Optimal Design of Brittle Composite Materials: a Nonsmooth Approach

Marina Prechtel (), Günter Leugering (), Paul Steinmann () and Michael Stingl ()
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Marina Prechtel: University of Erlangen-Nuremberg
Günter Leugering: University of Erlangen-Nuremberg
Paul Steinmann: University of Erlangen-Nuremberg
Michael Stingl: University of Erlangen-Nuremberg

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 3, No 12, 962-985

Abstract: Abstract 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.

Keywords: Shape optimization; Variational inequality; Nonsmooth optimization (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-0094-6

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