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The Quarterly Journal of Mechanics and Applied Mathematics 1982 35(2):197-217; doi:10.1093/qjmam/35.2.197
© 1982 by Oxford University Press
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A MATHEMATICAL THEORY OF ELASTIC-PLASTIC MATERIALS WITH MEMORY WITH GENERAL WORK-HARDENING

EIJI MATSUMOTO

( Department of Aeronautical Engineering, Kyoto Uniuersity Kyoto, Japan )

This paper analyzes an elastic-plastic material with memory whose admissible deformation histories are restricted to a closed domain in the history space. The constitutive relations consist of two functionals of the deformation history: a response functional and a scalar-valued functional prescribing the admissible domain. Typical concepts of elasto-plasticity are derived naturally from the functionals, e.g., a yield function for the stress with general work-hardening, decomposition of the deformation rate into elastic and plastic parts, flow rules and a flow potential. This paper discusses also the relation between this material and elastic-plastic materials with internal state variables


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