Direct integration of measured viscoelastic relaxation data in time-domain finite element simulations

Abstract

The current approach to modeling viscoelastic materials in most
commercial finite element packages is based on the General Maxwell Model, which
views these materials as combinations of spring and dashpot elements. However, the
data can be incorporated more directly into a transient finite element study by direct
interpolation of the relaxation function. This work explores a linear interpolation
scheme to the inclusion of viscoelastic relaxation functions on an example problem.
The results show several benefits over the General Maxwell Model for transient
studies. Included in the analysis are displacement solutions utilizing both approaches,
relaxation function error calculations for both approaches, and parametric runtime
studies comparing speed of calculation. The variation in computational flop counts is
considered and an argument is made for the preference of the proposed approach.