A Stable Formulation for Wave‐Induced Fracture in Peridynamics

Abstract

The bond‐associated quadrature point formulation is a very accurate peridynamic formulation for elasticity, but modeling fracture by the traditional deletion of bonds can trigger severe numerical instabilities. These instabilities are most pronounced for wave‐induced fracture, where stress waves continue to propagate through already damaged material. This contribution applies the recently introduced phase‐field peridynamics framework to overcome this limitation. Because the energetic contribution of each bond is degraded continuously through a bond phase‐field parameter instead of deleting bonds, the formulation stays stable under fracture, while a separate kinematic degradation enables fragmentation and localized cracks. The framework is demonstrated on the wave‐induced fracture of a curved bar, where the bond‐associated formulation with bond deletion becomes unstable while the phase‐field peridynamics formulation remains robust and reproduces a classical phase‐field reference solution.