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Towards a catastrophe theory for the mechanics of plasticity and fracture. (English) Zbl 0565.73039
The catastrophe theory has established that the conservative systems have only a few ways to lose their stability. We sketch a similar classification for a class of dissipative systems. Although our scope is limited to the case of two dissipative variables, we find six elementary catastrophes. We present examples from discrete plasticity, crack and friction mechanics.

MSC:
74G99 Equilibrium (steady-state) problems in solid mechanics
74H99 Dynamical problems in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
74R05 Brittle damage
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