WIAS Preprint No. 2817, (2021)

Derivation of effective models from heterogenous Cosserat media via periodic unfolding


Authors

  • Nika, Grigor
    ORCID: 0000-0002-4403-6908

2020 Mathematics Subject Classification

  • 35A15 35Q74 74M25 74Q15

Keywords

  • Cosserat continuum, size effects, homogenization, periodic unfolding

DOI

10.20347/WIAS.PREPRINT.2817

Abstract

We derive two different effective models from a heterogeneous Cosserat continuum taking into account the Cosserat intrinsic length of the constituents. We pass to the limit using homogenization via periodic unfolding and in doing so we provide rigorous proof to the results introduced by Forest, Pradel, and Sab (Int. J. Solids Structures 38 (26-27): 4585-4608 '01). Depending on how different characteristic lengths of the domain scale with respect to the Cosserat intrinsic length, we obtain either an effective classical Cauchy continuum or an effective Cosserat continuum. Moreover, we provide some corrector type results for each case.

Appeared in

Download Documents