Abstract
The modified spectral overlay finite element method is described for a two-dimensional antiplane viscoplastic problem under quasi-static, isothermal conditions. The essential feature of the spectral overlay method is that high resolution of localized steep gradients can be achieved by overlaying a spectral interpolant on a standard finite element mesh. In order to evaluate this method and compare it with the conventional finite element method, a closed-form solution of a shear localization problem in one dimension has been devised. The results show that this method is very powerful in capturing the shape of the gradient field and its peak value in the localization zone. Solutions for an antiplane crack problem are then given to illustrate the effectiveness of this method.
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