Non-integer viscoelastic constitutive law to model soft biological tissues to in-vivo indentation

Demirci, Nagehan
Tönük, Ergin
Purpose: During the last decades, derivatives and integrals of non-integer orders are being more commonly used for the description of constitutive behavior of various viscoelastic materials including soft biological tissues. Compared to integer order constitutive relations, non-integer order viscoelastic material models of soft biological tissues are capable of capturing a wider range of viscoelastic behavior obtained from experiments. Although integer order models may yield comparably accurate results, non-integer order material models have less number of parameters to be identified in addition to description of an intermediate material that can monotonically and continuously be adjusted in between an ideal elastic solid and an ideal viscous fluid.


Formulation and implementation of a fractional order viscoelastic material model into finite element software and material model parameter identification using in-vivo indenter experiments for soft biological tissues
Demirci, Nagehan; Tönük, Ergin; Department of Mechanical Engineering (2012)
Soft biological tissue material models in the literature are frequently limited to integer order constitutive relations where the order of differentiation of stress and/or strain is integer-valued. However, it has been demonstrated that fractional calculus theory applied in soft tissue material model formulation yields more accurate and reliable soft tissue material models. In this study, firstly a fractional order (where the order of differentation of stress in the constitutive relation is non-integer-valu...
Implementation of fractional order viscoelastic models to finite element method
Hesammokri, Parnian; Tönük, Ergin; Department of Mechanical Engineering (2019)
In the latest decades, fractional calculus has been commonly used to define the behavior of viscoelastic materials. Real viscoelastic materials such as rubbers, polymers, soft biological tissues, asphalt mixtures, soils, etc. represent power law creep and relaxation behaviors. In Scientific literature relaxation and creep of this type of material has been modelled, primarily through single and/or linear combinations of exponential functions, in an effort to capture the contributions of both solid and fluid ...
On the quasi-incompressible finite element analysis of anisotropic hyperelastic materials
Gueltekin, Osman; Dal, Hüsnü; Holzapfel, Gerhard A. (Springer Science and Business Media LLC, 2019-03-01)
Quasi-incompressible behavior is a desired feature in several constitutive models within the finite elasticity of solids, such as rubber-like materials and some fiber-reinforced soft biological tissues. The Q1P0 finite element formulation, derived from the three-field Hu-Washizu variational principle, has hitherto been exploited along with the augmented Lagrangian method to enforce incompressibility. This formulation typically uses the unimodular deformation gradient. However, contributions by Sansour (Eur ...
Non-linear viscoelasticity for epoxy-based polymers: theoretical modeling and numerical implementation
Koral, Ateş; Dal, Hüsnü; Department of Mechanical Engineering (2019)
The present thesis aims at modeling creep behaviour under hydrostatic and uniaxial loadings of a certain silica filled epoxy compound at various temperatures with numerical implementation of algorithms into finite element method. Time dependent behaviour of polymers has been examined and many approaches have been proposed by researchers. Some of the models are inspired from micro-mechanical structure of polymers. These models generally take relaxation of a single entangled chain in a polymer gel matrix upon...
A quasi-incompressible and quasi-inextensible finite element analysis of fibrous soft biological tissues
Gultekin, Osman; Rodoplu, Burak; Dal, Hüsnü (Springer Science and Business Media LLC, 2020-06-01)
The contribution presents anextensionandapplicationof a recently proposed finite element formulation for quasi-inextensible and quasi-incompressible finite hyperelasticity to fibrous soft biological tissues and touches in particular upon computational aspects thereof. In line with theoretical framework presented by Dal (Int J Numer Methods Eng 117:118-140, 2019), the mixed variational formulation is extended to two families of fibers as often encountered while dealing with fibrous tissues. Apart from that, ...
Citation Formats
N. Demirci and E. Tönük, “Non-integer viscoelastic constitutive law to model soft biological tissues to in-vivo indentation,” ACTA OF BIOENGINEERING AND BIOMECHANICS, pp. 13–21, 2014, Accessed: 00, 2020. [Online]. Available: