Computational homogenization analysis in finite elasticity: material and structural instabilities on the micro- and macro-scales of periodic composites and their interaction

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Multiscale aggregating discontinuities: A method for circumventing loss of material stability (2008, unknown): “[19] in an interesting study, developed”
Multiscale cohesive failure modeling of heterogeneous adhesives (2008, background): “…the microscale fluctuation displacements d1u are independent, we arrive at the variational energy condition (see, for example, references Hill, 1985; Miehe et al., 2002), Rb0ue ¼ N 1 jYj Z Y sdY t bd0ue ¼ 0, R1u ¼ 1 jYj Z Y s:rsYd 1u dY ¼ 0 ð17Þ and d1u 2 ½H1ðYÞ N; d1ujqYG c ¼ 0; d1u ¼ periodic…”
Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models (2016, methodology): “The use of RVE-based theories in situations of practical interest relies almost exclusively on techniques of computational homogenization, based on finite element methods [30,57,64,77,78,79,80,81,82, 93,115,121].”
Novel boundary conditions for strain localization analyses in microstructural volume elements (2012, methodology): “These methods have previously been applied to identify the onset of loss of material stability of the RVE homogenized response [17, 48].”
On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers (2007, unknown): “[50] for problems of finite elasticity.”