Finite element based micromechanical modeling of periodic composite microstructures

Abstract

The mechanical behavior of cellular solids, including stiffness and strength, can be tuned by tailoring the underlying geometry and material constituents of the microstructure. Here the effect of key parameters on the compressive deformation response of composite truss-based cellular solids was investigated. A simple periodic geometry was chosen and studied using finite element based micromechanical models. Simulations were conducted parametrically varying the volume fraction with a fixed strut length, the proportion of the polymer coating to the elastomer core used in the composite struts (coating fraction), and the size of the representative volume element (layer number). An analytical model based on energy methods for buckling columns with elastic restraints was also derived and compared to the simulation data. Materials were then fabricated using 3D printing and then tested in compression. Numerical and experimental results are compared. The simulations showed that an increase in volume fraction with coating fraction and layer number held constant increased the modulus in a linear manner, and increased the peak stress with a nonlinear dependence. An increase in coating fraction with volume fraction and layer number held constant significantly increased the modulus as the square of the volume fraction and the peak stress in a non-linear fashion. An increase in the layer number lowered the critical buckling strength of the geometry non-linearly, the trend verging asymptotically with increasing size and depending heavily on the effective buckling length of the structures. The experimental modulus agreed well with the simulated data for the polymer and elastomer samples, and the experimental peak stress was found to be a lower value than predicted, due mainly to imperfections in the struts. There was a disparity between experimentation and simulation for both the modulus and the peak stress of the composites. One potential cause for this is the non-uniformity of the 3D printed coating, which was examined microscopically and found to have many imperfections along the polymer coating. Off-axis loading of the samples was also determined as a cause. Future work depends on advances in the resolution and repeatability of 3D printing technology.