S udeep Kumar Sahoo

Université de Bordeaux, Laboratoire I2M, UMR CNRS 5295, Arts et Métiers Institute of Technology, Talence, France



Recently, Triply Periodic Minimal Surfaces (TPMS)-based lattices have received significant attraction in structural applications across a variety of engineering sectors, including automobile, aerospace, and biomedical, owing to their improved mechanical properties and lightweight potential. The mechanical characteristics of these lattices are intrinsically linked to the design-related topological descriptors that include the spatial arrangement of their topological cell wall, geometrical sizes, and relative density. In practical applications, however, these structures are often exposed to fluctuating loads that can induce depreciation of their mechanical properties and eventually fatigue failure. Therefore, it is crucial to conduct a comprehensive analysis of their orientational-dependent fatigue response and explore the structure-property relation under fatigue subjected to various loading conditions. To address this challenge, a novel numerical framework based on the Finite Element Method has been proposed and employed to investigate the fatigue strength of TPMS lattices under diverse loading conditions, including uniaxial tension, equi-biaxial and simple shear. The stress-based Crossland criterion has been adopted as the fatigue criterion, and the fatigue strength of the considered volume is computed using a fatigue indicator parameter (FIP).

The developed framework is undertaken to examine the performance of three sheet-based TPMS lattices, namely Schoen Gyroid, Schwarz Primitive, and Schoen IWP. Besides, the approach permitted to demonstrate the influence of localized material distribution and loading direction towards the evaluation of fatigue strength and structural efficiency. It is observed that among all the proposed lattices, Schoen Gyroid is shown to exhibit better fatigue properties in accordance with the existing literature studies. Our observations are consistent with these findings and through our proposed methodology, we demonstrate that its enhanced performance can be attributed to the helical configuration of its cell walls which facilitates load distribution evenly throughout the entire cell volume, regardless of the loading orientation. On the contrary, Schwarz Primitive and Schoen IWP lattices exhibited more localized stress fields in the loading direction relative to other directions, indicating their sensitivity to loading direction and thus their fatigue response. A comparative analysis is also conducted to determine whether a correlation exists between the fatigue response and the effective mechanical properties obtained through the homogenization approach. In conclusion, the proposed numerical framework serves as a promising means of solving topology optimization problems involving lattices, wherein not only the selection of the lattice but also their preferred orientation can be taken into account as design variables.


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