Uniform asymptotic approximations for accurate modeling of cracks in layered elastic media*

By Anthony Peirce, E. Siebrits. 2001

50 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f8da90c0695ac823625bd9d809ec54b58c9aa15d

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In Atomic and Molecular Physics, and Optics

In Mathematical Physics

In Mechanics of Materials

Citations in the corpus

Computer simulation of hydraulic fractures (2007, background): “If boundary integral schemes are employed, the 3D layered reservoir is assumed to be linear elastic, and the discretized equations (in the case of a PL3D model) can be rigorously reduced to a planar system of elements covering the fracture footprint [59,60].”
An implicit level set method for modeling hydraulically driven fractures (2008, methodology): “The assumption that E and m are homogeneous is not trivial to relax (see for example [30–32]), however we do assume a rectangular Eulerian grid on which an efficient multilayer algorithm can be implemented without revising the algorithm presented in this paper.”
Modeling multi-scale processes in hydraulic fracture propagation using the implicit level set algorithm (2015, methodology): “The assumption that E and ν are homogeneous is not trivial to relax (see for example [29, 30, 37]), however we do assume a rectangular Eulerian grid on which an efficient multi-layer algorithm can be implemented without revising the algorithm presented in this paper by merely replacing the Green’s f”
Implicit level set schemes for modeling hydraulic fractures using the XFEM (2013, methodology): “to a uniform pressure p1 within material I with E1 1⁄4 10 7 psi, m1 1⁄4 0:3, and a uniform [31] (black diamonds), [32] (solid black lines with triangles), and XFEM-s (solid blue r X 0 and n 1⁄4 X=b2 for X > 0.”
Enrichment strategies and convergence properties of the XFEM for hydraulic fracture problems (2015, background): “For the latter host rock, a boundary integral formulation of the elasticity problem is the most efficient numerical scheme, which has enjoyed considerable development [18–25].”
Analysis of the classical pseudo-3D model for hydraulic fracture with equilibrium height growth across stress barriers (2010, methodology): “A semi-analytic approach to this problem [15, 16, 36] involves the use of the Fourier transform to convert the elastic equilibrium partial differential equations to a system of ordinary differential equations, which can be solved analytically in each layer.”