An Experimentally Validated Combined Stiffness Formulation for a Finite Domain Considering Volume Fraction, Shape, Orientation, and Location of a Single Inclusion

Abstract

This work characterizes the stiffness of a finite domain containing one (biaxial ellipsoidal) void due to the combined effect of inclusion’s attributes: (1) size or volume fraction, VF, (2) shape or aspect ratio, AR, (3) angular orientation, and (4) location (position) within the matrix. The values and ranges of these ellipsoidal inclusion attributes are varied according to a matrix developed using design of experiments (DOE). Modified Mori–Tanaka method combined with dual-eigenstrain method (interior and exterior eigenstrain methods) is used to determine the effective stiffness tensor of the composite domain. Employing the numerically calculated normalized axial modulus [Formula: see text] values in SAS/STAT®, a nonlinear mathematical expression of [Formula: see text] as function of the void’s variables is arrived at Stiffness values found from the numerical homogenization scheme are experimentally corroborated using compression tests conducted on 3D-printed ABS cubes having a single ellipsoidal inclusion of various geometric attributes. In addition, finite element simulations were run of said uniaxial compression test cases to further validate the numerical homogenization results. Corroborated findings suggest that while the location of the inclusions in the matrix have no significant effect on normalized modulus [Formula: see text], the void’s volume fraction has the largest effect where it decreases with VF. The effect of the void’s orientation and elliptical aspect ratio are significant. [Formula: see text] increases with AR at angles ranging from 0–[Formula: see text]; at [Formula: see text][Formula: see text] are almost constant with AR, at angles of 60–[Formula: see text] values of [Formula: see text] decrease with AR. As AR approaches unity, the effect of orientation decreases significantly.