Abstract
We discuss the theory and approximate methods for solving boundary-value problems of thermoplasticity in a quasi-static formulation when the process of non-isothermal elastoplastic deformation of a body is a sequence of equilibrium states. In this case, the stress-strain state depends on the loading history, and the process of inelastic deformation is to be observed over the whole time interval being studied. The boundary-value problem is stated as a non-linear operator equation in the Hilbertian space. The conditions that provide the existence, uniqueness and continuous dependence of the generalized solution on the applied loads and initial strains are defined. A convergence of the methods of elastic solutions and variable elastic parameters is studied to solve the boundary-value problems describing the non-isothermal processes of active loading taking into account the initial strains dependent on the deformation history and heating.
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Translated from Problemy Prochnosti, No. 1, pp. 69–99, January–February, 2006.
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Chirkov, A.Y. Analysis of boundary-value problems describing the non-isothermal processes of elastoplastic deformation taking into account the loading history. Strength Mater 38, 48–71 (2006). https://doi.org/10.1007/s11223-006-0017-6
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DOI: https://doi.org/10.1007/s11223-006-0017-6