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Geometric linearization of theories for incompressible elastic materials and applications
ID Jesenko, Martin (Avtor), ID Schmidt, Bernd (Avtor)

URLURL - Izvorni URL, za dostop obiščite https://www.worldscientific.com/doi/abs/10.1142/S0218202521500202 Povezava se odpre v novem oknu

Izvleček
We derive geometrically linearized theories for incompressible materials from nonlinear elasticity theory in the small displacement regime. Our nonlinear stored energy densities may vary on the same (small) length scale as the typical displacements. This allows for applications to multiwell energies as, e.g. encountered in martensitic phases of shape memory alloys and models for nematic elastomers. Under natural assumptions on the asymptotic behavior of such densities we prove Gamma-convergence of the properly rescaled nonlinear energy functionals to the relaxation of an effective model. The resulting limiting theory is geometrically linearized in the sense that it acts on infinitesimal displacements rather than finite deformations, but will in general still have a limiting stored energy density that depends in a nonlinear way on the infinitesimal strains. Our results, in particular, establish a rigorous link of existing finite and infinitesimal theories for incompressible nematic elastomers.

Jezik:Angleški jezik
Ključne besede:nonlinear elasticity, geometrically linear theories, incompressibility, Gamma-convergence, nematic elastomers
Vrsta gradiva:Članek v reviji (dk_c)
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:FGG - Fakulteta za gradbeništvo in geodezijo
Leto izida:2021
Št. strani:Str. 829-860
Številčenje:Vol. 31, iss. 4
UDK:51
ISSN pri članku:0218-2025
DOI:/10.1142/S0218202521500202 Povezava se odpre v novem oknu
COBISS.SI-ID:92180483 Povezava se odpre v novem oknu
Datum objave v RUL:16.03.2022
Število ogledov:71
Število prenosov:7
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Gradivo je del revije

Naslov:Mathematical models and methods in applied sciences
Skrajšan naslov:Math. models methods appl. sci.
Založnik:World Scientific
ISSN:0218-2025
COBISS.SI-ID:1580821 Povezava se odpre v novem oknu

Sekundarni jezik

Jezik:Slovenski jezik
Ključne besede:matematika, gradbeništvo, nelinearna teorija elastičnosti, geometrijsko linearne teorije, nestisljivost, gama-konvergenca, nematični elastomeri

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