Benchmarking finite element analysis of linear viscoelastic materials using a beam model

The primary objective of this study was to evaluate the use of available off-the-shelf finite element software like ABAQUS Standard™, ANSYS Workbench™, and Sandia National Laboratory Sierra Mechanics™ to model linear viscoelastic materials and compare their results to an analytically exact model. The study makes use of a standard beam under constant extension loading originally proposed by R.H. MacNeal and R.L. Harder in 1984 for testing the accuracy of finite element analysis tools. The results indicate that these finite element codes approximate the viscoelastic effects of the analytical formulation. When mesh and time step convergence studies were performed, the displacement results obtained diverged by \(\pm 6\%\) from the analytical solution for a 3000-hour analysis as stipulated by ASTM D2990 and by \(\pm 16\%\) for a 12-year analysis. The computed results show a continuous divergence between the computational and analytical solutions in time. A parametric study on the effect of Poisson’s ratio on the tip displacement was also considered. The parametric studies suggest that the finite element algorithms apply a constant Poisson’s ratio for viscoelastic case studies.