PSI - Issue 35

Galina Eremina et al. / Procedia Structural Integrity 35 (2022) 115–123

120 6

Galina Eremina et al.,/ Structural Int grity Procedia 00 (2021) 00 –000

200

160

120

V , MPa

80

v=0.01 m/s v=1.00 m/s v=2.00 m/s v=10.0 m/s Novitskaya et al.,2011

40

0

0

0.3 0.6 0.9 1.2 1.5

H , %

c)

Fig. 3. Load-displacement curves for different materials at different loading rates: (a) uniaxial tension of the annulus; (b) uniaxial compression of the nucleus; (c) uniaxial compression of the cortical.

The nucleus is composed of 82% of water and is considered to be incompressible. In the disc structure, the nucleus takes on compressive loads; therefore, the mechanical properties of the nucleus are studied mainly in compression experiments. To analyze the sensitivity of the material of the nucleus to the loading rate, the velocity of the loading automata varied from 0.25 mm/s to 1 mm/s. The stress-strain diagrams (Fig. 3, b) obtained from numerical simulation were compared with the experimental data. The loading diagram has a form and value of elastic modulus (7.4 kPa for loading speed 0.25 mm/s from simulation corresponds to 5.39±2.56 kPa for strain rate 0.25 mm/s from experiment) similar to the curve presented in Cloyd et al., 2007. In addition, the sensitivity study to the loading rate showed that with an increase in the loading speed, the value of the effective elastic characteristics of the material increases. Cortical tissue is a shell for the vertebral body (Damm et al., 2019). The thickness of the cortical layer reaches 0.5 mm. Such a shell absorbs compressive stresses. Compression and three-point bending experiments are the basic methods to study the mechanical properties of compact tissue (Christiansen et al., 2011). This paper presents the results of a numerical experiment on the compression of cubic cortical tissue samples (Fig. 3, c). Velocity sensitivity analysis was also performed. The simulation results showed that the obtained diagrams and value of elastic modulus correlate with the experimental data (12.5 GPa for loading speed of 2 m/s from simulation corresponds to 12.8 GPa for strain rate 0.001s -1 from experiment) presented in the literature (Novitskaya et al., 2011). In addition, the sensitivity study showed that with an increase in the loading speed, the value of the effective elastic characteristics of the material increases. Cancellous tissue is subjected to a compressive load under physiological conditions in the body of the vertebrae. Therefore, it is relevant to study this type of bone tissue under compression. However, a cancellous tissue with a porosity of about 80 % is highly fluid-saturated, and the properties in a dry and fluid-saturated sample differ significantly (Banse et al., 2002). Therefore, indentation methods are most often used for the minimally invasive study of the mechanical characteristics of the specimen (Zysset et al., 2009, Jin et al., 2019). The loading velocity for the simulation was chosen to be 0.1 m/s. The Berkovich indenter was used for indentation (Hu et al., 2015). The load-displacement curves ( P - h ) shown in Fig. 4, a, were processed using the Oliver-Pharr method. The results obtained were compared with the data from real experiments. The calculated loading diagram and value of elastic modulus correlate with the experimental data (14.0 GPa from simulation corresponds to 14.4 GPa from experiment) presented by Polly et al., 2012.