Optimal Design of Brittle Composite Materials: a Nonsmooth Approach

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Prechtel M, Leugering G, Steinmann P, Stingl M
Zeitschrift: Journal of Optimization Theory and Applications
Verlag: Springer Verlag (Germany)
Jahr der Veröffentlichung: 2012
Band: 155
Heftnummer: 3
Seitenbereich: 962-985
ISSN: 0022-3239
Sprache: Englisch


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.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Leugering, Günter Prof. Dr.
Lehrstuhl für Angewandte Mathematik
Prechtel, Marina Dr.
Graduiertenzentrum der FAU
Steinmann, Paul Prof. Dr.-Ing.
Lehrstuhl für Technische Mechanik
Stingl, Michael Prof. Dr.
Professur für Angewandte Mathematik (Kontinuierliche Optimierung)


Zusätzliche Organisationseinheit(en)
Exzellenz-Cluster Engineering of Advanced Materials


Forschungsbereiche

A3 Multiscale Modeling and Simulation
Exzellenz-Cluster Engineering of Advanced Materials


Zitierweisen

APA:
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://dx.doi.org/10.1007/s10957-012-0094-6

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

BibTeX: 

Zuletzt aktualisiert 2019-14-03 um 10:50