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Unified viscoelasticity: applying discrete element models to soft tissues with two characteristic times

Unified viscoelasticity: applying discrete element models to soft tissues with two characteristic times
Unified viscoelasticity: applying discrete element models to soft tissues with two characteristic times
Discrete element models have often been the primary tool in investigating and characterising the viscoelastic behaviour of soft tissues. However, studies have employed varied configurations of these models, based on the choice of the number of elements and the utilised formation, for different subject tissues. This approach has yielded a diverse array of viscoelastic models in the literature, each seemingly resulting in different descriptions of viscoelastic constitutive behaviour and/or stress-relaxation and creep functions. Moreover, most studies do not apply a single discrete element model to characterise both stress-relaxation and creep behaviours of tissues. The underlying assumption for this disparity is the implicit perception that the viscoelasticity of soft tissues cannot be described by a universal behaviour or law, resulting in the lack of a unified approach in the literature based on discrete element representations. This paper derives the constitutive equation for different viscoelastic models applicable to soft tissues with two characteristic times. It demonstrates that all possible configurations exhibit a unified and universal behaviour, captured by a single constitutive relationship between stress, strain and time as: View the MathML source?+A??+B?¨=P??+Q?¨. The ensuing stress-relaxation G(t) and creep J(t ) functions are also unified and universal, derived as View the MathML sourceG(t)=c1e?A+A2?4B2Bt+(?0?c1)e?A?A2?4B2Bt and View the MathML sourceJ(t)=c2+(?0?c2)e-PQt+?0Pt, respectively. Application of these relationships to experimental data is illustrated for various tissues including the aortic valve, ligament and cerebral artery. The unified model presented in this paper may be applied to all tissues with two characteristic times, obviating the need for employing varied configurations of discrete element models in preliminary investigation of the viscoelastic behaviour of soft tissues.
viscoelasticity, discrete element models, stress-relaxation, creep, unified constitutive equation, soft tissues
0021-9290
3128-3134
Anssari-Benam, Afshin
176110a2-cb00-496f-89fb-a09368dc4514
Bucchi, Andrea
9a30ab33-8b04-4bca-ab3a-4e42723f8215
Bader, Dan L.
9884d4f6-2607-4d48-bf0c-62bdcc0d1dbf
Anssari-Benam, Afshin
176110a2-cb00-496f-89fb-a09368dc4514
Bucchi, Andrea
9a30ab33-8b04-4bca-ab3a-4e42723f8215
Bader, Dan L.
9884d4f6-2607-4d48-bf0c-62bdcc0d1dbf

Anssari-Benam, Afshin, Bucchi, Andrea and Bader, Dan L. (2015) Unified viscoelasticity: applying discrete element models to soft tissues with two characteristic times. Journal of Biomechanics, 48 (12), 3128-3134. (doi:10.1016/j.jbiomech.2015.07.015). (PMID:26232814)

Record type: Article

Abstract

Discrete element models have often been the primary tool in investigating and characterising the viscoelastic behaviour of soft tissues. However, studies have employed varied configurations of these models, based on the choice of the number of elements and the utilised formation, for different subject tissues. This approach has yielded a diverse array of viscoelastic models in the literature, each seemingly resulting in different descriptions of viscoelastic constitutive behaviour and/or stress-relaxation and creep functions. Moreover, most studies do not apply a single discrete element model to characterise both stress-relaxation and creep behaviours of tissues. The underlying assumption for this disparity is the implicit perception that the viscoelasticity of soft tissues cannot be described by a universal behaviour or law, resulting in the lack of a unified approach in the literature based on discrete element representations. This paper derives the constitutive equation for different viscoelastic models applicable to soft tissues with two characteristic times. It demonstrates that all possible configurations exhibit a unified and universal behaviour, captured by a single constitutive relationship between stress, strain and time as: View the MathML source?+A??+B?¨=P??+Q?¨. The ensuing stress-relaxation G(t) and creep J(t ) functions are also unified and universal, derived as View the MathML sourceG(t)=c1e?A+A2?4B2Bt+(?0?c1)e?A?A2?4B2Bt and View the MathML sourceJ(t)=c2+(?0?c2)e-PQt+?0Pt, respectively. Application of these relationships to experimental data is illustrated for various tissues including the aortic valve, ligament and cerebral artery. The unified model presented in this paper may be applied to all tissues with two characteristic times, obviating the need for employing varied configurations of discrete element models in preliminary investigation of the viscoelastic behaviour of soft tissues.

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Accepted/In Press date: 11 July 2015
Published date: 18 September 2015
Keywords: viscoelasticity, discrete element models, stress-relaxation, creep, unified constitutive equation, soft tissues
Organisations: Faculty of Health Sciences

Identifiers

Local EPrints ID: 390213
URI: https://eprints.soton.ac.uk/id/eprint/390213
ISSN: 0021-9290
PURE UUID: b03dc1fe-eb55-43e5-a695-86c17916a90d
ORCID for Dan L. Bader: ORCID iD orcid.org/0000-0002-1208-3507

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Date deposited: 22 Mar 2016 12:01
Last modified: 20 Jul 2019 00:45

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