic (OSB-PD) plastic model is proposed to simulate the large deformation of geomaterials. The PD dilatation, which is equivalent to the volumetric strain in terms of the logarithmic strain in classical continuum mechanics (CCM), is proposed. The PD material parameters are obtained by equaling the assumed PD energy density to the energy density in terms of the Kirchhoff stress and logarithmic strain in CCM. The PD force, which is obtained by calculating the Frechet derivative of PD energy density, is naturally collinear with the deformed bond. The OSB-PD plastic model with the Drucker-Prager criterion considering geometric nonlinearity is subsequently established. Benchmark problems including the plate under large deformation and the l-shaped panel test are simulated, which has verified the proposed model.