Creep and Relaxation of Thermo-viscoelasticity Using the Symplectic System Method

This paper discusses thermo-viscoelastic problems using the symplectic system method. With the aid of the symplectic character and the Laplace integral transformation, all general solutions of the homogeneous equation are obtained directly via zero eigensolutions and their Jordan forms of the corresponding symplectic dual equations. The special solution of the non-homogeneous equations are given by applying the the adjoint symplectic relation between the eigensolutions. Examples show the results of the direct symplectic method, and reveal the creep and relaxation properties of the time dependent viscoelastic materials.