Fractional strain tensor and fractional elasticity

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Fractional strain tensor and fractional elasticity

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Fractional strain tensor and fractional elasticity

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Elasticity

ISSN

0374-3535

e-ISSN

1573-2681

Svazek periodika

155

Číslo periodika v rámci svazku

1-5

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

23

Strana od-do

425-447

Kód UT WoS článku

000901954200002

EID výsledku v databázi Scopus

2-s2.0-85144458920