9. Thermal Stresses in Auxetic Solids

This chapter begins with some general considerations on the thermoelasticity of auxetic solids, followed by the thermal elasticity of 3D auxetic solids with geometrical constraints. Thereafter, the thermoelasticity of beams and plates arising from a given temperature profile is furnished. Based on a set of dimensionless thermal stresses for application in auxetic plates and shells, it was found that thermal stresses reduce as the material becomes more auxetic at constant Young’s modulus (E), and constant shear modulus (G), but the thermal stresses increase as the material becomes more auxetic at constant bulk modulus (K). In the case of constant product of EGK, the thermal stress is maximum at Poisson’s ratio of 0.303, but diminishes at Poisson’s ratios of −1 and 0.5. In most cases of solids considered in this chapter, the thermal stresses are minimized in the auxetic region. Finally a summary of thermal conductivity study in multi-re-entrant honeycombs by Innocenti and Scarpa (J Compos Mater 43(21):2419–2439, 2009) is given, in which the results suggest that auxetic honeycomb configurations exhibit higher out-of-plane conductivity, strong in-plane thermal anisotropy, and the lowest peak temperatures during heat transfer between the bottom and top faces of honeycomb panels.