Scale transition and enforcement of RVE boundary conditions in second‐order computational homogenization

By Ł. Kaczmarczyk, Chris J. Pearce, N. Bićanić. 2008

174 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0f076cca00d0a701a5127e5cb55adf24e7ad161f

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Computational homogenization of cellular materials (2014, methodology): “The non–linear system (47) is resolved by using the constraint projection strategy [26, 27] combined with the path following method with arc–length increment control as detailed in section 4.”
Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation (2012, methodology): “The enforcement of unique values for the degrees of freedom of matching nodes can then be done with the Lagrange multiplier method [2, 3, 7] or directly by constraint eliminations [2, 9].”
Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, background): “were developed [50, 60, 61, 65, 66, 112], in these kind of approaches it is not necessary to introduce artificially a length-scale parameter because it arrives naturally.”
Evaluation of generalized continuum substitution models for heterogeneous materials (2012, background): “In contrast, the boundary conditions proposed in Kaczmarczyk et al. (2008) assume that the mean average second gradient of the fluctuation vanishes.”
MULTISCALE CONTINUOUS AND DISCONTINUOUS MODELING OF HETEROGENEOUS MATERIALS: A REVIEW ON RECENT DEVELOPMENTS (2011, background): “We refer to Kouznetsova et al.,70 Larsson and Diebels,79 Kaczmarczyk et al.58,59 and references therein for recent studies on the second-order CH method.”
Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior (2020, methodology): “In [29,13], second-order coefficients have been obtained in a linear context using heuristic boundary conditions while, in [33], the issue of enforcing boundary conditions in secondorder computational homogenization has been addressed using constrained minimization.”