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Derivation of a rod theory for biphase materials with dislocations at the interface. (English) Zbl 1274.74064
Summary: Starting from three-dimensional elasticity we derive a rod theory for biphase materials with a prescribed dislocation at the interface. The stored energy density is assumed to be non-negative and to vanish on a set consisting of two copies of \(SO(3)\). First, we rigorously justify the assumption of dislocations at the interface. Then, we consider the typical scaling of multiphase materials and we perform an asymptotic study of the rescaled energy, as the diameter of the rod goes to zero, in the framework of \(\Gamma \)-convergence.

MSC:
74B20 Nonlinear elasticity
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74N05 Crystals in solids
49J45 Methods involving semicontinuity and convergence; relaxation
46E40 Spaces of vector- and operator-valued functions
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