Stress-free temperature fields in thermoelastic quasicrystals

Abstract

This paper studies the thermoelasticity of quasicrystal solids and identifies temperature distributions that do not induce thermal stresses. Unlike anisotropic crystalline solids, where a linear temperature distribution results in a stress-free state, such a distribution can generate thermal stresses in quasicrystal media. Thermal stresses arise due to incompatible thermal strain. Compatibility conditions for phason strain are derived, and stress-free linear temperature distributions are presented for different types of quasicrystals. Special attention is given to plane strain conditions, demonstrating the two-step mechanism by which thermal stresses develop in quasicrystals under plane strain. Using the Stroh formalism and a least-squares approach, the problem is solved for a finite quasicrystal solid, revealing a significantly nonlinear distribution of thermal stresses in response to certain linear temperature distributions (uniform heat flux).