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Rate independent Kurzweil processes. (English) Zbl 1212.49007
Summary: The Kurzweil integral technique is applied to a class of rate independent processes with convex energy and discontinuous inputs. We prove existence, uniqueness, and continuous data dependence of solutions in \(BV\) spaces. It is shown that in the context of elastoplasticity, the Kurzweil solutions coincide with natural limits of viscous regularizations when the viscosity coefficient tends to zero. The discontinuities produce an additional positive dissipation term, which is not homogeneous of degree one.

MSC:
49J40 Variational inequalities
49K40 Sensitivity, stability, well-posedness
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
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