Multiscale Modeling of Ligaments and Tendons - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 109

E fiber =350 MPa

E transverse =10 MPa

E shear =0.125 MPa

E compressive =0.05 MPa

Fig. 4 The elastic behavior of ligament is anisotropic and nonlinear. The tensile stiffness along
the fiber direction is an order of magnitude stiffer than in the transverse direction (left)[ 34 , 183 ].
In shear, ligament is two orders of magnitude more compliant than in the transverse direction
(center)[ 234 ]. In compression, ligament is over three times more compliant than in tension,
indicating compression-tension nonlinearity (right)[ 231 ]. Approximate linear modulus (E)is
shown for each test type

It has been hypothesized that the nonlinear toe region results from the uncrimping
and/or successive recruitment of the aligned collagen fibers, while the linear region
is understood as the tensile response of the collagen fibers. The reported linear
modulus varies widely between tissue types, location and studies [ 19 , 34 , 147 , 243 ,
245 , 250 ]. The tensile response in the direction transverse to the fiber axis is nearly
linear and an order of magnitude more compliant than the longitudinal response
(Fig. 4 , left). The shear response is nonlinear, with a tangent stiffness that is three
orders of magnitude less than the fiber stiffness (Fig. 4 , middle). Ligament stiffness
is lowest when tested in unconfined compression transverse to the fiber axis,
yielding a nonlinear response with a tangent compressive modulus nearly four
orders of magnitude less than the tensile modulus of the fiber family (Fig. 4 , right).
The elastic volumetric response describes the change in volume in response to
tensile or compressive loading. This has most commonly been reported as the
Poisson's ratio (which is a linear measure of volume change), and less commonly
as the Poisson's function (which is a nonlinear measure of volume change) [ 25 ,
187 ]. The Poisson's ratio (or function) is a kinematic measure that relates the
axially applied strain to the laterally induced strain [ 25 ]. Experimentally measured
Poisson's ratios for uniaxial tensile testing in the fiber direction have revealed
values ranging from 1.0 in capsular ligament to 3.0 for flexor tendon [ 105 , 147 ].
These values exceed the thermodynamic limit of 0.5 for isotropic tissues and are
indicative of volume loss under tensile loading. This volume loss is generally