Knee Joint Models for Kneeling Biomechanics - Computational Biomechanics of the Musculoskeletal System - page 87

table 7.1
material Properties and element types defined in the Finite element model

Component element type young's modulus e (mPa) Poisson's ratio v

Bony structures 8-node hexahedra 20,000 0.3

Cartilage 8-node hexahedra 10 0.45

Menisci 8-node hexahedra Circumferential: 140

Radial and axial: 20

In-plane: 0.2
Out-of-plane: 0.3

Ligaments and patellar
tendon

8-node hexahedra Hyperelastic 0.49

Ground support 8-node hexahedra Upper layer: 20,000

Lower layer: rigid

0.1
-

with a radial and axial modulus of 20 MPa and a circumferential modulus of 140 MPa. The in-
plane Poisson's ratio was 0.2 while the out-of-plane Poisson's ratio was 0.3 (Donahue et al. 2002;
Netravali et al. 2011). The ligaments were assumed to behave as an isotropic hyperelastic material.
Although attempts have been made to involve some sophisticated anisotropic hyperelastic descrip-
tions (Pena et al. 2006), in this chapter the ligament behavior was assumed to be homogeneous and
isotropic to avoid the coding process in ABAQUS's user-defined subroutine. To simply the process,
the coefficients form of input was not used. Instead, test data on the stress-strain relationship of
each ligament obtained from previous FE and experimental studies was inputted (Butler, Kay, and
Stouffer 1986; Shirazi-Adl and Mesfar 2005). The patellar tendon was set as compressible since it
would bear contact loads from the ground, while the ligaments were assumed to be incompressible.
In the literature, the testing data usually only includes tension since ligaments are considered to be
incompressible. Thus, in ABAQUS, the compressive side of the stress-strain curve needed to be
added. In practice, a completely incompressible material may lead to problems with convergence, so
a material with properties approaching incompressibility is preferable. By this approach, the input
process may be hastened, but attention should be paid to the results of the material evaluation to
determine whether the material description can fit the results. In this chapter, the Ogden model with
second-order energy potential was used. The summary of material properties and element types can
be seen in Table 7.1.

7.2.2 l oadinG and B oundary c onditionS
The inner surfaces of cartilages and the connecting faces of ligaments were assumed to be rigidly
fixed to corresponding bones, while for menisci only the two horns of each one were fixed. The
interaction between cartilages and menisci was defined with frictionless contact. The boundary
conditions for this kneeling model had the femur fixed in space with the tibia set totally free. The
ground plane was allowed to move only perpendicularly, with the other five degrees of freedom
limited. The end surface of the patellar tendon was constrained, as it can only have displacement
parallel to the direction of the femur. Muscle forces (quadriceps 215 N, biceps 31 N, and semimem-
branosus 54 N) were used to simulate the physiological loading of the knee joint (Wickiewicz et al.
1983; Hofer et al. 2011). An incrementally increased load up to 1000 N was applied to the ground,
which can only move perpendicularly towards the femur. Contact interaction was defined for carti-
lages, menisci, and possible contact regions between ligaments and bony structures. According to
the literature, prestrain for ligaments was also applied (Table 7.2), and ligaments were divided into
anterior and posterior parts.