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Calculating-band-gaps-of-nonlinear-mechanical-metamaterials

Band gaps of are intrinsic physical properties of periodic structures, for example, mechanical metamaterials or phononic crystals, which indicate attenuation of wave propagation within a specific frequency range. Band gap calculation of mechanical metamaterials is realized via discretizing a representative volume element (RVE) and imposing a complex-valued Bloch wave boundary conditions. It is highly desirable to implement Bloch wave analysis in real-valued commercial finite element softwares. We present and detail an ABAQUS and Python implementation of Bloch wave analysis. 2D soft as well 3D hard mechanical metamaterials are chosen as numerical examples. Material and geometric nonlinearities are tackled properly and the effects of pre-strains are explored. Our numerical results are validated either by similar results reported in literature or by our experimental measurement.

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