Abstract
Pantographic structures are examples of metamaterials with such a microstructure that higher-gradient terms’ role is increased in the mechanical response. In this work, we aim for validating parameters of a reduced-order model for a pantographic structure. Experimental tests are carried out by applying forced oscillation to 3D-printed specimens for a range of frequencies. A second-gradient coarse-grained nonlinear model is utilized for obtaining a homogenized 2D description of the pantographic structure. By inverse analysis and through an automatized optimization algorithm, the parameters of the model are identified for the corresponding pantographic structure. By comparing the displacement plots, the performance of the model and the identified parameters are assessed for dynamic regime. Qualitative and quantitative analyses for different frequency ranges are performed. A good agreement is present far away from the eigenfrequencies. The discrepancies near the eigenfrequencies are a possible indication of the significance of higher-order inertia in the model.
Highlights
Metamaterials are referred to as a group of engineered materials that possess peculiar properties, which are not commonly observed in regularly used materials [1,2,3,4]
The accuracy of the macro-scale model in predicting the mechanical behavior of the structure is quantified by an error measure
The displacement plots from numerical computations and the experimental tests for 40, 80, and 140 Hz are presented in Figs. 6, 7, and 8, respectively, where |ux| is the modulus of the displacement in the x-direction and |uy| is the modulus of the displacement in the y-direction
Summary
Metamaterials are referred to as a group of engineered materials that possess peculiar properties, which are not commonly observed in regularly used materials [1,2,3,4]. From a numerical point of view, this homogenized model is in favor These additional parameters have to be determined [15,16,17,18]. The pantographic structure is capable of undergoing large tensile deformation while remaining in the elastic regime [38], and it has a very favorable strength-to-weight ratio [39]. Since the deformation and kinetic energies are independent, we may determine the parameters in each part, separately For the former, quasi-static loading condition makes kinetic energy negligible. For the latter, loading around eigenfrequencies lets inertial terms dominate We focus on the former and use the formalism in [40], where an automatized optimization problem is utilized to determine the parameters of the mathematical models of metamaterials under static loading.
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