Calculating bandgaps of nonlinear mechanical metamaterials

Bandgaps 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. Bandgap calculation of mechanical metamaterials is realized via discretizing a representative voluame element (RVE) and imposing complex-valued Bloch wave boundary conditions. It is highly desirable to implement Bloch wave analysis in real-valued commercial finite element software. We present and detail an ABAQUS and Python implementation of Bloch wave analysis. Two-dimensional (2D) soft as well three-dimensional (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 the literature or by our experimental measurement. The presented numerical strategy would aid the design, analysis and utilization of mechanical metamaterials for dynamic applications. The codes and data of the paper could be downloaded from https://github.com/XJTU-Zhou-group/Calculating-band-gaps-of-nonlinear-mechanical-metamaterials.