On discontinuities when computing the stress-field from the strain: A finite volume discretization
On discontinuities when computing the stress-field from the strain: A finite volume discretization
This article focuses on developing a finite volume discretization for a recently-developed and widely-applicable system of PDEs, enabling computation of the full-field stress from a measured strain field and traction boundary conditions. This is applicable to datasets obtained via DIC, and applies when the material properties are unknown. Interestingly, the strain or strain-rate discontinuities at the interfaces between finite volumes cause reflection and transmission of the principal stresses. Hence, we analytically analyze the solution structure in this case, enabling the development of the discretization. In addition, analysis is conducted translating knowledge of the traction at the boundary into boundary conditions, so that the numerical method can be applied to a variety of loading conditions. The finite volume discretization is validated using strain fields obtained from finite element simulations. The developed discretization enables the system of equations to be applied to irregular geometries, finite deformation, general boundary conditions, and avoids instabilities that arise due to the Courant–Friedrichs–Lewy condition, significantly increasing the range of applications for which these PDEs can be applied.
Inverse problem, characteristics, constitutive behavior, mechanical testing, numerical algorithms
Cameron, Ben
97613b73-58fa-4f8c-85a6-316c4aef7578
Tasan, Cem
6a3a4be9-fa0b-4fb5-ab4f-d4f274881277
24 August 2022
Cameron, Ben
97613b73-58fa-4f8c-85a6-316c4aef7578
Tasan, Cem
6a3a4be9-fa0b-4fb5-ab4f-d4f274881277
Cameron, Ben and Tasan, Cem
(2022)
On discontinuities when computing the stress-field from the strain: A finite volume discretization.
International Journal of Solids and Structures, 254-255, [111912].
(doi:10.1016/j.ijsolstr.2022.111912).
Abstract
This article focuses on developing a finite volume discretization for a recently-developed and widely-applicable system of PDEs, enabling computation of the full-field stress from a measured strain field and traction boundary conditions. This is applicable to datasets obtained via DIC, and applies when the material properties are unknown. Interestingly, the strain or strain-rate discontinuities at the interfaces between finite volumes cause reflection and transmission of the principal stresses. Hence, we analytically analyze the solution structure in this case, enabling the development of the discretization. In addition, analysis is conducted translating knowledge of the traction at the boundary into boundary conditions, so that the numerical method can be applied to a variety of loading conditions. The finite volume discretization is validated using strain fields obtained from finite element simulations. The developed discretization enables the system of equations to be applied to irregular geometries, finite deformation, general boundary conditions, and avoids instabilities that arise due to the Courant–Friedrichs–Lewy condition, significantly increasing the range of applications for which these PDEs can be applied.
Text
On discontinuities when computing the stress-field from the strain. pdf
- Accepted Manuscript
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Accepted/In Press date: 26 July 2022
e-pub ahead of print date: 30 July 2022
Published date: 24 August 2022
Keywords:
Inverse problem, characteristics, constitutive behavior, mechanical testing, numerical algorithms
Identifiers
Local EPrints ID: 472653
URI: http://eprints.soton.ac.uk/id/eprint/472653
ISSN: 0020-7683
PURE UUID: 0b3053dc-dbbb-49b1-8b0d-85ec2e11a6cf
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Date deposited: 13 Dec 2022 17:42
Last modified: 30 Jul 2024 04:01
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Contributors
Author:
Ben Cameron
Author:
Cem Tasan
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