Determining the constitutive parameters of a macroscale second-gradient model for planar pantographic structures by using optimization algorithms

Pantographic structures have been proposed as a group of metamaterials that show high toughness in extension. Modeling such structures is technically possible through microscopic first-order continuum theories by using a suitably small length-scale, although the computational cost would be high. The aim of this research is to estimate the constitutive parameters of a planar pantographic structure by means of an optimization process. A previously-proposed macroscopic second-gradient model which is characterized by deformation energy is used for modeling the mechanical behavior of the structure. The macroscopic model will be developed based on the results of the numerical simulations of a microscopic model. In this problem, an evolutionary multi-objective optimization algorithm is utilized which minimizes the squared error of the outputs.