Computational stochastic homogenization of heterogeneous media from an elasticity random field having an uncertain spectral measure

Christian Soize (1)

1 MSME - Laboratoire Modélisation et Simulation Multi-Echelle

This paper presents the computational stochastic homogenization of a heterogeneous 3D-linear anisotropic elastic microstructure that cannot be described in terms of constituents at microscale, as live tissues. The random apparent elasticity field at mesoscale is then modeled in a class of non-Gaussian positive-definite tensor-valued homogeneous random fields. We present an extension of previous works consisting of a novel probabilistic model to take into account uncertainties in the spectral measure of the random apparent elasticity field. A probabilistic analysis of the random effective elasticity tensor at macroscale is performed as a function of the level of spectrum uncertainties, which allows for studying the scale separation and the representative volume element size in a robust probabilistic framework.

Mots clés: Stochastic homogenization; Non-Gaussian random fields; Uncertain spectral measure; Heterogeneous microstructure; Uncertainty Quantification; Live tissues

Domaines: Mécanique des matériaux [physics.class-ph]; Statistiques [math.ST]; Probabilités [math.PR]; Modélisation et simulation

Christian Soize. Computational stochastic homogenization of heterogeneous media from an elasticity random field having an uncertain spectral measure. Computational Mechanics, 2021, 68, pp.1003-1021. ⟨10.1007/s00466-021-02056-8⟩. ⟨hal-03321743⟩