Physics-constrained local convexity data-driven modeling of anisotropic nonlinear elastic solids

Xiaolong He, Qizhi He, Jiun Shyan Chen, Usha Sinha, Shantanu Sinha

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1 Scopus citations


As characterization and modeling of complex materials by phenomenological models remains challenging, data-driven computing that performs physical simulations directly from material data has attracted considerable attention. Data-driven computing is a general computational mechanics framework that consists of a physical solver and a material solver, based on which data-driven solutions are obtained through minimization procedures. This work develops a new material solver built upon the local convexity-preserving reconstruction scheme by He and Chen (2020) A physics-constrained data-driven approach based on locally convex reconstruction for noisy database. Computer Methods in Applied Mechanics and Engineering 363, 112791 to model anisotropic nonlinear elastic solids. In this approach, a two-level local data search algorithm for material anisotropy is introduced into the material solver in online data-driven computing. A material anisotropic state characterizing the underlying material orientation is used for the manifold learning projection in the material solver. The performance of the proposed data-driven framework with noiseless and noisy material data is validated by solving two benchmark problems with synthetic material data. The data-driven solutions are compared with the constitutive model-based reference solutions to demonstrate the effectiveness of the proposed methods.

Original languageEnglish (US)
JournalData-Centric Engineering
Issue number5
StatePublished - Dec 30 2020
Externally publishedYes

Bibliographical note

Funding Information:
The support of this work by the National Science Foundation under Award Number CCF-1564302 to the first, second, and the third authors, and the National Institute of Health under grant number 5R01AG056999-03 to the first, third, forth, and fifth authors is very much appreciated.

Publisher Copyright:


  • Anisotropy
  • convexity-preserving reconstruction
  • data-driven computational mechanics
  • manifold learning
  • reproducing kernel (RK) approximation


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