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A potential-of-mean-force approach for fracture mechanics of heterogeneous materials using the lattice element method

TitleA potential-of-mean-force approach for fracture mechanics of heterogeneous materials using the lattice element method
Publication TypeJournal Article
Year of Publication2017
AuthorsLaubie H, Radjaï F, Pellenq RJean-Marc, Ulm F-J
JournalJournal of the Mechanics and Physics of Solids
Volume105
Pagination116 - 130
Date PublishedAug-2017
ISSN00225096
Abstract

Fracture of heterogeneous materials has emerged as a critical issue in many engineering applications, ranging from subsurface energy to biomedical applications, and requires a rational framework that allows linking local fracture processes with global fracture descriptors such as the energy release rate, fracture energy and fracture toughness. This is achieved here by means of a local and a global potential-of-mean-force (PMF) inspired Lattice Element Method (LEM) approach. In the local approach, fracture-strength criteria derived from the effective interaction potentials between mass points are shown to exhibit a scaling commensurable with the energy dissipation of fracture processes. In the global PMF-approach, fracture is considered as a sequence of equilibrium states associated with minimum potential energy states analogous to Griffith’s approach. It is found that this global approach has much in common with a Grand Canonical Monte Carlo (GCMC) approach, in which mass points are randomly removed following a maximum dissipation criterion until the energy release rate reaches the fracture energy. The duality of the two approaches is illustrated through the application of the PMF-inspired LEM for fracture propagation in a homogeneous linear elastic solid using different means of evaluating the energy release rate. Finally, by application of the method to a textbook example of fracture propagation in a heterogeneous material, it is shown that the proposed PMF-inspired LEM approach captures some well-known toughening mechanisms related to fracture energy contrast, elasticity contrast and crack deflection in the considered two-phase layered composite material.

DOI10.1016/j.jmps.2017.05.006
Short TitleJournal of the Mechanics and Physics of Solids
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