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The plastic spin. (English) Zbl 0587.73052

A macroscopic formulation of large deformations elastoplasticity with tensorial structure variables is presented. The novel features are the effect of constitutive relations for the plastic spin and, to a lesser degree of importance, of elastically embedding the structure variables. The plastic spin constitutive relations are obtained for different kinds of initial and induced anisotropies on the basis of the representation theorems for isotropic second-order antisymmetric tensor-valued functions, and their role is illustrated by the analysis of several examples at large homogeneous deformations. In particular the analysis of simple shear with nonlinear kinematic hardening of the evanescent memory type provides, on the basis of the second Lyapunov method for stability, conditions on the material constants for the occurrence or not of stress oscillations with monotonically increasing shear strain.

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)
74A20 Theory of constitutive functions in solid mechanics
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