Finite element modelling of unit cells applied to problems of finite deformation
Finite element modelling of unit cells applied to problems of finite deformation
In this paper, application of unit cell (UC) modelling to problems involving finite deformation is presented. Formulation of UCs previously established for problems involving small strains was adapted and extended to cover cases involving geometric nonlinearity. There are two main differences between the two cases as far as the present paper is concerned. First one is the stress-strain output from the analysis, which in linear problems is conventionally given in terms of Cauchy stresses and small strains, while in nonlinear case different measures for both are employed. The second difference is related to the orientation of the local coordinates of the material, which remains unchanged in linear analysis, while re-orients in non-linear analysis. The nature of output out of finite element modelling in cases involving finite deformations has been revealed and explained, and the method for determining average stresses and strains from the analysis inputs and outputs has been developed. The procedures for stress and strain definition are presented, allowing to quantify the stress-strain state in terms of any nonlinear stress-strain characteristics in a straightforward manner. However, a major drawback in finite deformation formulation, as implemented in state-of-the-art FE codes have been exposed, indicating that finite deformation analyses of unit cells for applications to composites are far from been established.
Cauchy stress, Finite deformation, First and second Piola-Kirchhoff stresses, Total, Unit cells, Updated Lagrangian formulation
Sitnikova, Elena
e0c2f901-24fe-43d0-88e8-76f415675104
Li, Shuguang
f99c53b3-e42e-456f-97df-4c4e06de4a40
16 August 2019
Sitnikova, Elena
e0c2f901-24fe-43d0-88e8-76f415675104
Li, Shuguang
f99c53b3-e42e-456f-97df-4c4e06de4a40
Sitnikova, Elena and Li, Shuguang
(2019)
Finite element modelling of unit cells applied to problems of finite deformation.
22nd International Conference on Composite Materials, ICCM 2019, , Melbourne, Australia.
11 - 16 Aug 2019.
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Conference or Workshop Item
(Paper)
Abstract
In this paper, application of unit cell (UC) modelling to problems involving finite deformation is presented. Formulation of UCs previously established for problems involving small strains was adapted and extended to cover cases involving geometric nonlinearity. There are two main differences between the two cases as far as the present paper is concerned. First one is the stress-strain output from the analysis, which in linear problems is conventionally given in terms of Cauchy stresses and small strains, while in nonlinear case different measures for both are employed. The second difference is related to the orientation of the local coordinates of the material, which remains unchanged in linear analysis, while re-orients in non-linear analysis. The nature of output out of finite element modelling in cases involving finite deformations has been revealed and explained, and the method for determining average stresses and strains from the analysis inputs and outputs has been developed. The procedures for stress and strain definition are presented, allowing to quantify the stress-strain state in terms of any nonlinear stress-strain characteristics in a straightforward manner. However, a major drawback in finite deformation formulation, as implemented in state-of-the-art FE codes have been exposed, indicating that finite deformation analyses of unit cells for applications to composites are far from been established.
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Published date: 16 August 2019
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© 2019 International Committee on Composite Materials. All rights reserved.
Venue - Dates:
22nd International Conference on Composite Materials, ICCM 2019, , Melbourne, Australia, 2019-08-11 - 2019-08-16
Keywords:
Cauchy stress, Finite deformation, First and second Piola-Kirchhoff stresses, Total, Unit cells, Updated Lagrangian formulation
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Local EPrints ID: 497694
URI: http://eprints.soton.ac.uk/id/eprint/497694
PURE UUID: eab6a20c-f790-414c-829b-e6284656e2a9
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Date deposited: 29 Jan 2025 18:27
Last modified: 30 Jan 2025 03:32
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Author:
Elena Sitnikova
Author:
Shuguang Li
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