PSI - Issue 35

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

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simulation

Patel et al.,2018

Polly et al.,2012

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Fig. 4. Load-displacement curves for indentation of (a) cancellous tissue; (b) endplate.

The endplate serves as a damper zone between the hard bone and the gel-like body of the disc. The plates take on the main compressive load. However, the cartilaginous plates of the intervertebral discs have a small thickness (about 1–12 mm), as a result of which it is very difficult to carry out experiments on tension/compression. Therefore, to study the mechanical properties of cartilaginous plates, the methods of indentation are mainly used (Liu et al., 2016). From the simulation of indentation of a model sample from the material of a cartilaginous plate at the macroscale, a loading curve ( P-h ) was obtained (Fig. 4, b). The curve was analyzed using the Oliver-Pharr method. The shape of the curve and the recoverable characteristics (stiffness of 50 N/mm, the elastic modulus of 170 MPa) correspond to the experimental data presented in Patel et al., 2018 (stiffness of 61 N/mm, the elastic modulus of 194 MPa). 3. Conclusions This paper describes the verification, validation, and velocity sensitivity analysis of lumbar spine material models. For the first time, the method of movable cellular automata was used for the analysis of three-dimensional models of the above-mentioned materials. Because verification should always precede validation to ensure that errors associated with sampling the study area can be distinguished from errors caused by the incorrect choice of physical and mechanical parameters of the model, sensitivity of the developed numerical models to the number of discrete elements was studied first. The convergence analysis showed that model samples with side sizes of more than 30 automata per cubic sample side are representative. The material models of the main spine parts were validated using tensile/compression and indentation experiments. The obtained results of numerical calculations were compared with experimental data available from the literature. The correspondence of the output parameters of the models to the experimental results was more than 90 %. It is known that fluid-saturated porous materials are highly sensitive to loading rate. That is why the analysis of the speed sensitivity was performed as well. It was shown that with an increase in the loading speed the value of the effective elastic characteristics increases, which in turn is consistent with the experimental data. Thus, based on the results of the work, it was established that the developed numerical poroelastic models of the spine materials based on the MCA method can be used in the future to construct three-dimensional models of the lumbar spine in order to predict the stress-strain state of the system and assess the risk of injuries under dynamic loads.