PSI - Issue 25

G.M. Eremina et al. / Procedia Structural Integrity 25 (2020) 470–476 G.M. Eremina et al./ Structural Integrity Procedia 00 (2019) 000–000

473

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solution of the classical equation of the fluid density transfer. This equation is numerically solved using the finite volume method adopted for the ensemble of automata . 2.2. Model description In this paper, the femur bone is considered as a composition of the cortical layer and the inner cancellous bone. The poroelastic parameters are presented in Table 1. The fluid in both bone tissues is assumed to be the same and equivalent to salt water, with a bulk modulus K f = 2.4 GPa, and a density ρ f = 1000 kg/m 3 . A ceramic-coated titanium alloy is studied as an implant material. According to the literature data (TiMetal, 2000) the following parameter values were chosen for the calculations of Ti6Al4V implant: ρ = 4420 kg/m 3 , G = 41 GPa, K = 92 GPa, σ y0.02 = 0.99 GPa, σ y = 1.07 GPa and ε b = 0.10. In accordance with the literature data by Bonello et al. (2014), the following values of the coating parameters were chosen: ρ = 5220 kg/m 3 , G = 104 GPa, K = 173 GPa.

Table 1. Poroelastic parameters of cortical and cancellous bones.

Bulk modulus of the matrix, K , GPa

Shear modulus of the matrix, G , GPa

Density of the matrix, ρ kg/m 3

Bulk modulus of the solid phase, K s , GPa

Compression strengh, σ МПа

Permeability, m 2

Bone tissue

Porosity 

Cortical

17.0 17.0

14.0

5.55 1.32

1850

0.04 0.80

1.0∙10 −16 3.5∙10 −13

170

Cancellous

3.3

600

11

Next, a numerical model of the bone-endoprosthesis system was constructed for the resurfacing endoprosthesis with real geometric parameters. A CAD model was taken as a tubular femur, according to the parameters of which a personalized solid model for the endoprosthesis was created using FreeCAD software (Fig. 1,a). Based on these solid models of the femur and endoprosthesis, mesh models were constructed in “ast” format, which were then imported into the MCA preprocessor as it shown by Eremina et al. (2019). a b

Fig. 1. Model system “bone- endoprosthesis” (a) 3D view; (b) cross-section view with scheme of loading.

In this work, dynamic loading F res , which is equivalent to the physiological one for a person weighing 75 kg, is considered to be applied to the upper part of the implant (Fig. 1,b). According to Stansfield et al. (2003), this force lies in the medial plane ZX and is inclined under different angles relative to the bone axis Z for different kinds of activity. Standing up load is characterized by the total force of 3.6 kN and applied at the angle of 24°; sitting down load of 3 kN is applied at the angle of 20°; a load of walking is 3 kN and applied at the angle of 17°; jogging is characterized by 4.5 kN and applied under angles of 15°; stance position is characterized by 3.2 kN and applied under angle of 16°. Actually, the loading is simulated through the setting constant velocity to the automata of the external