Calculus of Variations and Geometric Measure Theory

G. Dal Maso - M. Negri - D. Percivale

Linearized elasticity as $\Gamma\mbox{-limit}$ of finite elasticity

created on 17 Dec 2001
modified on 31 Oct 2002


Published Paper

Inserted: 17 dec 2001
Last Updated: 31 oct 2002

Journal: Set-Valued Anal.
Volume: 10
Pages: 165-183
Year: 2002


Linearized elastic energies are derived from rescaled non-linear energies by means of $\Gamma\mbox{-convergence}$. For Dirichlet and mixed boundary value problems in a Lipschitz domain $\Omega$, the convergence of minimizers takes place in the weak topology of $H^1(\Omega,*R*^n)$ and in the strong topology of $W^{1,q}(\Omega,*R*^n)$ for $1\leq q <2$.

Keywords: Gamma-convergence, linearized elasticity