Expressing general constitutive models in FEniCSx using external operators and algorithmic automatic differentiation Article Swipe
Andrey Latyshev
,
Jérémy Bleyer
,
Corrado Maurini
,
Jack Hale
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.46298/jtcam.14449
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.46298/jtcam.14449
Many problems in solid mechanics involve general and non-trivial constitutive models that are difficult to express in variational form. Consequently, it can be challenging to define these problems in automated finite element solvers, such as the FEniCS Project, that use domain-specific languages specifically designed for writing variational forms. In this article, we describe a methodology and software framework for FEniCSx / DOLFINx that enables the expression of constitutive models in nearly any general programming language. We demonstrate our approach on two solid mechanics problems; the first is a simple von Mises elastoplastic model with isotropic hardening implemented with Numba, and the second a Mohr-Coulomb elastoplastic model with apex smoothing implemented with JAX. In the latter case we show that by leveraging JAX's algorithmic automatic differentiation transformations we can avoid error-prone manual differentiation of the terms necessary to resolve the constitutive model. We show extensive numerical results, including Taylor remainder testing, that verify the correctness of our implementation. The software framework and fully documented examples are available as supplementary material under the LGPLv3 or later license.
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- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.46298/jtcam.14449
- https://jtcam.episciences.org/16616/pdf
- OA Status
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- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
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https://openalex.org/W4403407056Canonical identifier for this work in OpenAlex
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https://doi.org/10.46298/jtcam.14449Digital Object Identifier
- Title
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Expressing general constitutive models in FEniCSx using external operators and algorithmic automatic differentiationWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2025Year of publication
- Publication date
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2025-10-01Full publication date if available
- Authors
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Andrey Latyshev, Jérémy Bleyer, Corrado Maurini, Jack HaleList of authors in order
- Landing page
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https://doi.org/10.46298/jtcam.14449Publisher landing page
- PDF URL
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https://jtcam.episciences.org/16616/pdfDirect link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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diamondOpen access status per OpenAlex
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https://jtcam.episciences.org/16616/pdfDirect OA link when available
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Automatic differentiation, Computer science, Mathematical economics, Mathematics, Algorithm, ComputationTop concepts (fields/topics) attached by OpenAlex
- Cited by
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1Total citation count in OpenAlex
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2025: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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