PSI - Issue 35

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

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

endplates. The intervertebral disc has a complex structure, which results in a redistribution of stresses in the vertebrae. Such damping properties of the intervertebral disc prevent premature wear of the vertebrae (Frost et al., 2019). Usually, such in-vitro methods as tensile, compression, and indentation tests are used to study the mechanical properties of the materials making up the spine. Computer modeling is used to assess the stress-strain state of different parts of the spine under dynamic loads equivalent to physiological conditions.

Nomenclature ȡ

density of the drained material density of the fluid bulk modulus of the fluid

ȡ f K f

porosity

ș k ı

permeability strength limit

linear size of the sides of the model sample diameter of the automata bulk modulus of the solid matrix Young’s modulus of the drained material Poisson’s ratio of the drained material

l

d

Ks

E

Ȟ

To investigate the factors influencing the defected disk the methods estimating the stress and strain fields obtained by numerical simulation are used (Gómez et al., 2017). To describe the mechanical behavior of the materials in the spine the following models are utilized: a single-phase elastic (Choi et al., 2017), two-phase mixture (Mow et al., 1980), viscoelastic (Schroeder 2010), poroelastic (Malandrino et al., 2009, Chagnon et al., 2010, Fan et al., 2018) and visco-poroelastic (Castro et al., 2020). The development of a three-dimensional model for studying the mechanical behavior of biological objects includes such stages as verification, validation, and sensitivity studies (Anderson et al., 2007). Therefore, first, it is necessary to carry out validation and verification of the models for the materials of the spine before the development of a three-dimensional model of the whole object (Park et al., 2011). Validation of the models for a biological tissue may be carried out by comparison with available experimental data on tension/compression, indentation, etc. (Donnelly et al., 2011). Verification and validation of spine material models is an important step in the development of a 3D computational model of the spine. Many works (Sacks et al., 2003, Henninger et al., 2010, Haj-Ali et al., 2017, Ghezelbash et al., 2020, Ghezelbash et al., 2021) have been devoted to verification and validation of in-silico models of materials of the spine. In addition, it is very important to consider the influence of a disc endoprosthesis and other factors on resorption processes in the near-contact zone, the likelihood of vertebral fractures under dynamic loads. Therefore, a critical requirement for the methods of numerical study is its ability to simulate discontinuities and fracture processes of the materials. The development of numerical models of the lumbar spine with the possibility of modeling destruction processes is urgent. In connection with the above-mentioned, the purpose of this work is to propose numerical models of spinal tissues possessing all required abilities and carry out their verification and validation. 2. Calculation 2.1. Movable cellular automaton method for poroelastic body To describe the mechanical behavior of biological tissues we used the model of a poroelastic medium implemented in the method of movable cellular automata (MCA) (Eremina et al., 2021), which is an efficient method of discrete (particle) computational mechanics. It has been established that discrete methods have proven themselves to be very promising for modeling contact problems at the micro and mesoscale (Psakhie et al., 2013,