Conti, Sergio and Dolzmann, Georg (2009) Gamma-convergence for incompressible elastic plates. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 34 (4). pp. 531-551. ISSN 0944-2669,
Full text not available from this repository.Abstract
We derive a two-dimensional model for elastic plates as a Gamma-limit of three-dimensional nonlinear elasticity with the constraint of incompressibility. The resulting model describes plate bending, and is determined from the isochoric elastic moduli of the three-dimensional problem. Without the constraint of incompressibility, a plate theory was first derived by Friesecke et al. (Comm Pure Appl Math 55: 1461-1506, 2002). We extend their result to the case of p growth at infinity with p is an element of [1, 2), and to the case of incompressible materials. The main difficulty is the construction of a recovery sequence which satisfies the nonlinear constraint pointwise. One main ingredient is the density of smooth isometries in W(2,2) isometries, which was obtained by Pakzad (J Differ Geom 66:47-69, 2004) for convex domains and by Hornung (Comptes Rendus Mathematique 346:189-192, 2008) for piecewise C(1) domains.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | NONLINEAR 3-DIMENSIONAL ELASTICITY; ISOMETRIC IMMERSIONS; GEOMETRIC RIGIDITY; VARIATIONAL LIMIT; MEMBRANE MODEL; JUSTIFICATION; DERIVATION; ELASTOMERS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Georg Dolzmann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 18 Sep 2020 08:46 |
| Last Modified: | 18 Sep 2020 08:46 |
| URI: | https://pred.uni-regensburg.de/id/eprint/29148 |
Actions (login required)
 |
View Item |
