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Data-Driven Finite Elasticity

Conti, S. and Müller, S. and Ortiz, M. (2020) Data-Driven Finite Elasticity. Archive for Rational Mechanics and Analysis, 237 (1). pp. 1-33. ISSN 0003-9527. https://resolver.caltech.edu/CaltechAUTHORS:20200313-132836970

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Abstract

We extend to finite elasticity the Data-Driven formulation of geometrically linear elasticity presented in Conti et al. (Arch Ration Mech Anal 229:79–123, 2018). The main focus of this paper concerns the formulation of a suitable framework in which the Data-Driven problem of finite elasticity is well-posed in the sense of existence of solutions. We confine attention to deformation gradients F ∈ L^p(Ω;R^(n x n)) and first Piola-Kirchhoff stresses P ∈ L^q(Ω;R^(n x n)), with (p,q) ∈ (1, ∞) and 1/p + 1/q = 1. We assume that the material behavior is described by means of a material data set containing all the states (F, P) that can be attained by the material, and develop germane notions of coercivity and closedness of the material data set. Within this framework, we put forth conditions ensuring the existence of solutions. We exhibit specific examples of two- and three-dimensional material data sets that fit the present setting and are compatible with material frame indifference.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00205-020-01490-xDOIArticle
ORCID:
AuthorORCID
Conti, S.0000-0001-7987-9174
Ortiz, M.0000-0001-5877-4824
Additional Information:© 2020 Springer Nature. Received 15 January 2020. Accepted 27 January 2020. Published 13 March 2020. This work was partially Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via Project 211504053 - SFB 1060 and Project 390685813 - GZ 2047/1 - HCM.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)211504053 - SFB 1060
Deutsche Forschungsgemeinschaft (DFG)390685813 - GZ 2047/1 - HCM
Issue or Number:1
Record Number:CaltechAUTHORS:20200313-132836970
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200313-132836970
Official Citation:Conti, S., Müller, S. & Ortiz, M. Data-Driven Finite Elasticity. Arch Rational Mech Anal 237, 1–33 (2020). https://doi.org/10.1007/s00205-020-01490-x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101904
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:16 Mar 2020 14:44
Last Modified:22 Apr 2020 15:29

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