%0 Journal Article
%T A potential-of-mean-force approach for fracture mechanics of heterogeneous materials using the lattice element method
%+ Department of Civil and Environmental Engineering [Cambridge] (CEE)
%+ Physique et Mécanique des Milieux Divisés (PMMD)
%+ Multiscale Material Science for Energy and Environment (MSE 2)
%+ Centre Interdisciplinaire de Nanoscience de Marseille (CINaM)
%A Laubie, Hadrien
%A Radjai, Farhang
%A Pellenq, Roland
%A Ulm, Franz-Josef
%< avec comité de lecture
%@ 0022-5096
%J Journal of the Mechanics and Physics of Solids
%I Elsevier
%V 105
%P 116 - 130
%8 2017-08
%D 2017
%R 10.1016/j.jmps.2017.05.006
%K Inhomogeneous material
%K Elastic material
%K Crack branching and bifurcation
%K Crack propagation and arrest
%K Fracture mechanisms
%K Fracture toughness
%Z Physics [physics]
%Z Physics [physics]/Mechanics [physics]Journal articles
%X 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.
%G English
%2 https://hal.science/hal-01720479/document
%2 https://hal.science/hal-01720479/file/Art_Radjai_al_JMPS_2_2017.pdf
%L hal-01720479
%U https://hal.science/hal-01720479
%~ CNRS
%~ UNIV-AMU
%~ LMGC
%~ CINAM
%~ MIPS
%~ UNIV-MONTPELLIER
%~ AMIDEX
%~ ANR
%~ UM-2015-2021