An Improved Peridynamic Framework to Eliminate Unphysical Stress and Fictitious Yield at Geometry Surface for Geomaterials’ Elastoplastic Deformation and Fracture Analysis

Abstract

This paper presents an improved non-ordinary state-based peridynamics (NOSB-PD) framework for modelling the elastoplastic behaviour and damage of geomaterials, such as soil, rock, and concrete, under quasi-static conditions. Conventional NOSB-PD for elastoplastic materials faces two primary challenges: the surface effect due to the low accuracy of the approximate deformation gradient (FPD) near boundaries and fictitious yielding during explicit time integration. These issues can lead to numerical errors, such as inaccurate crack predictions and potential simulation failure. The proposed framework thoroughly analyses the reason for the surface effect by demonstrating that FPD exhibits only first-order accuracy within a horizon radius (δ) from the surface but introduces residual stresses within a larger range of 2δ with significant surface effect. To mitigate this, a divergence formulation of the non-local differential operator (NDO) is applied to enforce a reasonable stress gradient within a 2δ subregion, alongside a traction boundary condition consistent with the divergence of stress. Additionally, a “loading-balance-correction” algorithm is introduced to enhance the conventional explicit time integration process. The model is validated by integrating it with a modified hyperbolic-hardening Drucker-Prager model, where the stress integration is performed using the closest point projection method (CMMP). Numerical results, compared with finite element simulations and experimental data, demonstrate the effective elimination of the surface effect and false yielding, providing a robust simulation of elastoplastic deformation and progressive failure in geomaterials.

Keywords: Improved peridynamics model, Surface effect, Fictitious yield, Progressive failure, Elastoplastic deformation