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Abstract Constitutive relations close the balance laws of continuum mechanics and serve as a surrogate for a material in the design and engineering process. The problem of obtaining the constitutive relations is an indirect inverse problem where both the relation and the quantities that define the relation have to be inferred from experimental observations. The advent of full-field observation techniques promises a new ability to learn constitutive relations under realistic operational conditions. However, this is done in two steps, first by obtaining deformations from the images and then by obtaining the constitutive relation from deformations and forces. This leads to a variety of difficulties. In this article, we propose a novel approach that enables us to obtain constitutive relations directly from the raw data consisting of images and force measurements.
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This content will become publicly available on February 1, 2026
Circumferential shear for an incompressible non-Green elastic cylindrical annulus
The circumferential shear of a nonlinear isotropic incompressible elastic annulus is studied using the neo-Hookean, Ogden constitutive relations in addition to a new constitutive relation for the Hencky strain in terms of the Cauchy stress. The predictions of the three constitutive relations to the specific boundary value problem are delineated. In view of the predictions being quite distinct between the new constitutive relation studied and that for the Ogden constitutive relation, it would be worthwhile to carry out an experiment to determine the efficacy of the models.
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- Award ID(s):
- 2307563
- PAR ID:
- 10644158
- Publisher / Repository:
- Sage
- Date Published:
- Journal Name:
- Mathematics and Mechanics of Solids
- Volume:
- 30
- Issue:
- 2
- ISSN:
- 1081-2865
- Page Range / eLocation ID:
- 340 to 355
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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