PSI - Issue 35

Galina Eremina et al. / Procedia Structural Integrity 35 (2022) 115–123 Galina Eremina et al.,/ Structural Integrity Procedia 00 (2019) 000–000

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deviation of ultimate strength did not exceed 4 %). Model samples with a size of 30 Â n were used for simulation of compression/tension test, while samples with a size of 60 Â n were used for simulation of indentation test. A larger size of the samples for indentation was used to simulate the condition of semi-infinite half-space and to avoid the influence of the faces of the model sample and the appearance of cracks before the formation of an imprint of the required size (Fischer-Cripps, 2003).

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Fig. 2. The convergence analysis for the mechanical properties of model samples of biological tissues: (a) ultimate strength; (b) elastic modulus (1– cancellous tissue, 2– cortical tissue, 3– cartilage, 4–annulus, 5–nucleus).

2.3.2. Validation The annulus is mainly prone to tensile stress. Therefore, the mechanical properties of the annulus material are investigated primarily through tensile experiments. The loading curves obtained from the simulation were compared with the data of experimental works. In the case of uniaxial tension of the annulus fibrous material, the stress-strain diagram (Fig. 3, a) and value of elastic modulus (35 MPa from simulation and 36 MPa from experimental) at a loading speed of 0.16 mm/s are in good numerical agreement with the experimental data presented in Holzapfel et al., 2005. In addition, the sensitivity studies to the loading rate showed that with an increase in the velocity of the loading automata, the value of the effective elastic characteristics of the material increases (Holzapfel et al., 2005).

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V , kPa

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v=1.6e-5 m/s v=1.0e-4 m/s v=1.0e-2 m/s Holzapfel et al.,2005

v=1.0e-3 m/s v=5.0e-4 m/s v=2.5e-4 m/s Cloyd et al,2007

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