Partial differential equations to determine elasto-plastic stress–strain behavior from measured kinematic fields
Partial differential equations to determine elasto-plastic stress–strain behavior from measured kinematic fields
A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed equations that assume pure plastic behavior without elasticity. A method to numerically solve these equations is also presented. In addition to force balance, the equations are derived from the elastic–plastic decomposition of the deformation gradient, the assumption of isotropy, and the assumption that the function mapping the elastic strain to stress is known. The system of equations can be directly applied to complex geometries, finite deformation, non-linear elasticity and plasticity, compressible materials, rate dependent materials, and a variety of hardening laws. This system of PDEs is non-linear and time dependent. Furthermore, it overcomes an important prior limitation: it can be directly applied to cases where some regions of a body are elastically deforming while others are elasto-plastically deforming. A two-dimensional case study of necking in a uniaxial tensile specimen is investigated to illustrate and validate the method. The governing equations are numerically solved using strain fields output from a finite element simulation and validated against this same simulation showing accurate results.
B constitutive behavior, B elastic–plastic material, C numerical algorithms, Digital image correlation
Cameron, Ben
97613b73-58fa-4f8c-85a6-316c4aef7578
Tasan, C. Cem
3e2b5f4f-5e2e-4964-94d4-b53c937fc350
25 January 2023
Cameron, Ben
97613b73-58fa-4f8c-85a6-316c4aef7578
Tasan, C. Cem
3e2b5f4f-5e2e-4964-94d4-b53c937fc350
Cameron, Ben and Tasan, C. Cem
(2023)
Partial differential equations to determine elasto-plastic stress–strain behavior from measured kinematic fields.
International Journal of Plasticity, 162, [103512].
(doi:10.1016/j.ijplas.2022.103512).
Abstract
A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed equations that assume pure plastic behavior without elasticity. A method to numerically solve these equations is also presented. In addition to force balance, the equations are derived from the elastic–plastic decomposition of the deformation gradient, the assumption of isotropy, and the assumption that the function mapping the elastic strain to stress is known. The system of equations can be directly applied to complex geometries, finite deformation, non-linear elasticity and plasticity, compressible materials, rate dependent materials, and a variety of hardening laws. This system of PDEs is non-linear and time dependent. Furthermore, it overcomes an important prior limitation: it can be directly applied to cases where some regions of a body are elastically deforming while others are elasto-plastically deforming. A two-dimensional case study of necking in a uniaxial tensile specimen is investigated to illustrate and validate the method. The governing equations are numerically solved using strain fields output from a finite element simulation and validated against this same simulation showing accurate results.
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e-pub ahead of print date: 14 January 2023
Published date: 25 January 2023
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The authors would like to thank Marie O'Hanrahan for proof reading the manuscript.
Keywords:
B constitutive behavior, B elastic–plastic material, C numerical algorithms, Digital image correlation
Identifiers
Local EPrints ID: 484666
URI: http://eprints.soton.ac.uk/id/eprint/484666
ISSN: 0749-6419
PURE UUID: e327c1fd-446e-447e-9b5c-7c5f4c01c51a
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Date deposited: 20 Nov 2023 17:36
Last modified: 06 Jun 2024 02:15
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Author:
Ben Cameron
Author:
C. Cem Tasan
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