Numerical simulation of elastic linear micropolar media based on the pore space length scale assumption

Abstract

The 3D micropolar theory numerical simulations have been performed on the brittle isotropic materials (amorphous glass, brittle rock and two different lightweight concretes) with different pore sizes using the cylindrical models under uniaxial compressive loading. To pursue this goal, it is assumed that first, second and third microrotation constants (α, β, and γ), which appear in the couple stress equilibrium equation, are proportional to the square of average pore diameter or so called characteristic length. Unexpectedly such an assumption leads to a constant polar ratio and consequently, the polar ratio cannot be accounted for as a material constant. The present phenomenon substantiates the existence of a redundant material constant for the 3D micropolar media. Accordingly, the micropolar shear constant κ is a material constant. Different coupling numbers N , with relevant domain are numerically investigated to explore the characteristic features of the micropolar shear constant κ. According to the results obtained, the present methodology shows a very good convergence and is consistent with the physically accepted results for the heterogeneous and homogeneous materials including nano-and microscale pores, whereas several unconverted or discontinuous stress fields are found out when using mesoscale pores. The latter disadvantage is believed to be caused by the impact of voids' ratio variation under quasistatic loading.

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