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A note on uniqueness in coupled thermoplasticity

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Summary

Criteria are derived for uniqueness in coupled thermoplasticity. A small strain thermoplastic constitutive model is developed within the framework of the 1965 Green and Naghdi [1] formulation. An energy balance equation is also formulated which accommodates thermal conduction: when plastic flow is suppressed, the equation reduces to the correct thermoelastic relation. For prescribed tractions and heat fluxes on the boundary, criteria are sought under which the solution of the boundary value problem, assumed unique at the current time, remains unique for a sufficiently short time interval. The criteria are in the form of several matrix inequalities. Since the various matrices are at most of rank 6, numerical application of the inequalities poses no significant difficulty.

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  1. Department of Mechanical Engineering, Stevens Institute of Technology, 07030, Hoboken, New Jersey, U.S.A.

    D. W. Nicholson

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  1. D. W. Nicholson
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Nicholson, D.W. A note on uniqueness in coupled thermoplasticity. Acta Mechanica 78, 161–168 (1989). https://doi.org/10.1007/BF01174007

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  • DOI: https://doi.org/10.1007/BF01174007

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