A Numerical Study of Geometry's Impact on the Thermal and Mechanical Properties of Periodic Surface Structures

Abstract

The paper focuses on thermal and mechanical analysis of Periodic Surface Structure (PSS). PSS is a continuous surface with a specific topology that is mathematically formulated by geometric factors. Cubic P-surface ("primitive"), D-surface ("diamond"), and G-surface ("gyroid") structures were simulated under load and heat transport using a numerical approach. We conducted our study by solving the stress and heat equations using the Finite Element Method (FEM). We achieved results using our software module, which generates PSS and simulates stress and temperature distribution. The stress model defined by dependence between stress and strain, gained from an experiment, and correlation of strain and displacement, gained from geometric conditions, was used in numerical experiments. The influence of geometric factors on the thermal and mechanical behavior of PSS was qualitatively determined. We showed decreasing effective stress values with an increased number of cells in the cubic domain for concerned PSS. It is important, because the increase in the number of cells does not increase the structure's volume.

Keywords: computer simulations; heat distribution; mechanical properties of advanced materials; modeling and simulation of material properties; numerical modeling; periodic surface structures; stress distribution; surface thickness.

Figure 1

The results of heat simulation after 250 s. Columns from left to right: diamond (D) surface, gyroid (G) surface, primitive (P) surface. Rows from top to bottom: 2 cells, thickness δ = 0.125; 2 cells, thickness δ = 0.2; 4 cells, thickness δ = 0.125; 4 cells, thickness δ = 0.2

Figure 2

Results for a reference cube. The following result from the upper-left clockwise results: (a) heat distribution after 250 s, (b) total displacement from stress analysis, (c) mesh deformation with scale ×250, and (d) von Mises stress distribution in MPa.

Figure 3

The results of total displacement from stress analysis. Columns from left to right: diamond (D) surface, gyroid (G) surface, primitive (P) surface. Rows from top to bottom: 2 cells, relative thickness δ = 0.125; 2 cells, relative thickness δ = 0.2; 4 cells, relative thickness δ = 0.125; 4 cells, relative thickness δ = 0.2.

Figure 4

Von Mises stress distribution in MPa. Columns from left to right: diamond (D) surface, gyroid (G) surface, primitive (P) surface. Rows from top to bottom: 2 cells, relative thickness δ = 0.125; 2 cells, relative thickness δ = 0.2; 4 cells, relative thickness δ = 0.125; 4 cells, relative thickness δ = 0.2.

Figure 5

Mesh deformation. Columns from left to right: diamond (D) surface, gyroid (G) surface, primitive (P) surface. Rows from top to bottom: 2 cells, relative thickness δ = 0.125; 2 cells, relative thickness δ = 0.2; 4 cells, relative thickness δ = 0.125; 4 cells, relative thickness δ = 0.2.