Thermal stresses in a viscoelastic trimaterial

Abstract

A general solution for a three dissimilar sandwiched medium subjected to a point heat source and a three-phase composite cylinder subjected to a remote uniform heat flow is presented in this work. The solutions to the heat conduction and thermoelastic problems are derived based on the method of analytic continuation associated with the alternation technique. A rapidly convergent series solution for both the temperature and the stress field, which is expressed in terms of an explicit general term of the corresponding homogeneous potential, is obtained in an elegant form. The hereditary integral in conjunction with the Kelvin–Maxwell model is applied to simulate the thermoviscoelastic properties while a thermorheologically simple material is considered. Based on the correspondence principle, the Laplace transformed thermoviscoelastic solution is directly determined from the corresponding thermoelastic one. The real-time solution can then be solved numerically by taking inverse Laplace transform. Two typical examples concerning interfacial stresses for plane-layered media and circularly cylindrical-layered media are discussed in detail.