Mechanical properties of anterior malleolar ligament from experimental measurement and material modeling analysis

Abstract

In this paper, mechanical properties of the anterior malleolar ligament (AML) of human middle ear were studied through the uniaxial tensile, stress relaxation and failure tests. The digital image correlation (DIC) method was used to assess the boundary effect in experiments and calculate the strain on specimens. The constitutive behavior of the AML was described by a transversely isotropic hyperelastic model which consists of a first-order Ogden model augmented by a I(4)-type reinforcing term. The material parameters of the model were estimated and the viscoelasticity of the AML was illustrated by hysteresis phenomena and stress relaxation function. The mechanical strength of the AML was obtained through the failure test and the mean ultimate stress and stretch ratio were measured as 1.05 MPa and 1.51, respectively. Finally, a linear Young's modulus-stress relationship of the AML was derived based on constitutive equation of the AML within a stress range of 0-0.5 MPa.

Fig. 1

The AML specimen harvested from the human temporal bone and installed into metal fixtures. A ruler was attached to the metal holder at the load cell side as a dimensional reference

Fig. 2

Preconditioning of one AML specimen. The first and second cycles are pointed with loading and unloading separately. The curve tends to stable starting from the third cycle. A hysteresis loop was observed for the AML with the unloading curve lagging the loading curve

Fig. 3

Illustration of the digital image correlation (DIC) method for calculating the strain distribution of the AML specimen during the uniaxial loading process. A grid (3×8) of 24 nodes was generated at the middle portion of each image. Two horizontal lines were identified along the top and bottom grids, as well as eight vertical lines connecting corresponding grid nodes on the horizontal lines. The length of each vertical line in the reference image was used as the original length (L₀) of the specimen, and the length of the corresponding vertical lines traced in subsequently deformed images was measured as the deformed length (L) of the specimen. The normal strain ϵ in the vertical direction was calculated by ε = (L – L₀)/L₀

Fig. 4

A scanning electron microscope picture of the AML at 5,000× magnification

Fig. 5

a Normal strain distribution across the transverse surface of the AML specimen calculated from DIC analysis at four time steps. The no. of nodes represents eight locations (from left to right) across the specimen in the middle part of the grid shown in Fig. 3. b Comparison of the strain obtained from MTS experiment (broken line) and DIC analysis (solid line)

Fig. 6

a Stress–stretch curves of nine AML specimens under uniaxial loading processes. The maximum stretch ratio λ was around 1.5 and the displacement rate was 0.01 mm/s. b The mean curve of stress–stretch relationships obtained from nine AML specimens with standard deviation bars

Fig. 7

a Normalized stress relaxation function G(t) obtained from nine AML specimens in stress relaxation tests. b The mean curve of G(t) of nine AML specimens with standard deviation bars

Fig. 8

The stress–stretch curve of the AML obtained from modeling analysis (k = 10) and the mean stress–strain curve measured from nine AML specimens in uniaxial tensile tests

Fig. 9

The Young’s modulus–stress relationship of the AML derived from material modeling analysis. The Young’s modulus is linearly increasing with the stress. The values varied from 0.22 to 4.70 MPa when the stress increases from 0 to 0.5 MPa