Thermal Stresses in Auxetic Plates and Shells

Abstract

Solids that possess negative Poisson's ratio are termed auxetic materials. This article considers the effect of auxeticity, i.e., the negative extent of Poisson's ratio on thermal stresses in plates, shells, and other solids. Results show that in cases where temperature gradient is in the through-thickness of a fully-clamped plate or when the temperature gradient is in the radial direction of fully-clamped shells, the thermal stresses can be significantly reduced by using auxetic materials. The same result applies to spheres and cylinders with radial temperature gradient. The maximum thermal stress is minimized if the selected material possesses Poisson's ratio of –1. However, the use of auxetic material is not always advantageous, nor does the use of materials with Poisson's ratio of –1 always minimize the maximum thermal stresses. It is herein suggested that, in addition to the use of materials with lower modulus and lower coefficient of thermal expansion, the use of auxetic materials offers an alternative route for lowering thermal stresses in some cases.