On application of Fung's quasi-linear viscoelastic model to modeling of impact experiment for articular cartilage

Abstract A one-dimensional impact problem for articular cartilage is considered. Behavior of the coefficient of restitution, peak strain, maximum stress in the drop-weight impact experiment is studied in detail. The non-linear viscoelastic Hunt–Crossley model previously used to fit experimental data is compared with a new quasi-linear viscoelastic Kelvin–Voigt model enriched in Fung's non-linear assumptions. It has been shown that the new model, having clear physical sense, better describes the experimental data.

[1]  W. Ehlers,et al.  A Linear Viscoelastic Two‐Phase Model for Soft Tissues.: Application to Articular Cartilage , 2000 .

[2]  Gennady Mishuris,et al.  Frictionless elliptical contact of thin viscoelastic layers bonded to rigid substrates , 2011 .

[3]  W. Goldsmith,et al.  Impact: the theory and physical behaviour of colliding solids. , 1960 .

[4]  Kumbakonam R. Rajagopal,et al.  Mechanical Response of Polymers: An Introduction , 2000 .

[5]  S L Woo,et al.  Relaxation and creep quasilinear viscoelastic models for normal articular cartilage. , 1984, Journal of biomechanical engineering.

[6]  L. Deseri,et al.  The state of fractional hereditary materials (FHM) , 2014 .

[7]  I. Argatov.  Mathematical modeling of linear viscoelastic impact: Application to drop impact testing of articular cartilage , 2012, 1206.2681.

[8]  Elliptical contact of thin biphasic cartilage layers: exact solution for monotonic loading. , 2011, Journal of biomechanics.

[9]  M. Sato.  [Mechanical properties of living tissues]. , 1986, Iyo denshi to seitai kogaku. Japanese journal of medical electronics and biological engineering.

[10]  Sophia Mã ¶ ller,et al.  Biomechanics — Mechanical properties of living tissue , 1982 .

[11]  Kumbakonam R. Rajagopal,et al.  Modeling the response of nonlinear viscoelastic biodegradable polymeric stents , 2012 .

[12]  V. Popov.  Contact Mechanics and Friction , 2010 .

[13]  R. Jackson,et al.  The fractal structure of equine articular cartilage. , 2012, Scanning.

[14]  B B Seedhom,et al.  The relationship of the compressive modulus of articular cartilage with its deformation response to cyclic loading: does cartilage optimize its modulus so as to minimize the strains arising in it due to the prevalent loading regime? , 2001, Rheumatology.

[15]  W Ehlers,et al.  A linear viscoelastic biphasic model for soft tissues based on the Theory of Porous Media. , 2001, Journal of biomechanical engineering.

[16]  W M Lai,et al.  An asymptotic solution for the contact of two biphasic cartilage layers. , 1994, Journal of biomechanics.

[17]  V. Popov.  Contact Mechanics and Friction: Physical Principles and Applications , 2010 .

[18]  R. Aspden,et al.  Impact testing to determine the mechanical properties of articular cartilage in isolation and on bone , 2008, Journal of materials science. Materials in medicine.

[19]  Arun R. Srinivasa,et al.  On the shear and bending of a degrading polymer beam , 2007 .

[20]  Richard L. Magin,et al.  Fractional-order elastic models of cartilage: A multi-scale approach , 2010 .

[21]  J Goodacre,et al.  Knee acoustic emission: a potential biomarker for quantitative assessment of joint ageing and degeneration. , 2011, Medical engineering & physics.

[22]  B B Seedhom,et al.  The 'instantaneous' compressive modulus of human articular cartilage in joints of the lower limb. , 1999, Rheumatology.

[23]  N. Selyutina,et al.  Impact problem for the quasi-linear viscoelastic standard solid model , 2015, 1503.04758.

[24]  Richard M. Aspden,et al.  Viscoelastic deformation of articular cartilage during impact loading , 2010 .

[25]  Excitation of the elastic half-space surface by normal rebounding impact of an indenter , 2009 .

[26]  E Amler,et al.  Biomechanical characterization of cartilages by a novel approach of blunt impact testing. , 2007, Physiological research.

[27]  I. Argatov.  Asymptotic modeling of the impact of a spherical indenter on an elastic half-space , 2008 .

[28]  Walter Herzog,et al.  An improved solution for the contact of two biphasic cartilage layers , 1997 .

[29]  Massimiliano Zingales,et al.  Power‐law hereditariness of hierarchical fractal bones , 2013, International journal for numerical methods in biomedical engineering.

[30]  Daniel J. Segalman,et al.  Characterizing damping and restitution in compliant impacts via modified K-V and higher-order linear viscoelastic models , 2000 .

[31]  M. Zhuravkov,et al.  Review of methods and approaches for mechanical problem solutions based on fractional calculus , 2016 .