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Existence results for energetic models for rate-independent systems. (English) Zbl 1161.74387
From the introduction: We consider mechanical models which are driven by an external loading on a time scale much slower than any internal time scale (like viscous relaxation times) but still much faster than the time needed to find the thermo-dynamical equilibrium. Typical phenomena involve dry friction, elasto-plasticity, certain hysteresis models for shape-memory alloys and quasistatic delamination or fracture. The main feature is the rate-independency of the system response, which means that a loading with twice (or half) the speed will lead to a response with exactly twice (or half) the speed. We refer to several articles for approaches to these phenomena involving either differential inclusions or abstract hysteresis operators. Our method is different, as we avoid time derivatives and use energy principles instead.

MSC:
74H20 Existence of solutions of dynamical problems in solid mechanics
49J10 Existence theories for free problems in two or more independent variables
74A45 Theories of fracture and damage
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74G65 Energy minimization in equilibrium problems in solid mechanics
74R10 Brittle fracture
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