Instabilities and pattern formations in 3D-printed deformable fiber composites

Abstract

Abstract We investigate elastic instabilities and pattern formations in 3D-printed deformable fiber composites. We experimentally realize the instability induced patterns in the deformable 3D systems of periodically distributed fibers embedded in soft matrix. We observe that the fiber composites exhibit significant softening upon achieving the critical strain at which the stiff fibers cooperatively buckle into wavy patterns. For periodically distributed fiber composites with square in-plane periodicity, we observe the transition of the instability induced patterns from small wavelength wavy pattern to long wave mode with an increase in fiber volume fraction. Both experimental results and rigorous Bloch-Floquet numerical analysis show that the critical wavenumber and critical strain decrease with an increase in fiber volume fraction. For composites with rectangular in-plane periodicity of fibers, we observe that the cooperative buckling mode develops in the direction, where the fibers are close to each other; and an increase in the periodicity aspect ratio leads to a decrease in critical wavenumber and critical strain. In addition, we present our theoretical, numerical, and experimental results for single fiber in soft matrix system. For the single fiber system, we observe that the critical wavelength has a linear dependence on fiber diameter. An explicit formula is derived to estimate the dependence of critical wavelength on shear modulus contrast, and further verified by experimental data and numerical simulations.