Studying the higher-order inertia in the second-order theory of elasticity for modeling metamaterials

Modeling the materials with a complex microstructure, such as metamaterials, is challenging especially in the dynamic regime. Higher-gradient models have been widely used for modeling the mechanical behavior of metamaterials. In dynamic loading problems, the inertia plays an important role. Including higher-order inertia in the model could possibly improve the accuracy of the model close to the eigenfrequencies of the structure. Such inertial terms have been presented in theory but they are not understood experimentally, therefore it has not been possible to quantify their value. Herein, we consider a macro-scale model for a pantographic structure and simulate a dynamic loading on it. We run the simulation for a range of frequencies of loading and for a number of arbitrary values for a higher-order inertial term that we have added to the model. The results show a clear relation between the value considered for the inertial term and the eigenfrequency of the structure that we get from the model. This result sheds light on finding an algorithm for determining the higher-order inertial terms experimentally in further studies.