Peridynamics modeling of cellular elastomeric metamaterials: Application to wave isolation

Abstract

We investigate how embedded geometrical imperfections can be designed to obtain significant reduction in wave amplitude and large band gap in periodic cellular metamaterials. A finite deformation peridynamics (PD) theory is developed to predict the static and dynamic responses of elastomeric metamaterials. Periodically structured cracks and volumetric geometrical imperfections, e.g., circular and elliptical holes, are embedded in elastomeric materials. Elastic wave propagation through these structured materials is studied by performing numerical simulations using PD. Two main mechanisms are exploited to enhance the energy absorption capacity compared to conventional metamaterials, viz. reflection of wave from crack surfaces and energy absorption due to local elastic instability of the cell walls. Slightly compressible neo-Hookean material model is considered, and plane strain condition is assumed. Nonlinear PD equations for quasi-static condition are solved using the Newton-Raphson method. The present model is validated against finite element solutions considering deformation of a solid elastomeric body subjected to tensile load. The model is also validated with experimental results considering rupture of a double notched elastomeric specimen assuming plane stress condition. PD predictions of nominal stress vs. strain for configurations with holes under quasi-static condition are validated against the experimental observations and numerical simulations through the finite element software ANSYS®. Newmark-beta method is employed to solve the PD equation of motion. At every time step, Newton-Raphson method is used, and convergence is established. The dynamic response obtained from the PD model is validated against finite element solutions using ANSYS® for a solid body. Various novel geometries combining cracks and holes are systematically developed guided by prediction of energy absorption capacity and band gap characteristics through numerical simulations. Wave propagation through these configurations is examined and the effects of microstructure topology on band gap and amplitude reduction are shown. Significant reduction of wave amplitude and large band gap demonstrate remarkable efficacy of the present proposal.