Abstract
In this paper, we develop a thermodynamically consistent description of the uniaxial behavior of thermovisco-elastoplastic materials for which the total stress σ contains, in addition to elastic, viscous and thermic contributions, a plastic component σp of the form σp(x,t)=Ρ[ε, θ(x,t)](x,t). Here ∈ and θ are the fields of strain and absolute temperature, respectively, and {Ρ[·, θ]}θ>0 denotes a family of (rate-independent) hysteresis operators of Prandtl-Ishlinskii type, parametrized by the absolute temperature. The system of momentum and energy balance equations governing the space-time evolution of the material forms a system of two highly nonlinearly coupled partial differential equations involving partial derivatives of hysteretic nonlinearities at different places. It is shown that an initial-boundary value problem for this system admits a unique global strong solution which depends continuously on the data.
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Krejčí, P., Sprekels, J. Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity. Applications of Mathematics 43, 173–205 (1998). https://doi.org/10.1023/A:1023224507448
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DOI: https://doi.org/10.1023/A:1023224507448