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Polyconvex neural networks for hyperelastic constitutive models: A rectification approach

Publication ,  Journal Article
Chen, P; Guilleminot, J
Published in: Mechanics Research Communications
October 1, 2022

A simple approach to rectify unconstrained neural networks for hyperelastic constitutive models is proposed with the aim of ensuring both mathematical well-posedness (in terms of existence theorems) and physical consistency. The surrogate involves neural networks that are made admissible by selecting a proper parameterization, following standard results in continuum mechanics, and by enforcing polyconvexity through integral representations. The relevance of the formulation is demonstrated by considering digitally synthesized and experimental datasets for isotropic and anisotropic materials, including the case of soft biological tissues.

Duke Scholars

Published In

Mechanics Research Communications

DOI

ISSN

0093-6413

Publication Date

October 1, 2022

Volume

125

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4901 Applied mathematics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics
 

Citation

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Chen, P., & Guilleminot, J. (2022). Polyconvex neural networks for hyperelastic constitutive models: A rectification approach. Mechanics Research Communications, 125. https://doi.org/10.1016/j.mechrescom.2022.103993
Chen, P., and J. Guilleminot. “Polyconvex neural networks for hyperelastic constitutive models: A rectification approach.” Mechanics Research Communications 125 (October 1, 2022). https://doi.org/10.1016/j.mechrescom.2022.103993.
Chen P, Guilleminot J. Polyconvex neural networks for hyperelastic constitutive models: A rectification approach. Mechanics Research Communications. 2022 Oct 1;125.
Chen, P., and J. Guilleminot. “Polyconvex neural networks for hyperelastic constitutive models: A rectification approach.” Mechanics Research Communications, vol. 125, Oct. 2022. Scopus, doi:10.1016/j.mechrescom.2022.103993.
Chen P, Guilleminot J. Polyconvex neural networks for hyperelastic constitutive models: A rectification approach. Mechanics Research Communications. 2022 Oct 1;125.
Journal cover image

Published In

Mechanics Research Communications

DOI

ISSN

0093-6413

Publication Date

October 1, 2022

Volume

125

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4901 Applied mathematics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics