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Some remarks on nonlocal interactions and hysteresis in phase transitions

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Abstract

This paper examines models of shape memory alloys in which the usual multiwell, nonconvex elastic energy is modified by the addition of a nonlocal interaction term. It is shown that minimizing such an energy over uniform Young-measures yields a good prediction of hysteresis in a material subjected to biaxial loading. In addition, the relationship between the nonlocal interaction energy and the coherency energy is discussed.

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Authors and Affiliations

  1. Department of Mathematics and ICAM, Virginia Tech, 24061-0123, Blacksburg, Virginia, USA

    Robert C. Rogers

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  1. Robert C. Rogers
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Additional information

This work has been partially supported by the National Science Foundation under grants number DMS-9204304 and DMS-9403844

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Rogers, R.C. Some remarks on nonlocal interactions and hysteresis in phase transitions. Continuum Mech. Thermodyn 8, 65–73 (1994). https://doi.org/10.1007/BF01175752

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  • DOI: https://doi.org/10.1007/BF01175752

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