Porous materials possess light weight and excellent thermal insulation performance. For disordered porous structures, the number of seed points is an important design parameter which is closely related to the morphology and mean pore size of the structure. Based on the arrangement of points in three-dimensional space, seven kinds of structures were designed by spatial Voronoi tessellation in this paper. The effect of the number of seed points on effective thermal conductivity for Voronoi was studied. Numerical simulation was conducted to research the effects of structural porosity, filling material and structural orientation on the effective thermal conductivity and heat transfer characteristics. The results showed that the effective thermal conductivity is closely related to the porosity and the matrix material. Different number and arrangement of seed points make the structure have different anisotropic performance due to different thermal paths. In addition, required the least number of seed points was obtained for the designation of isotropic random Voronoi.

Due to their outstanding mechanical properties and biocompatibility, additively manufactured titanium porous structures are extensively utilized in the domain of medical metal implants. Implants frequently undergo cyclic loading, underscoring the significance of predicting their fatigue performance. Nevertheless, a fatigue life model tailored to additively manufactured titanium porous structures is currently absent. This study employs multiple linear regression, artificial neural networks, support vector machines, and random forests machine learning models to assess the impact of structural and mechanical factors on fatigue life. Four standard maximum likelihood models were trained, and their predictions were compared with fatigue experiments to validate the efficacy of the machine learning models. The findings suggest that the fatigue life is governed by both the fatigue stress and the overall yield stress of the porous structures. Furthermore, it is recommended that the optimal combination of hyperparameters involves setting the first hidden layer of the artificial neural network model to three or four neurons, establishing the gamma value of the support vector machine model at 0.0001 with C set to 30, and configuring the n_estimators of the random forest model to three with max_depth set to seven.

Porous materials are a new type of engineering material with both functional and structural properties. Compared with regular porous structures and random porous structures, a gradient porous structure is a porous structure with a spatial variation mechanism, which can adjust the layout of the structure by changing its own load and boundary conditions according to different situations, thus obtaining better performance. In this paper, three spatial Voronoi structures with different spatial gradients are designed using the spatial Voronoi tessellation method. The differences in thermal protection performances between the Voronoi spatial gradient structure and the regular structure and the effects of porosity, gradient direction and heat flow density on the three-dimensional Voronoi stochastic gradient structure were investigated via data simulation. The results show that the effective thermal conductivity of the Voronoi spatial gradient structure is lower than that of the regular structure. The effective thermal conductivity of the structure gradually decreases with increasing porosity. Taking the gradient Voronoi structure consisting of 3 × 3 × 3 units as an example, when the porosity increases from 83% to 94.98%, its effective thermal conductivity decreases from 0.586 to 0.149 Wm${}^{-1}$K${}^{-1}$. The anisotropy of the random structure leads to effective thermal conductivity errors of more than 5% in all three gradient directions. In addition, according to the principle of thermal resistance superposition, we designed a battery pack set for calculating the effective thermal conductivities of pillar-based porous materials, including three-dimensional Voronoi gradient random porous materials on the Grasshopper platform. In this way, the effective thermal conductivity of a pillar-based porous material can be predicted more accurately. The predicted calculation results and the simulation results basically agree with each other, and the relative errors of both are within 10%.

Porous materials have significant advantages, such as their light weight and good specific energy absorption. This paper presents the designs of two ordered Voronoi structures, a truncated octahedron (Octa) and a rhombic dodecahedron (Dodeca), based on spatial Voronoi tessellation. Through a numerical analysis, the dynamic behavior, deformation and energy absorption of the two porous structures under different impact energies were explored. According to the energy-absorption index, the effects of porosity, rotating unit cell and unit-cell shape on the energy absorption of the porous structures were quantitatively evaluated. The study shows that, for Dodeca and Octa structures subjected to various impact energies, the force-displacement curves exhibit three modes. The porosity, rotational unit cell and unit-cell shape play a crucial role in affecting the impact resistance of porous structures. The work in this paper proposes an effective way to improve the energy-absorption capacity of porous structures under different impact energies. At the same time, a new understanding of the deformation mechanism of Octa and Dodeca was obtained, which is significant for the impact-resistance design and energy-absorption evaluation of porous structures.