Summary
In this paper we develop agradient theory of internal variables using a variational principle in conjunction with the dissipation inequality. The basic findings are (i), that the internal variables are, non-local in that they obey field equations instead of evolution equations and (ii) they are subject to boundary conditions that are dictated by the applied tractions and displacements as well as the physical structure of the material domain. As a consequence, spatiallyinhomogeneous strain fields exist in the presence ofuniform boundary tractions and/or displacements. This phenomenon is illustrated in the simple case of one dimension.
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Valanis, K.C. A gradient theory of internal variables. Acta Mechanica 116, 1–14 (1996). https://doi.org/10.1007/BF01171416
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DOI: https://doi.org/10.1007/BF01171416