Finite element modeling of one-dimensional viscoelastic structures using anelastic displacement fields

A physically motivated approach to modeling the dynamic behavior of viscoelastic structures using augmenting thermodynamic fields was previously reported. Anelastic displacement fields, special kinds of augmenting thermodynamic fields, are now introduced. Instead of addressing physical damping mechanisms directly, as in the earlier approach, their effects on the displacement field are considered. In this approach, the total displacement field comprises two parts: 1) an elastic part and 2) an anelastic part. The material constitutive equations are developed, as well as the governing differential equations and boundary conditions for a one-dimensional structural member, and are compared to the results developed previously using the augmented thermodynamic fields approach. In addition, a physical interpretation of some of the quantities involved is advanced in terms of a classical mechanical analogy. Because the anelastic displacement field(s) and the total displacement field may be treated similarly in analytical or numerical study, the key practical benefit of this anelastic displacement fields approach is that it leads to the straightforward development of time-domain finite element models. Modal analyses and frequency response analyses have been implemented using the matrix manipulation capabilities of a commercial finite element code.