Reinforcement problems in the calculus of variations. (English) Zbl 0607.73018

The authors investigate the torsion of an elastic bar which is surrounded by an increasingly thin layer with an increasingly hard material. The equations of this model problem may be fully nonlinear. Three different expressions of the limit problem depending on the link between thickness and hardness are obtained. The direct methods of the calculus of variations and \(\Gamma\)-convergence allow to give some answers even in the fully nonlinear case. Paper is important for mathematicians interested in reinforcement, \(\Gamma\)-convergence, integral functionals, and non-equicoercive problems.
Reviewer: H.Bufler


74S30 Other numerical methods in solid mechanics (MSC2010)
49J45 Methods involving semicontinuity and convergence; relaxation
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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