Ruga mechanics of composite media with soft inclusions

This thesis presents an investigation for the elastic deformation of two-phase fibril composites with soft inclusions, specifically, the influence of soft inclusions on the behavior of fibrils under compressive loading. It is demonstrated that the inclusion of soft material in the fibril matrix substantially alters the post-bifurcation response of elastic fibrils. First, nonlinear finite element analysis is used to demonstrate that due to localized instabilities, fibrils with soft inclusions exhibit negative post-buckling stiffness. The local instability is postulated to follow the same post- buckling behavior as a beam on an elastic foundation, through a semi-analytical approach, it is shown that an unstable post-bifurcation response emerges. Additionally, using numerical analysis, careful patterning of the inclusions is shown to induce complex surface topography attributed to the local buckling modes, such as wrinkles and folds. Furthermore, through natural frequency eigenvalue analysis, it is demonstrated that fibrils with soft inclusions in the post-buckling region have local modes with negative ω2. Negative ω2 is only observed in negative stiffness systems and associated with local modes of instability. Through Bloch wave analysis it is observed that due to the complex deformation modes of buckled fibrils with soft inclusions widening band-gaps that are proportional to the prescribed load emerge. The findings presented in this thesis provide alternatives to the manufacturing of negative stiffness systems that relies on curved beam elements. It also serves to introduce the possibility of utilizing soft inclusions in achieving controllable surface morphologies. Finally, demonstrates the possibility of modulating acoustic bandgaps and optimizing damping properties of composites through end-shortening