Analysis of the adequacy and selection of phenomenological models of the elastic properties of porous powder materials

This article offers a phenomenological model of the moduli of elasticity of porous powder materials, which assumes only the deformation of the solid phase volume. The new model correlates the deformable volumes at the shear, tension, and volumetric compression and allows calculating the remaining moduli of elasticity of porous materials by the known values of one modulus of elasticity. It is found that, despite the dispersion of the experimental data, the averaged values of relative Young’s modulus \( E_{r} \) of porous metals and ceramics are identical. A number of theoretical models have been tested based on the averaged reference dependence of \( E_{r} \) on porosity ϕ. The results of calculations for the theoretical models, with the exception of the proposed model, are not consistent with the reference values of the Young’s modulus. The testing of one-dimensional phenomenological models has been provided by the limiting (linear and strongly nonlinear) experimental dependences \( E_{r} (\phi) \). According to the combined test results, the most accurate and versatile model is the new phenomenological one.