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Stability of flow processes for dissipative solids with internal imperfections. (English) Zbl 0564.73051

The description of the postcritical behaviour of dissipative solids is presented. A simple model of an elastic-viscoplastic material with internal imperfections is proposed. This model is justified by physical mechanisms of polycrystalline matter flow in some regions of temperature and strain rate changes. A model proposed satisfies the requirement that during the deformation process in which the effective strain rate is equal to the assumed static value the response of a material becomes elastic-plastic. The identification procedure for all material functions and constants are based on available experimental data. Both the mechanical test data and physical, metallurgical observations are used.
As an example of a quasi-static, isothermal flow process the boundary- initial-value problem describing the necking phenomenon is considered. The problem is formulated in such a way that enables discussion of the influence of strain rate effects, as well as imperfection and diffusion effects on the onset of localization. Comparison of theoretical predictions with available experimental results is given.

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)
74G99 Equilibrium (steady-state) problems in solid mechanics
74H99 Dynamical problems in solid mechanics
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