PSI - Issue 71

A. Kumar et al. / Procedia Structural Integrity 71 (2025) 453–460

458

Fig. 5. (a) The FE model of RCE, (b) a deformed model of RCE in 2-3 plane

C3D20R elements are used to model the RCE in Fig. 5 (a). For homogenization, the Micromechanics module in Abaqus® was employed ( Micromechanics Plugin for ABAQUS/CAE. Version 1.15-12/11/2017 Ed., Dassault Systèmes Simulia Corp , n.d.). Six distinct strains were applied to an RCE to detect unknown components in C , resulting in six different load conditions. The material was then homogenized, and the orthotropic component matrix was generated using FE simulations. A deformed model in 2-3 plane is shown in Fig. 5(b). 4. Results and Discussions For all calculations, the inclined cell wall has a length and thickness of 3.70 mm and 0.08 mm, respectively, and RCE's Young's modulus is considered as 70 GPa and Poission’s ratio of 0.3. It is evident in Fig. 6(a) that the analytical solutions of Sorohan et al . (Stefan et al. (2015)) are consistent with the derived analytical and FE results. E 3 values are decreasing with increases in h/l ratios and cell angles. Fig. 6(b) compares percent error in the computed FEM results and theoretical values for E 3 vs. h/l ratio at different cell angles ( θ ). On average, there is an absolute percentage inaccuracy of around 1.88%.

Fig. 6. (a) Plot for E 3 at various θ and h/l ratios; (b) % error E 3 in theoretical and FE results at various θ and h/l ratios

There is no shearing in the direction perpendicular to the cell wall (straight walls); instead, the shear stress in the 1-3 plane is transferred to the inclined cell walls. Whereas the 23  in 2-3 plane is transmitted to both inclined and straight walls of the RCE. The shear modulus ( G 13 ) in the 1-3 plane increases with cell angles at specific values, then decreases at h/l =2.5, 3, whereas at h/l =1.5, it decreases with increased cell angles (Fig.7(a)). At certain θ and for all h/l ratios, the trend in the % error in G13 is almost consistent (Fig. 7(b)). The % error in G 13 increases with decreased cell angles, and the average absolute percentage error is approximately 2.27 %.