Experimentally validated combined stiffness expression for finite domain containing multiple inclusions

Abstract

Traditional homogenization formulations for finite volume are extended to allow for the consideration of multiple inclusions and their spatial distributions along with their corresponding individual geometric attributes. For all inclusions present in different states, a combined homogenization formulation (dubbed generalized stiffness formulation, GSF) is posed for summing the five geometric attributes of volume fraction (VF), shape or aspect ratio (AR), orientation, location (position within the domain), and number of inclusions in the domain. For verification, the solutions are compared to two literature-reported calculations of simple cases of domains containing one inclusion of specific shape and orientation in which only one attribute is varied. Once verified for simple cases, GSF stiffness solutions were run for 5040 cases of domains containing multi inclusions with various configuration combinations. These solutions were compared against 36 identical cases of 3-dimensional (3D) domains printed using acrylonitrile butadiene styrene (ABS) and experimentally tested under mechanical compression. Additionally, finite element method (FEM) simulations are run of these test structures under compression. For these test cases, effective composite stiffness values are compared for numerical solutions, experimental tests, and FEM. Relative effects on stiffness of the five inclusion geometric attributes are assessed.

Keywords

• Composite homogenization
• Stiffness formulation
• Multiple inclusions