Equilibrium configurations of crystals. (English) Zbl 0673.73012

Chipot, Michel; Kinderlehrer, David

Arch. Ration. Mech. Anal. 103, No. 3, 237-277 (1988).

The aim of the paper is to determine equilibrium configurations of elastic crystals under displacement loding conditions by using direct methods. It is proved that for homogeneous deformation the minimum energy configuration is determined by the subenergy density of the energy density W. The results are extended for more general boundary conditions and also for some special homogeneous configurations admitting parametrized measure minima. Stable parametrized measure minimizers are introduced and also parametrized measures which minimize energy with respect to small compactly supported perturbations are studied for which the rank-one convexity of W is proved.

Reviewer: V.Tigoiu

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
74E10	Anisotropy in solid mechanics
49S05	Variational principles of physics

Keywords:

displacement loding conditions; homogeneous deformation; minimum energy configuration; Stable parametrized measure minimizers; rank-one convexity

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