Fractional strain tensor and fractional elasticity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00588499" target="_blank" >RIV/67985840:_____/24:00588499 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10659-022-09970-9" target="_blank" >https://doi.org/10.1007/s10659-022-09970-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10659-022-09970-9" target="_blank" >10.1007/s10659-022-09970-9</a>

Result language
angličtina
Original language name
Fractional strain tensor and fractional elasticity
Original language description
A new fractional strain tensor ϵα(u) of order α (0<α<1) is introduced for a displacement u of a body occupying the entire three-dimensional space. For α↑1, the fractional strain tensor approaches the classical infinitesimal strain tensor of the linear elasticity. It is shown that ϵα(u) satisfies Korn’s inequality (in a general Lp version, 1<p<∞) and the fractional analog of Saint-Venant’s compatibility condition. The strain ϵα(u) is then used to formulate a three-dimensional fractional linear elasticity theory. The equilibrium of the body in an external force f is determined by the Euler-Lagrange equation of the total energy functional. The solution u is given by Green’s function Gα: (Formula presented.) For an isotropic body the equilibrium equation reads (Formula presented.) where λ, μ are the Lamé moduli of the material and (−Δ)α, ∇α and divα are the fractional laplacean, gradient and divergence. Green’s function can be determined explicitly in this case: (Formula presented.) x∈R3, x≠0, where I is the identity tensor (matrix), and cα a normalization factor (determined below). For α↑1 the function Gα approaches Green’s function of the standard linear elasticity. Similar approach applies to the equilibrium solution.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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