Development of an asymptotic modeling methodology for tibio-femoral contact in multibody dynamic simulations of the human knee joint

A new methodology for modeling articular tibio-femoral contact based on the recently developed asymptotic model of frictionless elliptical contact interaction between thin biphasic cartilage layers is presented. The developed mathematical model of articular contact is extended to the case of contact between arbitrary viscoelastic incompressible coating layers. The approach requires use of the smooth contact surface geometry and efficient contact points detection methods. A generalization of the influence surface theory based method for representing articular surfaces from the unstructured noisy surface data is proposed. The normal contact forces are determined analytically based on the exact solution for elliptical contact between thin cartilage layers modeled as viscoelastic incompressible layers. The effective geometrical characteristics of articular surfaces are introduced for use in the developed asymptotic models of elliptical contact between articular surfaces.

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