Analysis of a model of field crack mechanics for brittle materials

Léo Morin,Amit Acharya

doi:10.1016/j.cma.2021.114061

Abstract

A computational model for arbitrary brittle crack propagation, in a fault-like layer within a 3-d elastic domain, and its associated quasi-static and dynamic fields is developed and analyzed. It uses a FFT-based solver for the balance of linear momentum and a Godunov-type projection-evolution method for the crack evolution equation. As applications, we explore the questions of equilibria and irreversibility for crack propagation with and without surface energy, existence of strength and toughness criteria, crack propagation under quasi-static and dynamic conditions, including Modes I, II and III, as well as multiaxial compressive loadings.

Highlights

This paper develops a computational strategy and uses it to critically evaluate the capabilities of a recently proposed continuum mechanical model of fracture that we shall refer to as Field Crack Mechanics (FCM) [1,2], restricted here to brittle bulk response and to evolution of arbitrary crack patterns in a fixed plane
Our computational strategy adapts the prior work of Morin et al [23] for the computation of the Field Dislocation Mechanics (FDM) model of plasticity to FCM, with extension to the entire range of crack evolution under quasi-static to dynamic balance of forces
We have developed and demonstrated a pde-based tool for the modeling and analysis of brittle fracture, restricted here to crack propagation in a single fault layer

Summary

Introduction

This paper develops a computational strategy and uses it to critically evaluate the capabilities of a recently proposed continuum mechanical model of fracture that we shall refer to as Field Crack Mechanics (FCM) [1,2], restricted here to brittle bulk response and to evolution of arbitrary crack patterns in a fixed plane. [18,19,20]); of note is the work of Smyshlyaev and Willis [21] on accounting for crack-face contact constrains in dynamic fracture, and the extension of the variational approach to fracture to elastodynamics [22]. Our computational strategy adapts the prior work of Morin et al [23] for the computation of the Field Dislocation Mechanics (FDM) model of plasticity to FCM, with extension to the entire range of crack evolution under quasi-static to dynamic balance of forces.

Objectives

Methods

Conclusion