We rigorously determine the scale-independent short range elastic parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure. This is done using both classical periodic homogenization and a new procedure involving the concept of apparent material stiffness of a unit-cell under affine Dirichlet boundary conditions and Neumann's principle on the overall representation of anisotropy. We explain our idea of "maximal" stiffness of the unit-cell and use state of the art first order numerical homogenization methods to obtain the needed parameters for a given tetragonal unit-cell. These results are used in the accompanying paper [16] to describe the wave propagation including band-gaps in the same tetragonal metamaterial.
@article{arxiv.1909.13624,
title = {Identification of scale-independent material parameters in the relaxed micromorphic model through model-adapted first order homogenization},
author = {Patrizio Neff and Bernhard Eidel and Marco Valerio d'Agostino and Angela Madeo},
journal= {arXiv preprint arXiv:1909.13624},
year = {2019}
}
Comments
To appear in Journal of Elasticity. arXiv admin note: text overlap with arXiv:1709.07054