Linearization of elasticity models for incompressible materials-Reference-Cited by-同舟云学术

Linearization of elasticity models for incompressible materials

Published:2022-06-25 Issue:4 Volume:73 Page:
ISSN:0044-2275
Container-title:Zeitschrift für angewandte Mathematik und Physik
language:en
Short-container-title:Z. Angew. Math. Phys.

Author:

Mainini Edoardo^ORCID,Percivale Danilo

Abstract

AbstractWe obtain linear elasticity as

$$\Gamma $$

Γ-limit of finite elasticity under incompressibility assumption and Dirichlet boundary conditions. The result is shown for a large class of energy densities for rubber-like materials.

Funder

Ministero dell’Istruzione, dell’Università e della Ricerca

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,General Physics and Astronomy,General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00033-022-01768-y.pdf

Reference57 articles.

1. Agostiniani, V., Blass, T., Koumatos, K.: From nonlinear to linearized elasticity via Gamma-convergence: the case of multiwell energies satisfying weak coercivity conditions. Math. Models Methods Appl. Sci. 25, 1–38 (2015)

2. Agostiniani, V., Dal Maso, G., De Simone, A.: Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions. Ann. Inst. Henri Poincaré Anal. Non Linéaire 29, 715–735 (2012)

3. Ali, A., Hosseini, M., Sahari, B.B.: A review of constitutive models for rubber-like materials Am. J. Eng. Appl. Sci. 3, 232–239 (2010)

4. Alicandro, R., Dal Maso, G., Lazzaroni, G., Palombaro, M.: Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals. Arch. Ration. Mech. Anal. 230, 1–45 (2018)

5. Amrouche, C., Bernardi, C., Dauge, M., Girault, V.: Vector potentials in three dimensional non-smooth domains. Math. Methods Appl. Sci. 21, 823–864 (1998)

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Finite-strain Poynting–Thomson model: Existence and linearization;Mathematics and Mechanics of Solids;2024-08-19

2. Pressure live loads and the variational derivation of linear elasticity;Proceedings of the Royal Society of Edinburgh: Section A Mathematics;2022-12-09

3. Asymptotic Behavior of Constrained Local Minimizers in Finite Elasticity;Journal of Elasticity;2022-10-25