Application of a matrix operator method to the thermoviscoelastic analysis of composite structures

The problem of thermal stress development in composite structures containing one linear isotropic viscoelastic phase is considered. The time-temperature superposition principle is assumed to be applicable to the viscoelastic media under consideration. Two methods of solution based on the reduction of the original viscoelastic problem to the corresponding elastic one are discussed. It is argued that the use of a method based on the Laplace transform is impractical for some problems, such as those involving viscoelastic asphalt binders. However, the solution can be obtained by means of the second method considered in the paper, the Volterra correspondence principle, in which the integral operator corresponding to the master relaxation modulus is presented in matrix form. The Volterra principle can be applied to the solution of viscoelastic problems with complex geometry if the analytical solution for the corresponding elastic problem is known. Numerical examples show that the proposed method is simple and accurate. The approach is suitable to the solution of problems involving viscoelastic materials, whose rheological properties strongly depend on temperature. In particular, it can be found useful in the analysis of the low-temperature thermal cracking of viscoelastic asphalt binders.