Microstructural Randomness Versus Representative Volume Element in Thermomechanics

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Towards gigantic RVE sizes for 3D stochastic fibrous networks (2014, unknown): “Ostoja-Starzewski (2002) considers the RVE to be only deﬁned over a periodic unit-cell or a non-periodic cell containing an inﬁnite number of heterogeneities.”
Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, background): “It is defined as a microstructural subregion and must be large enough to be statistically representative of the composite material including all its microscopic heterogeneities [18, 33, 53, 71, 90, 120].”
Scale effects in plasticity of random media: status and challenges (2005, background): “Scale dependent hierarchies of bounds on them, similar in vein to what we have discussed in this paper, may be developed along the lines suggested in ( Ostoja-Starzewski, 2002a, b, 2004).”
Material spatial randomness: From statistical to representative volume element☆ (2006, background): “Since (almost) all constitutive behaviors in continuum mechanics may be brought under the single umbrella of thermomechanics [65,66], a generalization of respective Legendre transformations of free energy and dissipation functionals to mesoscales in random media can also be pursued [67,68].”