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Data-driven computational mechanics

Kirchdoerfer, T. and Ortiz, M. (2016) Data-driven computational mechanics. Computer Methods in Applied Mechanics and Engineering, 304 . pp. 81-101. ISSN 0045-7825. http://resolver.caltech.edu/CaltechAUTHORS:20160316-133550600

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Abstract

We develop a new computing paradigm, which we refer to as data-driven computing, according to which calculations are carried out directly from experimental material data and pertinent constraints and conservation laws, such as compatibility and equilibrium, thus bypassing the empirical material modeling step of conventional computing altogether. Data-driven solvers seek to assign to each material point the state from a prespecified data set that is closest to satisfying the conservation laws. Equivalently, data-driven solvers aim to find the state satisfying the conservation laws that is closest to the data set. The resulting data-driven problem thus consists of the minimization of a distance function to the data set in phase space subject to constraints introduced by the conservation laws. We motivate the data-driven paradigm and investigate the performance of data-driven solvers by means of two examples of application, namely, the static equilibrium of nonlinear three-dimensional trusses and linear elasticity. In these tests, the data-driven solvers exhibit good convergence properties both with respect to the number of data points and with regard to local data assignment. The variational structure of the data-driven problem also renders it amenable to analysis. We show that, as the data set approximates increasingly closely a classical material law in phase space, the data-driven solutions converge to the classical solution. We also illustrate the robustness of data-driven solvers with respect to spatial discretization. In particular, we show that the data-driven solutions of finite-element discretizations of linear elasticity converge jointly with respect to mesh size and approximation by the data set.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1510.04232arXivDiscussion Paper
http://dx.doi.org/10.1016/j.cma.2016.02.001DOIArticle
http://www.sciencedirect.com/science/article/pii/S0045782516300238PublisherArticle
Additional Information:© 2016 Elsevier. Received 10 September 2015, Revised 19 January 2016, Accepted 1 February 2016, Available online 8 February 2016. The support of Caltech's Center of Excellence on High-Rate Deformation Physics of Heterogeneous Materials, AFOSR Award FA9550-12-1-0091, is gratefully acknowledged.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0091
Subject Keywords:Data science; Big data; Approximation theory; Scientific computing
Record Number:CaltechAUTHORS:20160316-133550600
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160316-133550600
Official Citation:T. Kirchdoerfer, M. Ortiz, Data-driven computational mechanics, Computer Methods in Applied Mechanics and Engineering, Volume 304, 1 June 2016, Pages 81-101, ISSN 0045-7825, http://dx.doi.org/10.1016/j.cma.2016.02.001. (http://www.sciencedirect.com/science/article/pii/S0045782516300238)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65395
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Mar 2016 20:49
Last Modified:05 Jan 2017 00:11

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