Study on property model for porous materials 3: mathematical deduction

Based on the "octahedral structure model" of three-dimensional reticulated porous materials, the mathematical deductions are introduced one by one for the mathematical relations of their basic physical and mechanical properties in this paper. The present review on these deductions covers the unidirectional tension and the multidirectional tension/compression of porous materials, as well as the conductivity and the fatigue property. Emphasis is placed on describing the equivalent circuit of the inner structure of porous materials, and the force action model both of quasi-rigid body and deformed body structure of porous materials under unidirectional tension. On this basis, the compressive strength is discussed, and the biaxial tension and triaxial tension/compression are mathematically deducted and analyzed. According to this octahedron model, the mathematical relations of mechanical properties can be also obtained from the deduction of unidirectional tension and compression, for porous materials under loading of non-direct tension and compression.