Peridynamics-based simulation of viscoelastic solids and granular materials

Abstract

Viscoelastic solids and granular materials have been extensively studied in Classical Continuum Mechanics (CCM). However, CCM faces inherent limitations when dealing with discontinuity problems. Peridynamics, as a non-local continuum theory, provides a novel approach for simulating complex material behavior. We propose a unified viscoelasto-plastic simulation framework based on State-Based Peridynamics (SBPD) which derives a time-dependent unified force density expression through the introduction of the Prony model. Within SBPD, we integrate various yield criteria and mapping strategies to support granular flow simulation, and dynamically adjust material stiffness according to local density. Additionally, we construct a multi-material coupling system incorporating viscoelastic materials, granular flows, and rigid bodies, enhancing computational stability while expanding the diversity of simulation scenarios. Experiments show that our method can effectively simulate relaxation, creep, and hysteresis behaviors of viscoelastic solids, as well as flow and accumulation phenomena of granular materials, all of which are very challenging to simulate with earlier methods. Furthermore, our method allows flexible parameter adjustment to meet various simulation requirements.