Developing an automatized optimization problem in FEniCS for parameter determination of metamaterials

In this work, a novel automatized optimization process is developed for the inverse analysis and parameter determination of metamaterials. Metamaterials are the family of materials designed to have tailored material properties, such as high strength-to-weight ratio or extreme elasticity, by using an optimized topology. Due to metamaterials' inner substructure, it is of interest to simulate their mechanical behaviour using reduced-order modelling utilizing the generalized mechanics. We determine the constitutive parameters of such models by developing an automatized optimization process in FEniCS. This process utilizes the Trust Region Reflective optimization method, from Scipy, for minimizing the deviation of the continuum model from a detailed micro-scale model. The parameter identification procedure proves to be robust and reliable by testing it for the pantographic structures as an example of metamaterials.