Comptes Rendus
no. 1
Elasticity of fractal materials using the continuum model with non-integer dimensional space
Vasily E. Tarasov1
1 Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia
Comptes Rendus. Mécanique, Volume 343 (2015) no. 1, pp. 57-73.

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2014.09.006
Mots clés : Fractal material, Non-integer dimensional space, Elasticity, Gradient elasticity, Thermoelasticity, Fractional continuum model
Vasily E. Tarasov 1

1 Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia 
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Vasily E. Tarasov. Elasticity of fractal materials using the continuum model with non-integer dimensional space. Comptes Rendus. Mécanique, Volume 343 (2015) no. 1, pp. 57-73. doi : 10.1016/j.crme.2014.09.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.09.006/

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