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A finite element method for analyzing localization in rate dependent solids at finite strains. (English) Zbl 0688.73042
Summary: The finite element method for localization analysis 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.

74S05 Finite element methods applied to problems in solid mechanics
74B99 Elastic materials
74C99 Plastic materials, materials of stress-rate and internal-variable type
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
Full Text: DOI
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