A blended approach for evolving phase fields using peridynamics: Cyclic loading in quasi-brittle fracture
A field theory is presented for predicting damage and fracture in quasi brittle materials. It is an expression of Newton's second law for an elastic-plactic continuum. The theory satisfies energy balance, with positive energy dissipation rate in accordance with the laws of thermodynamics. The formulation delivers a mesh free method for predicting crack patterns in quasi-brittle media and simulations show quantitative and qualitative agreement with experiments, including hysteresis and damage associated with three-point bending tests on concrete and size effects for quasi-brittle materials. We conduct numerical experiments exhibiting the competition between plastic yield strength and Griffith strength on fracture nucleation. This work has appeared in the Journal of the Mechanics and Physics of Solids, 216 (2026).