dc.contributor.author
Dondi, P.
dc.contributor.author
Maione, A.
dc.contributor.author
Wolff-Vorbeck, S.
dc.date.accessioned
2024-10-14T07:27:03Z
dc.date.accessioned
2024-12-09T12:34:56Z
dc.date.available
2024-10-14T07:27:03Z
dc.date.available
2024-12-09T12:34:56Z
dc.identifier.uri
http://hdl.handle.net/2072/537861
dc.description.abstract
We derive a model for the optimization of the bending and torsional rigidities of nonhomogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both rigidities as objectives. We then formulate a phase field approximation of the optimization problem and show the convergence to the aforementioned sharp interface model via Gamma-convergence. In the final part of this work we numerically approximate minimizers of the phase field problem by using a steepest descent approach and relate the resulting optimal shapes to the development of the morphology of plant stems.
eng
dc.description.sponsorship
The authors would like to thank the livMatS Cluster of Excellence (Living, Adaptive and Energy-autonomous Materials Systems) and, in particular, the members Olga Speck and Thomas Speck, from the Plant Biomechanics Group Freiburg, for sharing their knowledge on Plant Biomechanics. The authors would also like to thank Thomas Speck for providing the picture in Figure 2, Laura Melas for useful discussions on the topic and the anonymous referees for their careful reading. P. Dondl and A. Maione are supported by the DFG SPP 2256 project. P. Dondl and S. Wolff-Vorbeck acknowledge the support of the DFG SPP 1886 project (DFG Projects number 422730790). A. Maione is also supported by the INdAM-GNAMPA projects Equazioni differenziali alle derivate parziali di tipo misto o dipendenti da campi di vettori (Project number CUPE53C22001930001) and Pairing e div-curl lemma: estensioni a campi debolmente derivabili e differenziazione non locale (Project number CUPE53C23001670001).
dc.publisher
EDP Sciences
dc.relation.ispartof
ESAIM: Control, Optimisation and Calculus of Variations
dc.rights
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Gamma-convergence
dc.subject.other
Shape optimization
dc.subject.other
Mathematical modeling
dc.subject.other
Sharp interface
dc.subject.other
Phase field problems
dc.subject.other
Diffuse interface
dc.subject.other
Optimality conditions
dc.subject.other
Numerical simulations
dc.subject.other
Steepest descent
dc.subject.other
Plant morphology
dc.title
Phase Field Model for Multi-Material Shape Optimization of Inextensible Rods
dc.type
info:eu-repo/semantics/article
dc.type
info:eu-repo/semantics/publishedVersion
dc.identifier.doi
10.1051/cocv/2024039
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
