Mathematical analysis of nonlinear elasticity for elucidation of fracture phenomena

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With application to fracture phenomena in mind, we studied mathematical analyses for the following nonlinear problems and obtained the results. First, in nonlinear elasticity which has a crack and the stress-strain relation is governed by power law, we showed a unique solvability of the weak solution for the boundary value problem. Second, we proved a solvability of the solution of a boundary value problem as a model of interfacial crack under the nonlinear condition (Coulomb friction law and non-penetration condition) between two bonded dissimilar linearized elastic media. Further, we investigated the behavior of the solution near the crack tip.