Quantitative stochastic homogenization of nonlinearly elastic, random laminates

  • Stefan Neukamm

    Technische Universität Dresden, Germany
  • Mathias Schäffner

    MLU Halle, Halle (Saale), Germany
  • Mario Varga

    Technische Universität Dresden, Germany
Quantitative stochastic homogenization of nonlinearly elastic, random laminates cover

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Abstract

In this paper we study quantitative stochastic homogenization of a nonlinearly elastic composite material with a laminate microstructure. We prove that for deformations close to the set of rotations, the homogenized stored energy function is and that , the stress tensor , and the tangent-moduli can be represented with the help of stochastic correctors. Furthermore, we study the error of an approximation of these quantities via representative volume elements. More precisely, we consider periodic representative volume elements (RVEs) obtained by periodizing the distribution of the random material. For materials with a fast decay of correlations on scales larger than a unit scale, we establish error estimates on the random and systematic error of the RVE with optimal scaling in the size of the RVE and with a multiplicative random constant that has exponential moments.

Cite this article

Stefan Neukamm, Mathias Schäffner, Mario Varga, Quantitative stochastic homogenization of nonlinearly elastic, random laminates. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024), published online first

DOI 10.4171/AIHPC/113