Geometric linearization of theories for incompressible elastic materials and applications

Jesenko, Martin (avtor), Schmidt, Bernd (avtor)

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
• 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
• PID: 20.500.12556/RUL-135490
• UDK: 51
• ISSN pri članku: 0218-2025
• DOI: /10.1142/S0218202521500202
• COBISS.SI-ID: 92180483
• Datum objave v RUL: 16.03.2022

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

Sekundarni jezik

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