A SPECTRAL OVERLAY METHOD FOR QUASI-STATIC VISCOPLASTICITY - APPLICATIONS TO ANTIPLANE CRACK AND COMPARISON WITH CLOSED-FORM SOLUTIONS

The modified spectral overlay finite element method is described for a two-dimensional antiplane viscoplastic problem under quasi-static, is othermal conditions. The essential feature of the spectral overlay met hod is that high resolution of localized steep gradients can be achiev ed by overlaying a spectral interpolant on a standard finite element m esh. In order to evaluate this method and compare it with the conventi onal finite element method, a closed-form solution of a shear localiza tion problem in one dimension has been devised. The results show that this method is very powerful in capturing the shape of the gradient fi eld and its peak value in the localization zone. Solutions for an anti plane crack problem are then given to illustrate the effectiveness of this method.