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Research Papers

Finite Element Modeling of the Contact Geometry and Deformation in Biomechanics Applications1

[+] Author and Article Information
Ahmed A. Shabana

Department of Mechanical and
Industrial Engineering,
University of Illinois at Chicago,
Chicago, IL 60607

A version of this paper was presented at the 2012 ASME Design Engineering Technical Conferences and Computer and Information in Engineering Conference.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received August 21, 2012; final manuscript received April 26, 2013; published online June 10, 2013. Assoc. Editor: Aki Mikkola.

J. Comput. Nonlinear Dynam 8(4), 041013 (Jun 10, 2013) (11 pages) Paper No: CND-12-1127; doi: 10.1115/1.4024541 History: Received August 21, 2012; Revised April 26, 2013

The main contribution of this paper is to demonstrate the feasibility of using one computational environment for developing accurate geometry as well as performing the analysis of detailed biomechanics models. To this end, the finite element (FE) absolute nodal coordinate formulation (ANCF) and multibody system (MBS) algorithms are used in modeling both the contact geometry and ligaments deformations in biomechanics applications. Two ANCF approaches can be used to model the rigid contact surface geometry. In the first approach, fully parameterized ANCF volume elements are converted to surface geometry using parametric relationship that reduces the number of independent coordinate lines. This parametric relationship can be defined analytically or using a spline function representation. In the second approach, an ANCF surface that defines a gradient deficient thin plate element is used. This second approach does not require the use of parametric relations or spline function representations. These two geometric approaches shed light on the generality of and the flexibility offered by the ANCF geometry as compared to computational geometry (CG) methods such as B-splines and NURBS (Non-Uniform Rational B-Splines). Furthermore, because B-spline and NURBS representations employ a rigid recurrence structure, they are not suited as general analysis tools that capture different types of joint discontinuities. ANCF finite elements, on the other hand, lend themselves easily to geometric description and can additionally be used effectively in the analysis of ligaments, muscles, and soft tissues (LMST), as demonstrated in this paper using the knee joint as an example. In this study, ANCF finite elements are used to define the femur/tibia rigid body contact surface geometry. The same ANCF finite elements are also used to model the MCL and LCL ligament deformations. Two different contact formulations are used in this investigation to predict the femur/tibia contact forces; the elastic contact formulation which allows for penetrations and separations at the contact points, and the constraint contact formulation in which the nonconformal contact conditions are imposed as constraint equations, and as a consequence, no separations or penetrations at the contact points are allowed. For both formulations, the contact surfaces are described in a parametric form using surface parameters that enter into the ANCF finite element geometric description. A set of nonlinear algebraic equations that depend on the surface parameters is developed and used to determine the location of the contact points. These two contact formulations are implemented in a general MBS algorithm that allows for modeling rigid and flexible body dynamics.

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Figures

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Fig. 2

Femur and tibia profile

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Fig. 3

Surface parameterization

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Fig. 4

ANCF 3D beam element

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Fig. 5

X-displacement of the femur's center of mass ( ECF, ECCF)

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Fig. 6

Z-displacement of the femur's center of mass ( ECF, ECCF)

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Fig. 7

Normal contact force for the knee lateral side ( ECF, ECCF)

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Fig. 8

Normal contact force for the knee medial side ( ECF, ECCF)

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Fig. 9

Sum of normal contact forces (lateral side, medial side, sum)

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Fig. 10

Deformation of the ACL ligament ( ECF, ECCF)

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Fig. 11

Deformation of the PCL ligament ( ECF, ECCF)

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Fig. 12

MCL cross section deformation at the midpoint ( ECF, ECCF)

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Fig. 13

Axial strain at the midpoint for MCL ( ECF, ECCF)

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Fig. 14

Axial strain at the midpoint for MCL (—— previous knee model, actual knee model)

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Fig. 15

Normal contact force for the knee lateral side (—— ECF, ECCF)

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Fig. 16

Normal contact force for the knee medial side (—— ECF, ECCF)

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