Optimal control of cracks in elastic bodies with thin rigid inclusions. (English) Zbl 1370.74136
Summary: We consider the control of cracks in elastic bodies with rigid inclusion. We first describe the problem statement, provide an equivalent formulation as a variational inequality and prove existence and uniqueness of solutions. Furthermore, we consider this problem as a limiting problem when the elasticity parameters of the inclusion tend to infinity. Then we formulate the optimal control problems and derive an explicit formula for the crack sensitivity and for the energy release rate. We show existence of optimal solutions.
MSC:
| 74R10 | Brittle fracture |
| 49N90 | Applications of optimal control and differential games |
| 74P05 | Compliance or weight optimization in solid mechanics |
| 74Q05 | Homogenization in equilibrium problems of solid mechanics |
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