Peridynamics for Quasistatic Fracture Modeling

TL;DR

This paper introduces a fast, mathematically rigorous peridynamics-based method for modeling quasistatic fracture, capturing stable and unstable crack growth in brittle materials across different loading conditions.

Contribution

It develops a new numerical approach using fixed point theory and analytic stiffness matrices for efficient, stable simulation of quasistatic fracture in continuum mechanics.

Findings

The method accurately models stable crack growth under hard loading.

It predicts crack instability after reaching material strength under soft loading.

Mathematical analysis confirms convergence for various load paths.

Abstract

Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the perspective of mechanics fracture should appear as an emergent phenomena generated by a continuum field theory eliminating the need for a supplemental kinetic relation describing crack growth. We develop a new fast method for modeling quasi-static fracture using peridynamics. We apply fixed point theory and model stable crack evolution for hard and soft loading. For soft loading we recover unstable fracture. For hard loading we recover stable crack growth. We show existence of quasistatic fracture solutions in the neighborhood of stable critical points for appropriately defined energies. The numerical method uses an analytic stiffness matrix for fast numerical implementation. A rigorous mathematical analysis shows that the method converges for load paths associated with soft and hard loading. For soft loading the crack becomes unstable shortly after the stress at the tip of the pre-crack reaches the material strength.