PSI - Issue 80

Thi Ngoc Diep Tran et al. / Procedia Structural Integrity 80 (2026) 378–391 Thi Ngoc Diep Tran/ Structural Integrity Procedia 00 (2019) 000–000

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maximum service temperature among ceramics (De Faoite et al. (2011)). This work is divided into three distinct sections in the following. Firstly, the FE modeling of TPMS structures is presented. Numerical modeling of the damage propagation was performed by removing the finite elements in which the appropriate damage criterion was reached. The next section focuses on the structural morphology, including the algorithm to calculate the cross-sectional area and the inclination angle of each TPMS unit cells. In the final section, the numerical results are discussed and compared within four TPMS unit cells to verify the effect of local geometry on crack propagation and compressive strength. These results are in keeping with previous experimental studies by Abueidda et al. (2019), Abueidda et al. (2017), Yu et al. (2019), in which the deformation regions and crack direction within these cellular structures fabricated by 3D printer polymeric/titanium alloy materials were observed. 2. Modeling 2.1. TPMS model design As mentioned before, the design of a TPMS-based structure can be completely expressed by mathematical equations. TPMS are classified as implicit surfaces, which can be described as ( , , ) = as follows: Primitive (P) ( , , ) = cos( � ) + cos� � � + cos( � ) = ; (1) Gyroid (G) ( , , ) = sin� � �cos( � ) + sin( � )cos� � � + sin( � )cos( � ) = ; (2) Neovius (N) ( , , ) = 3[ ( � ) + cos� � � + ( � )] + 4 ( � ) ( � ) ( � ) = ; (3) IWP (I) ( , , ) = 2[cos( � ) cos� � � + cos� � � cos( � ) + cos( � ) cos( � )] −�cos(2 � ) + cos�2 � � + cos(2 � )� = ; (4) where � and denote the period and the expansion of the surface in space, respectively. This minimal surface divides the space into two intertwined parts. By offsetting two non-thickness surfaces in opposite directions and connecting the corresponding nodes in turn, a three-dimensional TPMS structure with a given wall thickness can be constructed. This can be mathematically expressed as: = ( − )( + ). (5) Eq. (5) can represent a solid object by considering where <0 as solid and where >0 as void. The structure was generated using MATLAB (2022), remeshed in MeshLab (2022), and processed as a solid body using FreeCAD (2023) for further FE simulations. The ceramic volume fraction is controlled by modifying the offset parameter . Fig.1 shows the relation between the function value and its corresponding volume fraction calculated using Eq. (5) in four TPMS structures. To focus on the geometry of each structure in further studies, the effect of volume fraction is neglected. FE models of four investigated TPMS unit cells have the same ceramic volume fraction of about 22% regarding different offset parameters ( � = 0.40, � = 0.35, � = 0.52, and � = 0.87) . The linear regressions between the offset parameter and volume fraction are also indicated in Fig. 1. The corresponding coefficients of determination �� = 0.9999, �� = 0.9999 , �� = 0.9997, � � = 0.9999 exhibit a nearly linear relation.