Constitutive memory equations for auxetic materials
DOI: https://doi.org/10.3846/mma.2025.23135Abstract
In this note we suggest a set of constitutive equations for anelastic materials whose internal structure can present anomalous variations resulting from external effects of tension/compression, as in auxetic media. For these problems we require of a new function related with the variation of internal structure, which allows us to define a threshold separating the internal structure media from the classic ones. The equations are formulated in the case of static problems but also when the material has memory or plastic properties in addition to auxetic ones. In order to limit the complexity of the formulae, the discussion is limited to the case where the perturbation is one dimensional, which however does not limit the significance of the results.
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auxetic media, constitutive equations, plasticity, memory, structure transitionHow to Cite
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References
R. Blumenfeld and S.F. Edwards. Theory of strain in auxetic materials. J. Supercond. Nov. Magn., 25:565–571, 2012. https://doi.org/10.1007/s10948-012-1464-x
M. Caputo. Linear models of dissipation whose q is almost frequency independent II. Geophys. J. R. Astron. Soc., 13(5):529–539, 1967. https://doi.org/10.1111/j.1365-246X.1967.tb02303.x
M. Caputo. Memory in constitutive equations and auxetic media. Atti Accad. Naz. Lincei Rend. Lincei Sci. Fis. Natur., 29(5):7–9, 2017. https://doi.org/10.1007/s12210-017-0661-8
M. Caputo and M. Fabrizio. A new definition of fractional derivative without singular kernel. Prog. Fract. Differ. Appl., 1(2):73–85, 2015.
M. Ciarletta, M. Fabrizio and V. Tibullo. Shape memory and phase transition for auxetic materials. Math. Methods Appl. Sci., 37(18):2864–2871, 2013. https://doi.org/10.1002/mma.3025
S. Hongong, X. Fang, X. Feng and B. Yan. Temperature-dependent modulus of metals based on lattice vibration theory. J. Appl. Mech., 81(4):041017, 2014. https://doi.org/10.1115/1.4025417
L.G. Landau and V.L. Ginzburg. On the theory of superconductivity. Zh. Eksp. Teor. Fiz., 30:1064–1082, 1950.
I. Podlubny. Fractional differential equations. New York: Academic, 1999.
M. Wang, Z.M Li, W. Shi, B.-H. Xie and M.-B. Yang. Review on auxetic materials. J. Mater. Sci., 39(10):3269–3279, 2004. https://doi.org/10.1023/B:JMSC.0000026928.93231.e0
L. Yanping and H. Hong. A review on auxetic structures and polymeric materials. Sci. Res. Essays, 5(10):1052–1063, 2010.
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Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.