Abstract Summary
Recent studies carried out in the literature have shown that the mechanical properties of bioinspired periodic composite materials can be strongly influenced by finite deformations effects leading to highly nonlinear static and dynamic behaviors at multiple length scales. For instance, microscopic and macroscopic instabilities may occur during macrostrain-driven uniaxial loading processes in elastomeric nacre-like composite materials and wave attenuation properties in lightened periodic nacre-like microstructures may evolve as a function of microstructural evolution, in turn, depending on the level of applied deformations. Consequently, finite deformation effects, in conjunction with specific micro-geometrical arrangements, give the opportunity for obtaining metamaterial properties not available in natural materials. In order to give a better understanding of the complex nonlinear phenomena occurring in the above materials, the nonlinear static and dynamic responses of novel periodic microstructures subjected to biaxial macroscopic compressive loading processes are analyzed. Firstly, the static response was investigated by solving the nonlinear boundary value problem based on the periodic homogenization theory while the onset of primary instabilities with short (microscopic instability) or long (macroscopic instability) wavelength was performed by solving the related frequency domain wave equation by exploiting the Floquet-Bloch theorem. Secondly, the dynamic response was investigated in terms of dispersion relations by solving the eigenvalue problem considering small amplitude motions superimposed on a finitely deformed configuration based on the Floquet-Bloch technique. Then the dispersion curves, relating the wavelength of the propagating waves to their frequency, were analyzed to determine the evolution of the complete bandgaps as a function of the applied strains. The numerical calculations were carried out by means of a finite element discretization performed on the simulation software COMSOL Multiphysics v5.6 together with some Java subroutines written in COMSOL Application Builder environment which can automate specific analysis procedures. To the best of the author’s knowledge, the scientific understanding of the wave attenuation properties in soft bioinspired composite materials subjected to high deformations is still limited. Thus, this work provides a valuable opportunity for researchers to further improve their knowledge in this research field by investigating how large deformations and the onset of instabilities affects the vibration control and band gap phenomena in new advanced bioinspired metamaterials. We proposed a new lightened nacre-like microstructure containing periodically arranged solid and hollow platelets and we investigate the propagation of elastic waves superimposed on a deformed state for increasing strains. The results have shown that wide complete bandgaps can be found also at lower contrast between the platelets and the matrix by suitably setting the percentage value of platelets volume fraction and the percentage of void inclusion given by the insertion of hollow platelets. In addition, was found that the onset of microscopic instability leads to a microstructural pattern transformation which, together with the level of applied deformations, strongly influences (sometimes positively and sometimes negatively) the wave propagation properties of lightened nacre-like composite metamaterials. Definitively, the obtained numerical outcomes provide new opportunities to design bioinspired soft composite metamaterials characterized by high deformability and enhanced waves attenuation capabilities.
