Influence of the contact model on the dynamic response of the human knee joint

Abstract

The goal of this work is to study the influence of the contact force model, contact geometry, and contact material properties on the dynamic response of a human knee joint model. For this purpose, a multibody knee model composed by two rigid bodies, the femur and the tibia, and four non-linear spring elements that represent the main knee ligaments, is considered. The contact force models used were the Hertz, the Hunt-Crossley, and the Lankarani-Nikravesh approaches. Results obtained from computational simulations show that Hertz law is less suitable to describe the dynamic response of the cartilage contact, because this pure elastic model does not account for the viscoelastic nature of the human articulations. Since knee can exhibit conformal and non-conformal contact scenarios, three different geometrical configurations for femur-tibia contact are considered, that is convex-convex sphere contact, convex-concave sphere contact, and convex sphere-plane contact. The highest level of contact forces is obtained for the case of convex-convex sphere contact. As far as the influence of the material contact properties is concerned, the dynamic response of a healthy and natural knee is analysed and compared with three pathological and two artificial knee models. The obtained results demonstrate that the presence of the cartilage reduces significantly the knee contact forces.

A new shoulder model with a biologically inspired glenohumeral joint

“…force developed in the contact between the humeral head and the glenoid cavity is modelled by the Hertz contact law, which assumes the contacting materials to be homogeneous, linear elastic, and isotropic [48] . In other words, its applicability to the GH joint is limited because it does not take into account the viscoelastic nature of the biological joints [49] . Furthermore, the generalized stiffness constant considered is related to the tibio-femoral joint, instead of the GH joint, because no data was found for it.…”

Articular Contact Mechanics from an Asymptotic Modeling Perspective: A Review

“…There is a vast literature on modeling of reaction contact forces generated in joints (Silva et al, 1997; Flores et al, 2011; Machado et al, 2011; Monteiro et al, 2011). A majority of the employed models represent variations of the following model introduced by Hunt and Crossley, 1975: $FMathClass-rel=\text{italicbk}{x}^n\dot{x}MathClass-bin+k{x}^{n}MathClass-punc.$…”

“…On the other hand, the analytical modeling of articular contact is necessary in formulating equations for the reaction forces generated in joints during multibody simulations of human and animal movements (Delp and Loan, 2000; Machado et al, 2011). …”

A comparative study of the viscoelastic constitutive models for frictionless contact interfaces in solids

“…In this approach, there are no impulses at the instant of contact, and hence, there is no need for impulse dynamics calculations and the contact loss can easily be determined from the position and velocity data [47]. One of the main drawbacks associated with the penalty approach deals with the difficulty to choose the contact parameters that contribute to the evaluation of the contact force, such as the stiffness and damping of the contacting surfaces and the degree of nonlinearity of the indentation, especially for complex scenarios or nonmetallic materials [48,49]. Another disadvantage of this formulation is that it can introduce highly-frequency dynamics into the system, due to the presence of stiff springs in compliant surfaces.…”