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Composites such as architected metamaterials made from elastic materials can display energy absorbing or dissipative behavior associated with snap-through and other instabilities. These instabilities result in conversion of elastic strain energy of the elastic parent material of the composite to kinetic energy which is then dissipated over longer time scales via processes including air drag. Here we propose a new approach at modelling such composites by appealing to ideas from statistical mechanics, viz. we postulate that the state of such a composite comprising a large number of unit cells is given by maximization of entropy. We first develop the theoretical homogenization framework for such a composite and provide expressions of the effective properties. Solution of the governing equations requires sampling over all the states that the composite can attain, and this is efficiently done by employing the Nested Sampling algorithm to construct a sample with the required distribution. Using this numerical scheme , we present predictions of the volumetric compressive response of two model materials, i.e. two-dimensional (2D) architected materials with honeycomb-like microstructures and cell walls made from an elastic material. Unlike traditional homogenization schemes, the volumetric stress versus strain response now depends on an additional internal state variable that characterizes the vibrational modes of the microstructure, i.e., the predictions are akin to what is commonly known as an Equation-of-State (EoS). We finally demonstrate the utility of the method by using the predicted EoS to extract the shock response of the architected material and compute the dissipation within the shock. |
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