Derivation of the simplest exponential and power-law relations for the effective tensile modulus of porous ceramics via functional equations

Establishment of the microstructure of porous materials and its relationship with effective mechanical properties

In this study, a porous structure for a porous liquid storage medium is generated, and the homogenization theory based on displacement boundary conditions is used to predict the effective mechanical properties. The relationship between the porous material's macroscopic mechanical properties and microstructure is next analyzed. In order to establish the relationship between the microstructure of porous materials and their macroscopic mechanical properties, assuming that the pores grow along the z direction, a method is proposed to generate 3D open-cell porous materials based on six design parameters (i.e., the number of pores, porosity, irregularity of pore distribution, the randomness of pore growth in the x and y directions, and randomness of pore size). Since the porosity of oil-bearing materials ranges from 20 to 30%, the porosity of the RVE (Representative Volume Element) was kept under control at about 25%, and the effect of the six design factors on the mechanical properties of the RVE was investigated. Utilizing SLA 3D printing technology, specimens were produced, and compression tests were used to show how useful the results of the numerical analysis were. The results demonstrated that after the number of RVE pores reaches 9, the numerical results have good repeatability. The irregularity of the initial pore distribution has little effect on the effective mechanical properties of the RVE. At the same time, the increase in the randomness of pore growth and the randomness of pore size increases the degree of weakening of the mechanical properties in the z-direction, while reducing the degree of weakening in the x and y directions, but the latter has a smaller impact. Furthermore, there is a superimposition effect of design parameters on the RVE.