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Monotonicity of operators of viscoplastic response: Application to the model of Bodner-Partom. (English) Zbl 0987.74019

Summary: A class of viscoplastic constitutive models relating strain rate to stress and state variables (of the Bodner-Partom type) is considered, and the monotonicity of the related operator is studied. The considered operator is not of monotone type, but here we introduce an extended class of monotone constitutive equations (class \({\mathcal L}{\mathcal M}\)), and study the evolution of total energy of viscoplastic body for this class. It is shown that, assuming vanishing external forces, homogeneous boundary conditions and non-vanishing initial state in the dissipative system, the total energy cannot blow up in finite time. The noncoercive model of Bodner-Partom is approximated by a sequence of coercive inelastic constitutive equations.

MSC:

74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
47N60 Applications of operator theory in chemistry and life sciences
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