Comparison of full field and single pore approaches to homogenization of linearly elastic materials with pores of regular and irregular shapes

• Packing algorithm for irregular shapes and mixtures of shapes is presented.
• Effective elastic properties of microstructures with irregular pores are calculated.
• Homogenization is performed via direct FEA and micromechanical modeling.
• Direct FEA results are in good agreement with Mori-Tanaka and Maxwell schemes.
• Compliance contribution tensors for cubic, octahedral, tetrahedral pores are given.

Two approaches to predict the overall elastic properties of solids with regularly and irregularly shaped pores are compared. The first approach involves direct finite element simulations of periodic representative volume elements containing arrangements of pores. A simplified algorithm of collective rearrangement type is developed for generating microstructures with the desired density of randomly distributed pores of regular and irregular shapes. Homogeneity and isotropy (where appropriate) of the microstructures are confirmed by generating two-point statistics functions. The second approach utilizes Mori-Tanaka and Maxwell micromechanical models implemented via the cavity compliance contribution tensor (H-tensor) formalism. The effects of pore shape and matrix Poisson's ratio on compliance contribution parameters of different shapes are discussed. H-tensors of cubical, octahedral and tetrahedral pores for several values of matrix Poisson's ratio are published in explicit form for the first time. Good correspondence between the direct finite element simulations and micromechanical homogenization is observed for randomly oriented and parallel pores of the same shape, as well as mixtures of pores of various shapes up to 0.25 pore volume fractions.