An approach to generalized one-dimensional self-similar elasticity

Abstract : We employ a self-similar Laplacian in the one-dimensional infinite space and deduce a model for one-dimensional self-similar elasticity. As a consequence of self-similarity this Laplacian assumes the non-local form of a self-adjoint combination of fractional integrals. The linear elastic constitutive law becomes a non-local convolution with the elastic modulus function being a power-law kernel. We outline some principal features of a linear self-similar elasticity theory in one dimension. We find an anomalous behavior of the elastic modulus function reflecting a regime of critically slowly decreasing interparticle interactions in one dimension. The approach can be generalized to the n dimensional physical space (Michelitsch, Maugin, Nowakowski, Nicolleau, & Rahman, to be published).
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International Journal of Engineering Science, Elsevier, 2012, 61, pp.103 - 111. 〈10.1016/j.ijengsci.2012.06.014〉
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https://hal.sorbonne-universite.fr/hal-01587115
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Soumis le : mercredi 13 septembre 2017 - 16:38:00
Dernière modification le : lundi 9 avril 2018 - 12:20:07

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Thomas M. Michelitsch, Gérard A. Maugin, Mujibur Rahman, Shahram Derogar, Andrzej F. Nowakowski, et al.. An approach to generalized one-dimensional self-similar elasticity. International Journal of Engineering Science, Elsevier, 2012, 61, pp.103 - 111. 〈10.1016/j.ijengsci.2012.06.014〉. 〈hal-01587115〉

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