Transient thermal stress analysis of temperature-dependent anisotropic viscoelastic solids

Abstract

Consider the transient thermal stress analysis for a material that is anisotropic (direction-dependent), viscoelastic (time-dependent), and thermorheologically simple (temperature-dependent). To solve this problem, three fundamental theories are employed: (1) complex variable Stroh formalism for anisotropic elasticity, (2) elastic-viscoelastic correspondence principle (EVCP) or time-stepping method (TSM) for viscoelasticity, and (3) time-temperature superposition principle (TTSP) for thermorheologically simple materials. By using the Stroh formalism, all different kinds of anisotropic elastic materials can be analyzed by using the same formulae. With EVCP and TSM, the problem of viscoelasticity can be solved via its corresponding problem of elasticity. By TTSP, the temperature-dependent constitutive relation can be expressed by using the reference temperature and the reduced time defined through shift factor. Thus, through the combined use of these theories, the complicated problems of transient anisotropic thermo-viscoelasticity can be solved by using the available solution tool for anisotropic elasticity such as the boundary element method (BEM). Based upon this concept, two novel BEMs are developed for the transient thermal stress analysis of temperature-dependent anisotropic viscoelastic solids. One is BEM-EVCP, and the other is BEM-TSM. The final results show that both of them can provide accurate solutions, and BEM-TSM is much more efficient than BEM-EVCP.