A finite element method for analyzing localization in rate dependent solids at finite strains

Abstract

The finite element method for localization analysis of Ortiz et al. [Comp. Methods Appl. Mech. Engrg. 61] is generalized to account for finite deformations and for material rate dependence. Special shape functions are added to the finite element basis to reproduce band-like localized deformation modes. The amplitudes of these additional modes are eliminated locally by static condensation. The performance of the enhanced element is illustrated in a problem involving shear localization in a plane strain tensile bar. Solutions based on the enhanced element are compared with corresponding results obtained from the underlying compatible isoparametric quadrilateral element and from crossed-triangular and uniformly reduced integration elements. In the finite deformation context, the enhanced element solution is not very sensitive to the precise specification of initial orientation of the additional band-like modes. The enhanced element formulation described here can be used for a broad range of rate independent and rate dependent material behaviors in two dimensional and three dimensional problems.

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