×

zbMATH — the first resource for mathematics

Linearized elasticity as \(\Gamma\)-limit of finite elasticity. (English) Zbl 1009.74008
Linearized elastic energies are derived from rescaled nonlinear energies by means of \(\Gamma\)-convergence. For Dirichlet and mixed boundary value problems in a Lipschitz domain \(\Omega\), the convergence of minimizers takes place in the weak topology of \(H^1(\Omega,\mathbb{R}^n)\) and in the strong topology of \(W^{1,q}(\Omega,\mathbb{R}^n)\) for \(1\leq q<2\).

MSC:
74B15 Equations linearized about a deformed state (small deformations superposed on large)
74B20 Nonlinear elasticity
74G65 Energy minimization in equilibrium problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
PDF BibTeX XML Cite
Full Text: DOI