Bistability in thermomechanical metamaterials structured as three-dimensional composite tetrahedra

Abstract The letter begins with the thermomechanical model of a three degree-of-freedom tetrahedral unit cell subject to cycles of heating and cooling. Geometric nonlinearity, mechanical constraint and dissimilar material properties of thermoelastic elements lead to a build-up of thermally-driven stored strain energy as dictated by the thermomechanical potential. For certain geometric configurations and combinations of material properties in the composite structure, the solution bifurcates at a critical thermal load causing a discontinuous buckling or ‘pop-through’ of the interior triad. Interestingly, if the pop-through action coincides with an abrupt inward displacement of the tetrahedral vertices then the effective volume of the unit cell shrinks. The phenomenon is termed negative ‘intermittent’ volumetric thermal expansion. In total, six types of thermal load–response curves are identified. By systematic nonlinear analysis of the thermomechanical potential, the stability diagram and phase diagram pinpoint the locations of bifurcations, cusps and features that mark a shifts in hysteretic behavior. The diagrams map the thermomechanical response to the design of the unit cell. A region is identified in the phase diagram corresponding to the sets of design parameters that lead to the metamaterial response.