Simulation of the multi-scale convergence in computational homogenization approaches

By Kenjiro Terada, Muneo Hori, T. Kyoya, Noboru Kikuchi. 2000

604 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/af605699ed418e734038bea0f794cf8dd2741510

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In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Non linear constitutive models for lattice materials (2014, methodology): “The choice of the RVE plays an important role in the framework of a computational homogenisation approach (Gusev, 1997; Kanit et al., 2003; Gitman et al., 2007; Terada et al., 2000; Graham and Yang, 2003; Stroeven et al., 2004).”
Concurrent multi-level model for damage evolution in microstructurally debonding composites (2007, neutral): “…tackled by multi-scale modeling methods e.g. in Smit et al. (1998), Fish and Shek (2000), Fish et al. (1999), Oden and Zohdi (1997), Vemaganti and Oden (2001), Ghosh et al. (2001), Raghavan and Ghosh (2004a,b), Terada and Kikuchi (2000), Zohdi and Wriggers (1999) and Tamma and Chung (1999).”
Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, methodology): “It is shown in literature that the Periodic boundary fluctuations provide a better apparent stiffness estimation for both periodic as well as random microstructures [52, 53, 74, 76, 97, 120, 126].”
Computational homogenization of cellular materials (2014, background): “Many numerical studies show that the periodic boundary condition provides a better estimation than other boundary condition types [39, 40, 41, 42].”
Particulate random composites homogenized as micropolar materials (2014, background): “posed to perform classical homogenization for nonperiodic assemblies [4, 6, 19, 20, 22].”
Computational homogenization for adhesive and cohesive failure in quasi‐brittle solids (2010, neutral): “[25, 26].”
Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation (2012, background): “Many numerical studies show that the periodic boundary condition is the most efficient choice, even if the arrangement of the micro-structure is non-periodic [11, 12, 13].”
Extended multiscale finite element method for elasto-plastic analysis of 2D periodic lattice truss materials (2010, methodology): “Since the method has the ability to evaluate the microscopic variables within the unit cells, it has been extended to solve various nonlinear multiscale problems: the evaluation of local damage [16,17], small deformation elastoplastic problems [18–20], etc.”
Multi-scale boundary element modelling of material degradation and fracture (2007, methodology): “In order to be able to use the averaging theorems presented in Section 3, for transferring information through the scales, four types of boundary conditions can be used; these are uniform tractions, uniform displacements, mixed boundary conditions and periodic boundary conditions [7, 36,43,44].”