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Variational and projection methods for the volume constraint in finite deformation elasto-plasticity. (English) Zbl 0554.73036

This paper focuses on the treatment of volume constraints which in the context of elasto-plasticity typically arise as a result of assuming volume-preserving plastic flow. Projection methods based on the modification of the discrete gradient operator B, often proposed on an ad-hoc basis, are systematically obtained in the variational context furnished by a three-field Hu-Washizu principle. The fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume-preserving and dilatational parts, without relying on rate forms of the weak form of momentum balance. This approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient, and enables one to exactly enforce the condition of volume-preserving plastic flow. Within the framework proposed in this paper, rate forms and incrementally objective algorithms are entirely bypassed.

MSC:

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)
74S30 Other numerical methods in solid mechanics (MSC2010)
74B20 Nonlinear elasticity
49S05 Variational principles of physics

Software:

Nike2D
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