On a class of nonconvex functionals and applications. (Sur une classe de fonctionnelles non convexes et applications.) (French) Zbl 0738.73025

Tahraoui, Rabah

SIAM J. Math. Anal. 21, No. 1, 37-52 (1990).

Existence theorems in finite elasticity can not rely on the convexity of the energy functional — to assume this would contradict material objectivity. In this paper there are existence and regularity results for a very special situation, namely when the domain is an annulus or a ring. The techniques used draw heavily on the method of relaxation. In the end the author gives some applications to finite elasticity.

Reviewer: H.Matthies (Hamburg)

MSC:

74B20	Nonlinear elasticity
58E30	Variational principles in infinite-dimensional spaces
74S30	Other numerical methods in solid mechanics (MSC2010)
74P10	Optimization of other properties in solid mechanics
74A20	Theory of constitutive functions in solid mechanics
49J40	Variational inequalities
58J32	Boundary value problems on manifolds

Keywords:

existence; finite elasticity; convexity of the energy functional; regularity results