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A weakly nonlinear analysis of elasto-plastic-microstructure models. (English) Zbl 0815.73022

At certain critical values of the hardening modulus, the governing equations of elasto-plastic flow may lose their hyperbolicity and exhibit two modes of ill-posedness: shear-band and flutter ill-posedness. These modes of ill-posedness are characterized by the uncontrolled growth of modes at infinitely fine scales, which ultimately violates the continuum assumption. Linear analysis demonstrated the regularizing effect of the microstructure and provided a relationship between the width of the localized instabilities and the microlength scale. In this paper, a weakly nonlinear analysis is used to explore the immediate postcritical behavior of the solutions.

MSC:

74C99 Plastic materials, materials of stress-rate and internal-variable type
74G99 Equilibrium (steady-state) problems in solid mechanics
74H99 Dynamical problems in solid mechanics
74A60 Micromechanical theories
74M25 Micromechanics of solids
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