A three-dimensional nonlinear model for dissipative response of soft tissue

Rubin, M. B.; Bodner, S. R.

doi:10.1016/s0020-7683(02)00237-8

Cited by 122 publications

(136 citation statements)

References 18 publications

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“…Several studies, e.g., Helfenstein et al [14], Annaidh et al [1] and Nolan et al [22], have reported the erroneous analysis results of fiber-reinforced anisotropic material models for soft biological tissues (Weiss et al [37], Holzapfel et al [16] and Rubin and Bodner [25]) when they are mistakenly used in the compressible domain; e.g., a sphere reinforced with one family of fibers would be deformed into a sphere with a smaller size upon hydrostatic pressure instead of taking on an ellipsoidal shape. One remedy for (ii) is to implement the computationally (rather) expensive augmented Lagrangian method to bring the analysis towards the incompressibility limit, see Glowinski and Le Tallec [8,9] and Simo and Taylor [31] among others.…”

Section: Introductionmentioning

confidence: 99%

On the quasi-incompressible finite element analysis of anisotropic hyperelastic materials

2018

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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 J Mech A Solids 27: [28][29][30][31][32][33][34][35][36][37][38][39] 2007) and Helfenstein et al. (Int J Solids Struct 47:2056-2061 conspicuously demonstrate an alternative concept for analyzing fiber reinforced solids, namely the use of the (unsplit) deformation gradient for the anisotropic contribution, and these authors elaborate on their proposals with analytical evidence. The present study handles the alternative concept from a purely numerical point of view, and addresses systematic comparisons with respect to the classical treatment of the Q1P0 element and its coalescence with the augmented Lagrangian method by means of representative numerical examples. The results corroborate the new concept, show its numerical efficiency and reveal a direct physical interpretation of the fiber stretches.

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Section: Introductionmentioning

confidence: 99%

On the quasi-incompressible finite element analysis of anisotropic hyperelastic materials

2018

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“…These include viscoelasticity of the collagen fibers (Rubin and Bodner, 2002), the extracellular matrix (Weiss et al, 2002), collagen fibril crosslinking (Bailey et al, 1974;Puxkandl et al, 2002;Redaelli et al, 2003) and fluid content (Chimich et al, 1992) and fluid movement within and in/out of the tissue during loading (Atkinson et al, 1997;Butler et al, 1997). However, most proposals have been based on conjecture and there is little experimental data available to support or refute the proposed mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Permeability of human medial collateral ligament in compression transverse to the collagen fiber direction

Weiss

Maakestad

2006

Journal of Biomechanics

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This study quantified the apparent and intrinsic hydraulic permeability of human medial collateral ligament (MCL) under direct permeation transverse to the collagen fiber direction. A custom permeation device was built to apply flow across cylindrical samples of ligament while monitoring the resulting pressure gradient. MCLs from 5 unpaired human knees were used (donor age 55 AE 16 yr; 4 males, 1 female). Permeability measurements were performed at 3 levels of compressive pre-strain (10%, 20% and 30%) and 5 pressures (0.17, 0.34, 1.03, 1.72 and 2.76 MPa). Apparent permeability was determined from Darcy's law, while intrinsic permeability was determined from the zero-pressure crossing of the pressure-permeability curves at each compressive pre-strain. Resulting data were fit to a finite deformation constitutive law [Journal of Biomechanics 23 (1990) 1145-1156. The apparent permeability of human MCL ranged from 0:40 AE 0:05 to 8:60 AE 0:77 Â 10 À16 m 4 =N s depending on pre-strain and pressure gradient. There was a significant decrease in apparent permeability with increasing compressive pre-strain ðp ¼ 0:024Þ and pressure gradient ðpo0:001Þ; and there was a significant interaction between the effects of compressive pre-strain and pressure ðpo0:001Þ: Intrinsic permeability was 14:14 AE 0:74; 6:30 AE 2:13 and 4:29 AE 1:71 Â 10 À16 m 4 =N s for compressive pre-strains of 10%, 20% and 30%, respectively. The intrinsic permeability showed a faster decrease with increasing compressive pre-strain than that of bovine articular cartilage. These data provide a baseline for investigating the effects of disease and chemical modification on the permeability of ligament and the data should also be useful for modeling the poroelastic material behavior of ligaments. r

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“…In line with the theory outlined in [Rubin, 1994a[Rubin, ,b, 1996Rubin and Bodner, 2002] the material rates of the kinematic quantities relating to these elastic deformations are expressed in a general form bẏ…”

Section: Kinematic Frameworkmentioning

confidence: 99%

“…The soft tissue model proposed by Rubin and Bodner [2002] provides a versatile framework [Helfenstein et al, 2010] to represent the mechanical behavior of collagenous tissues [Mazza et al, 2005;Barbarino et al, 2011;Weickenmeier and Jabareen, 2014;Flynn and Rubin, 2014;Safadi and Rubin, 2014] offering the possibility to include dissipative, inelastic characteristics. In application to FM tissues, Jabareen et al [2009] used an elastic isotropic formulation of the Rubin-Bodner (RB) model to represent the uniaxial response of the amnion.…”

Section: Introductionmentioning

confidence: 99%

A model for the compressible, viscoelastic behavior of human amnion addressing tissue variability through a single parameter

Mauri

Ehret

Focatiis

et al. 2015

Biomech Model Mechanobiol

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A viscoelastic, compressible model is proposed to rationalize the recently reported response of human amnion in multiaxial relaxation and creep experiments. The theory includes two viscoelastic contributions responsible for the short-and long-term timedependent response of the material. These two contributions can be related to physical processes: water flow through the tissue and dissipative characteristics of the collagen fibers, respectively. An accurate agreement of the model with the mean tension and kinematic response of amnion in uniaxial relaxation tests was achieved. By variation of a single linear factor that accounts for the variability among tissue samples, the model provides very sound predictions not only of the uniaxial relaxation but also of the uniaxial creep and strip-biaxial relaxation behavior of individual samples. This suggests that a wide range of viscoelastic behaviors due to patient-specific variations in tissue composition * AM and AEE share first authorship of this article.

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A three-dimensional nonlinear model for dissipative response of soft tissue

Cited by 122 publications

References 18 publications

On the quasi-incompressible finite element analysis of anisotropic hyperelastic materials

On the quasi-incompressible finite element analysis of anisotropic hyperelastic materials

Permeability of human medial collateral ligament in compression transverse to the collagen fiber direction

A model for the compressible, viscoelastic behavior of human amnion addressing tissue variability through a single parameter

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