Representative volume: Existence and size determination

By I. Gitman, H. Askes, Lambertus J. Sluys. 2007

705 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/11ea14d4a74a2d07a011f9b59b8453d3c21ba553

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In Mechanics of Materials

Citations in the corpus

Computational homogenization for adhesive and cohesive failure in quasi‐brittle solids (2010, methodology): “For such micro models the definition of representative volume elements has been demonstrated to be troublesome when a classical homogenisation approach is used [13].”
Towards gigantic RVE sizes for 3D stochastic fibrous networks (2014, neutral): “…samples is chosen cubic for simplicity of computational implementation; an alternative could have been spherically-shaped samples as developed in Glüge et al. (2012), in which the authors have found that spherical volume elements lead to a faster convergence of the effective properties in…”
Scale{dependent homogenization of random composites as micropolar continua (2015, background): “Usually, homogenization techniques for random media are based on the solution of boundary value problems (BVPs) over finite–size mesoscales (Terada et al., 2000; Kanit et al., 2003; Sab and Nedjar, 2005; Gitman et al., 2007; Hatami–Marbini and Picu , 2009; Ghosh, 2011; Salmi et al., 2012).”
Computational homogenization of elasto-plastic porous metals (2012, background): “For hardening composites, the RVE size was found in Gitman et al. (2007) to be generally larger than for linear elastic case, and not to exist for softening materials.”
Particulate random composites homogenized as micropolar materials (2014, background): “In this view, a possible solution has been indicated in [4, 19] enforcing the periodicity of the material between corresponding edges of the windows.”
Determination of the size of the representative volume element for random quasi-brittle composites (2009, methodology): “The review of Gitman et al. (2007) reveals that: the RVE should contain enough information on the microstructure (Hashin, 1983); the RVE should be sufﬁciently smaller than the macroscopic structural dimensions (Zaoui, 2001) and sufﬁciently larger than the microstructural size (Drugan and Willis,…”
A computational library for multiscale modeling of material failure (2013, background): “Also as discussed in [46], the RVE looses representativeness in case of strain localization.”
Homogenization-based multiscale crack modelling: from micro diffusive damage to macro cracks (2011, methodology): “That might explain the existence of various definitions of the RVE, see [11] for a recent review.”
Monte Carlo Simulations of Mesoscale Fracture of Concrete with Random Aggregates and Pores: a Size Effect Study (2015, background): “The mechanical behaviour of concrete is often characterised by a single specimen or a small number of specimens [24,26,35–38].”
MULTISCALE CONTINUOUS AND DISCONTINUOUS MODELING OF HETEROGENEOUS MATERIALS: A REVIEW ON RECENT DEVELOPMENTS (2011, background): “Gitman et al.(36) did an interesting study on the existence of an RVE for quasi-brittle heterogeneous materials that exhibit localization of deformation.”
Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, background): “The dissipated energy by the failure mechanisms must be consistent through the scales and, unaffected by RVE size [33] and convergent with mesh refinement.”
Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models (2016, background): “Classical, standard RVE-based formulations are inherently non-objective in this sense as the inherent size-effect associated with strain localization [6] at the micro-scale translates into a lack of objectivity of the macro-scale response with respect to RVE size [37].”