PSI - Issue 42

Aleksandr Shalimov et al. / Procedia Structural Integrity 42 (2022) 1153–1158 A. Shalimov et al. / Structural Integrity Procedia 00 (2019) 000 – 000 = − (5) where is the maximum length of the crack in the element, which was taken equal to 0.06 mm; is the characteristic length of a finite element equal to a cubic root of the volume of a particular finite element = √ 3 . Table 2. Model parameters for different loading regimes Tension Compression 0.95 0.5 0.33% 0.81% − 1.57% 2.5% Finite-element simulations were implemented with Abaqus v.2022 software (Dassault Systems Simulia Corp., Providence, RI, USA). A UMAT custom subroutine was written to implement this model in Abaqus. It describes a model of a porous isotropic trabecular bone material with a permanent degradation of elastic properties when the criterion of maximum equivalent strain is met. During each computational time step, the subroutine is compiled and allows Abaqus/Standard to obtain the required information about the material state and the mechanical response of each element. 3. Results and discussion Figure 2 presents the calculated plots of force-displacement diagrams for the trabecular unit cell in tension and compression.

1156 4

Fig. 2. Force-displacement curve for structure 3 with a pore volume fraction of 0.552 under tension and compression obtained with model of elastic property degradation

The field of degradation-coefficient values for tensile (compression) loading of unit cells obtained with the model of degradation of elastic properties is presented in Fig. 3. The maximum value of the degradation coefficient was 0.95 in case of tension and 0.5 in case of compression. The brittle-elastic model exhibited different stress and strain behaviors in tension and compression. Although the trabecular ligaments that are oriented predominantly along the load axis acted as stress concentrators in both loading cases, the location of these stress concentrators and, hence, the damage regions varied in tension and compression. Figure 3 shows the difference between the patterns of areas with property degradation both for different unit cells of as well as for tension and compression for each structure.