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Data-Driven Problems in Elasticity

Conti, S. and Müller, S. and Ortiz, M. (2018) Data-Driven Problems in Elasticity. Archive for Rational Mechanics and Analysis, 229 (1). pp. 79-123. ISSN 0003-9527. https://resolver.caltech.edu/CaltechAUTHORS:20180131-140932556

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Abstract

We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of approximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within this Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to material data sets that are not graphs.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00205-017-1214-0DOIArticle
https://link.springer.com/article/10.1007%2Fs00205-017-1214-0PublisherArticle
http://rdcu.be/FZLtPublisherFree ReadCube access
https://arxiv.org/abs/1708.02880arXivDiscussion Paper
ORCID:
AuthorORCID
Conti, S.0000-0001-7987-9174
Ortiz, M.0000-0001-5877-4824
Additional Information:© 2018 Springer-Verlag GmbH Germany, part of Springer Nature. Received: 16 August 2017; Accepted: 19 December 2017; First Online: 20 January 2018. This work was partially supported by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 1060 “The mathematics of emergent effects”.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SFB 1060
Issue or Number:1
Record Number:CaltechAUTHORS:20180131-140932556
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180131-140932556
Official Citation:Conti, S., Müller, S. & Ortiz, M. Arch Rational Mech Anal (2018) 229: 79. https://doi.org/10.1007/s00205-017-1214-0
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84607
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:31 Jan 2018 22:17
Last Modified:09 Mar 2020 13:18

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