Inverse analysis of metamaterials and parameter determination by means of an automatized optimization problem

In this paper, a novel parameter determination technique is developed for mate- rial models in continuum mechanics aimed at describing metamaterials. Owing to their peculiar mechanical properties and behaviors, such as extreme elasticity or high strength-to-weight ratio, metamaterials are of interest to be simulated by reduced-order modeling by means of the generalized mechanics. Such models incorporate constitutive parameters to be determined; we develop an automa- tized optimization process specifically for obtaining metamaterials parameters. The process aims at minimizing a mechanically meaningful error function mea- suring the deviation of the continuum from a detailed description by using the Trust Region Reflective optimization method. The parameter identification pro- cedure is tested for an exemplary extension experiment of a metamaterial, prov- ing to be robust and reliable.