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- W2336153615 abstract "A method for the regularization of continuum damage material models based on gradient-type enhancement of the free-energy functional is presented. Direct introduction of the gradient of the damage variable would require C 1 interpolation of the displacements, which is a complicated task to achieve with quadrilateral elements. Therefore a new variable field is introduced, which makes the model non-local in nature, while preserving C 0 interpolation order of the variables at the same time. The strategy is formulated as a pure minimization problem, therefore the LBB-condition does not apply in this case. However, we still take the interpolation of the displacement field one order higher than the interpolation of the field of additional (non-local) variables. That leads to increased accuracy and removes the post-processing step necessary to obtain consistent results in the case of equal interpolation order. Several numerical examples which show the performance of the proposed gradient enhancement are presented. The pathological mesh dependence of the damage model is efficiently removed, together with the difficulties of numerical calculations in the softening range. Calculations predict a development of the damage variable which is mesh-objective for fixed internal material length. When utilizing conventional inelastic material models with softening effects, the presence of softening leads to ill-posed boundary value problems due to the loss of ellipticity of the governing field equations. Ill-posedness manifests itself by the fact that the resulting algebraic system has no unique solution or by a strong mesh dependence of the obtained results. For softening material behavior the deformation tends to localize in a narrow band, the band width only restricted by the mesh resolution. To overcome this problem there are several strategies proposed that take into consideration an internal material length scale. The most effective ones introduce non-local terms in the model. That task can be accomplished following two approaches: integral-type and gradient-type. The integral strategy introduces non-local variables as weighted averages of the local internal variables of the" @default.
- W2336153615 created "2016-06-24" @default.
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- W2336153615 date "2008-01-01" @default.
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- W2336153615 title "A Method for Gradient Enhancement of Continuum Damage Models" @default.
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