Optimal Design of Brittle Composite Materials: a Nonsmooth Approach

Prechtel M, Leugering G, Steinmann P, Stingl M (2012)

Publication Language: English

Publication Type: Journal article

Publication year: 2012


Publisher: Springer Verlag (Germany)

Book Volume: 155

Pages Range: 962-985

Journal Issue: 3

DOI: 10.1007/s10957-012-0094-6


Our goal is to design brittle composite materials yielding maximal energy dissipation for a given static load case. We focus on the effect of variation of fiber shapes on resulting crack paths and thus on the fracture energy. To this end, we formulate a shape optimization problem, in which the cost function is the fracture energy and the state problem consists in the determination of the potentially discontinuous displacement field in the two-dimensional domain. Thereby, the behavior at the crack surfaces is modeled by cohesive laws. We impose a nonpenetration condition to avoid interpenetration of opposite crack sides. Accordingly, the state problem is formulated as variational inequality. This leads to potential nondifferentiability of the shape-state mapping. For the numerical solution, we derive first-order information in the form of subgradients. We conclude the article by numerical results.

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Prechtel, M., Leugering, G., Steinmann, P., & Stingl, M. (2012). Optimal Design of Brittle Composite Materials: a Nonsmooth Approach. Journal of Optimization Theory and Applications, 155(3), 962-985. https://doi.org/10.1007/s10957-012-0094-6


Prechtel, Marina, et al. "Optimal Design of Brittle Composite Materials: a Nonsmooth Approach." Journal of Optimization Theory and Applications 155.3 (2012): 962-985.

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