Numerically explicit potentials for the homogenization of nonlinear elastic heterogeneous materials

By Julien Yvonnet, David González, Qi-Chang He. 2009

146 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6abbcc660778753af891bacb8e68d44dfcd86d55

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In Mechanics of Materials

Citations in the corpus

MULTISCALE CONTINUOUS AND DISCONTINUOUS MODELING OF HETEROGENEOUS MATERIALS: A REVIEW ON RECENT DEVELOPMENTS (2011, background): “Yvonnet et al.161 presented such a model for nonlinear elastic heterogeneous materials.”
Routes for Efficient Computational Homogenization of Nonlinear Materials Using the Proper Generalized Decompositions (2010, methodology): “[40, 41, 43] for the case of nonlinear elasticity).”
Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review (2016, background): “Xia and Breitkopf [148] have further integrated a reduced database model namely Numerically EXplicit Potentials (NEXP, [74, 181, 182]) to the simultaneous design framework.”
Deep learning predicts path-dependent plasticity (2019, unknown): “This has been achieved for nonlinear elastic constitutive laws where data are created by ﬁnite element analysis (FEA) of representative volume elements (RVEs) (18, 19) and, more recently, to determine property maps obtained from plasticity and fracture simulations of RVEs (19).”
A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality (2017, methodology): “The overwhelming majority of the design examples reported in the literature [11,15,19,20,93,94] fall in this category where reduced order models are not needed since the simulations to obtain data are computationally inexpensive.”
Multiscale structural topology optimization with an approximate constitutive model for local material microstructure (2015, unknown): “In our successive work [7], we made a step further and adapt the Numerically EXplicit Potentials (NEXP) model [8] to represent this new regime of nonlinearity due to material optimization.”
Computational homogenization of nonlinear elastic materials using neural networks (2015, methodology): “…and the components of the tangent matrix required to perform the nonlinear structure problem are evaluated similarly by Several interpolation schemes have been proposed in our previous works [15, 16] such as multidimensional spline functions or techniques based on variables separation techniques.”
Computational homogenization in magneto-mechanics (2013, background): “…studied extensively (Suquet, 1987; Guedes and Kikuchi, 1990; Terada and Kikuchi, 1995; Ponte Castañeda, 1996; Smit et al., 1998; Michel et al., 1999; Feyel and Chaboche, 2000; Terada and Kikuchi, 2001; Miehe, 2002; Aboudi et al., 2003; Asada and Ohno, 2007; Yvonnet et al., 2009, among many others).”