@article {242,
	title = {A potential-of-mean-force approach for fracture mechanics of heterogeneous materials using the lattice element method},
	journal = {Journal of the Mechanics and Physics of Solids},
	volume = {105},
	year = {2017},
	month = {Aug-2017},
	pages = {116 - 130},
	abstract = {<p>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\&rsquo;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.</p>
},
	issn = {00225096},
	doi = {10.1016/j.jmps.2017.05.006},
	author = {Hadrien Laubie and Farhang Radja{\"\i} and Roland Jean-Marc Pellenq and Franz-Josef Ulm}
}
@article {327,
	title = {Plane-Strain Crack Problem in Transversely Isotropic Solids for Hydraulic Fracturing Applications},
	journal = {Journal of Engineering Mechanics},
	volume = {140},
	year = {2014},
	month = {Dec-2014},
	pages = {Article Number: 04014092 },
	abstract = {<p>This paper aims at understanding and predicting how pressurized cracks propagate in anisotropic brittle solids, a situation frequently encountered in hydraulic fracturing. Special attention is paid to transverse isotropy, often used to model shale. Although the theory of linear elastic fracture mechanics of anisotropic solids is well established at present, this paper shows that the application of Muskhelishvili\&rsquo;s formalism to Lekhnitskii\&rsquo;s anisotropic complex potentials provides a powerful tool to extend the validity of the classical tools of isotropic fluid-driven crack models to the anisotropic case, provided that the appropriate elastic constants are used. These elastic constants are identified and derived in closed form for transversely isotropic solids. The constants are shown to be directly related to quantities easily measured in a laboratory at macroscopic scale through indentation tests and acoustic measurements. Moreover, several crack-kinking criteria are compared. Contrary to the isotropic case, the crack-kinking criteria are not consistent among themselves, even in the case of a pure pressure loading. The orientation at which it is easier to propagate an already existing crack is sought. A critical crack length, below which this crack orientation is the one of minimal stiffness felt by the crack, is identified.</p>
},
	issn = {0733-9399},
	doi = {10.1061/(ASCE)EM.1943-7889.0000807},
	author = {Hadrien Laubie and Franz-Josef Ulm}
}
