The Effective Mechanical Properties Of The Random 3D Porous Materials

Porous materials have received extensive attentions in the past decades and have been widely applied in engineering areas due to their excellent properties.Since their mechanical properties are of great importance when the porous materials are applied in the engineering structures.In this paper,the representative volume element(RVE)models with randomly distributed non-overlapping spherical voids and Voronoi-structured polyhedral voids with various porosities are created to simulate the random 3D closed-cell porous materials,respectively.The effective properties of the porous materials are comprehensively investigated through theoretical formulations,finite element method(FEM)simulations and experimental tests.The main contents are shown as follows:(1)Simple universal models are developed to predict the elastic properties of the elastic porous materials under small deformations by considering the effects of porosity,void shape and the Poisson's ratio of matrix.The high accuracys of the proposed models are validated by the numerical and experimental results.Motivated by the numerical results find that the three-phase model(TPM)provides the best predictions of the effective bulk and shear moduli of the porous materials with various Poisson's ratios of the matrix,respectively,for the entire range of porosity(0~1).A simple universal model(SUM)is developed based on a proper Taylor expansion of the TPM to predict the effective shear modulus.The effective Young's modulus and Poisson's ratio of ultra-simple form are then formulated based on the TPM and SUM.The findings show that the theoretical estimates agree well with the numerical results for all the effective elastic properties.The 3D printing technology is utilized to fabricate the porous nylon specimens with various porosities of closed-cells.The uniaxial compression tests combine with digital image correlation(DIC)are implemented to measure the effective Young's modulus of the porous nylon materials.The results suggest that the theoretical predictions of the ultra-simple form,formulated by the TPM and SUM,agree very well with the effective Young's moduli of the porous materials,covering a wide range of porosity.(2)A novel constitutive model is proposed for linear viscoelastic porous materials under small deformations in time domain.The high precision of the derived model is numerically validated in both time and frequency domains.After decomposing the deformation into its volumetric and deviatoric parts,the long-term responses of the linear viscoelastic materials are utilized to formulate the constitutive model.Based on the micromechanics and homogenization approach,the constitutive model for linear viscoelastic porous materials is derived by assuming the strain energy density of the voids to be zero.RVE models with various porosities(0~0.9)are used to validate the constitutive model numerically.The effects of the porosity,strain rate,and material parameters of the matrix(including elastic and viscous)on the effective viscoelastic behaviors of the porous materials are investigated in time domain,while the effects of the porosity and frequency are studied in frequency domain.The results reveal that the proposed constitutive model can predict well the effective properties of linear viscoelastic porous materials in both time and frequency domains.(3)The effective properties of the hyperelastic porous materials are investigated under finite deformations.The effective strain energy and macroscopic nominal stress of the porous neo-Hookean materials under both hydrostatic and isochoric deformations are firstly computed using a numerical homogenization approach on the RVE models.The constitutive relations(strain energy density function and nominal stress)under corresponding deformations are then developed based on the numerical results.It is also verified that the effective shear modulus of the porous neo-Hookean material(a parameter in the constitutive models)can be well predicted by the TPM or SUM.The volumetric multiplicative decomposition is employed to decompose the deformation gradient of a general finite deformation into the corresponding hydrostatic and isochoric part.A new constitutive model to emtimate the effective behaviors of the incompressible neo-Hookean porous materials under general finite deformations are then proposed by superposing the constitutive relations of the hydrostatic and isochoric deformations.Various general finite deformations are then simulated and all the numerical results show that the proposed constitutive model can offer good estimates on the effective mechanical behaviors of the porous neo-Hookean materials.Other constitutive models are studied and compared with our model.The results suggest that our model can better capture mechanical behaviors in many repects of the porous neo-Hookean materials than the models.