Finite Element Analysis of Thermoelastic Properties of Metamaterials with Multifaceted Symmetries

Novel structural metamaterials with negative Poisson’s ratios (auxetic) or negative coefficients of thermal expansion are very promising for use in extreme environments such as high strain-rate impact and abrupt temperature changes which are critical to many aerospace and defense applications. This paper presents a unified approach for the finite element analysis of the effective thermoelastic properties of metamaterials consisting of unit cells with multifaceted symmetries. For an auxetic configuration, boundary conditions accounting for the mirror and rotational symmetries are determined and the size of the unit cell is reduced up to one-sixteenth of the full model. For a hybrid microstructure manifesting a negative coefficient of thermal expansion, it is illustrated that a one-eighth model is sufficient for the thermal stress analysis under temperature changes.