Contact problem for a thin elastic layer with variable thickness: Application to sensitivity analysis of articular contact mechanics

Abstract In the framework of the recently developed asymptotic models for tibio-femoral contact incorporating frictionless elliptical contact interaction between thin elastic, viscoelastic, or biphasic cartilage layers, we apply an asymptotic modeling approach for analytical evaluating the sensitivity of crucial parameters in joint contact mechanics due to small variations in the thicknesses of the contacting cartilage layers. The four term asymptotic expansion for the normal displacement at the contact surface is explicitly derived, which recovers the corresponding solution obtained previously for the 2D case in the compressible case. It was found that to minimize the influence of the cartilage thickness non-uniformity on the force–displacement relationship, the effective thicknesses of articular layers should be determined from a special optimization criterion.

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

[2]  James Barber.  Contact problems for the thin elastic layer , 1990 .

[3]  Ferenc Horkay,et al.  Determination of elastic moduli of thin layers of soft material using the atomic force microscope. , 2002, Biophysical journal.

[4]  Ivan Argatov,et al.  Development of an asymptotic modeling methodology for tibio-femoral contact in multibody dynamic simulations of the human knee joint , 2012 .

[5]  M. Matthewson,et al.  Axi-symmetric contact on thin compliant coatings , 1981 .

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

[7]  H W Wevers,et al.  Femoral articular shape and geometry. A three-dimensional computerized analysis of the knee. , 1996, The Journal of arthroplasty.

[8]  Benjamin J Fregly,et al.  Multibody dynamic simulation of knee contact mechanics. , 2004, Medical engineering & physics.

[9]  ELLIPTICAL CONTACT ON ELASTIC INCOMPRESSIBLE COATINGS , 2008 .

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

[11]  Peter Eberhard,et al.  Investigations for the Dynamical Analysis of Human Motion , 1999 .

[12]  Fuqian Yang,et al.  Indentation of an incompressible elastic film , 1998 .

[13]  Walter Herzog,et al.  An articular cartilage contact model based on real surface geometry. , 2005, Journal of biomechanics.

[14]  H. Yoshikawa,et al.  Three-dimensional distribution of articular cartilage thickness in the elderly talus and calcaneus analyzing the subchondral bone plate density. , 2012, Osteoarthritis and cartilage.

[15]  M. Jaffar,et al.  Asymptotic behaviour of thin elastic layers bonded and unbonded to a rigid foundation , 1989 .

[16]  G. Pavliotis,et al.  A perturbation-based numerical method for solving a three-dimensional axisymmetric indentation problem , 2002 .

[17]  Contact Problem For Thin Biphasic Cartilage Layers: Perturbation Solution , 2011 .

[18]  W Herzog,et al.  Modeling axi-symmetrical joint contact with biphasic cartilage layers--an asymptotic solution. , 1996, Journal of biomechanics.

[19]  R Huiskes,et al.  The role of computational models in the search for the mechanical behavior and damage mechanisms of articular cartilage. , 2005, Medical engineering & physics.

[20]  Timo Rantalainen,et al.  Flexible multibody approach in forward dynamic simulation of locomotive strains in human skeleton with flexible lower body bones , 2011 .

[21]  V. M. Aleksandrov.  Asymptotic solution of the contact problem for a thin elastic layer , 1969 .

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

[23]  I. Argatov.  The pressure of a punch in the form of an elliptic paraboloid on a thin elastic layer , 2005 .

[24]  S. I. Barry,et al.  Asymptotic behaviour of thin poroelastic layers , 2001 .

[25]  Benjamin J. Ellis,et al.  Effects of Idealized Joint Geometry on Finite Element Predictions of Cartilage Contact Stresses in the Hip , 2022 .

[26]  V. M. Aleksandrov,et al.  Contact problems for an elastic layer of slight thickness , 1966 .

[27]  Effective approach to the contact problem for a stratum , 2005 .

[28]  Richard S. Chadwick,et al.  Axisymmetric Indentation of a Thin Incompressible Elastic Layer , 2002, SIAM J. Appl. Math..