title: Unified viscoelasticity: Applying discrete element models to soft tissues with two characteristic times.
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: σ+Aσ̇+Bσ¨=Pε̇+Qε¨. The ensuing stress-relaxation G(t) and creep J(t) functions are also unified and universal, derived as [Formula: see text] and J(t)=c2+(ε0-c2)e(-PQt)+σ0Pt, 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.
authors.affiliation: School of Engineering, University of Portsmouth, Anglesea Road, Portsmouth PO1 3DJ, United Kingdom. Electronic address: afshin.anssari-benam@port.ac.uk.
authors.forename: Afshin
authors.initials: A
authors.lastname: Anssari-Benam
authors.affiliation: School of Engineering, University of Portsmouth, Anglesea Road, Portsmouth PO1 3DJ, United Kingdom.
authors.forename: Andrea
authors.initials: A
authors.lastname: Bucchi
authors.affiliation: Faculty of Health Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.
authors.forename: Dan L
authors.initials: DL
authors.lastname: Bader
mesh_terms: D001021:Aortic Valve; D001696:Biomechanical Phenomena; D002536:Cerebral Arteries; D004548:Elasticity; D006801:Humans; D008022:Ligaments; D013314:Stress, Mechanical; D013997:Time Factors; D014783:Viscosity
keywords: Creep; Discrete element models; Soft tissues; Stress-relaxation; Unified constitutive equation; Viscoelasticity