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   Statistical extraction of process zones and representative subspaces in fracture of random composites; ; et al in International Journal for Multiscale Computational Engineering (2013), 11(3), 253-287 We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly ... [more ▼] We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on precomputed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localized phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced-order model. © 2013 by Begell House, Inc. [less ▲] Detailed reference viewed: 423 (11 UL)Molecular dynamics/xfem coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture; ; Bordas, Stéphane  et alin International Journal for Multiscale Computational Engineering (2013), 11(6), 527-541 We propose a method to couple a three-dimensional continuum domain to a molecular dynamics domain to simulate propagating cracks in dynamics. The continuum domain is treated by an extended finite element ... [more ▼] We propose a method to couple a three-dimensional continuum domain to a molecular dynamics domain to simulate propagating cracks in dynamics. The continuum domain is treated by an extended finite element method to handle the discontinuities. The coupling is based on the bridging domain method, which blends the continuum and atomistic energies. The Lennard-Jones potential is used to model the interactions in the atomistic domain, and the Cauchy-Born rule is used to compute the material behavior in the continuum domain. To our knowledge, it is the first time that a three dimensional extended bridging domain method is reported. To show the suitability of the proposed method, a threedimensional crack problem with an atomistic region around the crack front is solved. The results show that the method is capable of handling crack propagation and dislocation nucleation. © 2013 by Begell House, Inc. [less ▲] Detailed reference viewed: 187 (0 UL) |
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