Mechanical metamaterials are carefully engineered materials whose properties are controlled by their structure, not by their composition, which allows using metamaterials to study and control... Show moreMechanical metamaterials are carefully engineered materials whose properties are controlled by their structure, not by their composition, which allows using metamaterials to study and control physical effects in detail. Here we develop metamaterials to study the sequential, complex response of frustrated materials that are cyclically driven. In particular, we focus on metamaterials that act as collections of hysteretic, bistable elements called hysterons. We create hysterons in metamaterials by using local frustration at defects and by using a competition between two global, incompatible deformations modes. We show how we can tune these hysterons, both by rational design and by using spatial gradients in the mechanical driving. Then we show that collectively, our samples exhibit complex transition pathways, including those with avalanches, and study the role of hysteron interactions. Finally, we explore how to control the frustration by local defects in so-called monoholar metamaterials. Show less
A foam is not a homogeneous material, but consists of a large number of small air bubbles. The whole is more than the sum of its parts: even though the behavior of a single bubble is easy... Show more A foam is not a homogeneous material, but consists of a large number of small air bubbles. The whole is more than the sum of its parts: even though the behavior of a single bubble is easy to understand, their collective behavior is much more complicated and completely different. The reason for this is that a deformation of the whole is only reflected partially in the deformation of individual bubbles. Instead, a large part of the deformation is reflected in a change in the structure of the foam. In this thesis, we investigate this change in structure. In the first part of this thesis, we use a simple microscopic computer model to simulate the response of a foam when it is deformed by a tiny amount, and measure how far we need to deform the foam until it is irreversibly deformed. In the second part of this thesis, we focus on an experiment, where we measure the response of a two-dimensional foam when it is deformed at the edges. We observe that the response of bubbles in the center of the foam qualitatively depends on how densely the bubbles are packed together. Show less
Geometric frustration occurs when local order cannot propagate through space. A common example is the surface of a soccer ball, which cannot be tiled with hexaganons only. Geometric frustration can... Show moreGeometric frustration occurs when local order cannot propagate through space. A common example is the surface of a soccer ball, which cannot be tiled with hexaganons only. Geometric frustration can also be present in materials. In fact, geometry can act as an instrument to design the mechanical, optical or physical properties of fluids and solids. The first two parts of this thesis discuss frustrated liquid crystals confined to droplets of various shapes and sizes. The droplet shape determines the orientation of the liquid crystal molecules and in turn its response to light. In the final part we study the fracture mechanics of curved elastic plates. By tuning the curvature of the plate, the critical length at which the crack starts growing can be controlled. Finally, we find that the path that the crack takes depends on the curvature. Show less
Many materials, like foams, emulsions, suspensions and granular media obtain finite rigidity once their constituent particles are brought in contact. Nevertheless, all these materials can be made... Show moreMany materials, like foams, emulsions, suspensions and granular media obtain finite rigidity once their constituent particles are brought in contact. Nevertheless, all these materials can be made to flow by the application of relatively small stresses. By varying thermodynamic (temperature or density) and mechanical (applied stress) variables, one can bring about a transition from a freely flowing to a jammed state. What is the elastic response of foams close to the jamming point? How much can these materials be loaded before they flow? What is their behavior like in the bulk? These problems are of great interest in academics, as well as industrial applications (oil/gas extraction, cosmetics, pharmaceuticals and food processes). I study the transition from the flowing to the non-flowing regime in foams and analyze the non-affine behavior at this critical point. Additionally, whereas the usual rheological approach is to study the shear, I have developed a technique to measure compressive response in a real-world, foam system, taking gravity and temperature fluctuations into account. Show less
Many disordered materials display a so-called jamming transition between solid-like and fluid-like states. In this thesis, we investigate jamming in granular media by studying granular packings at... Show moreMany disordered materials display a so-called jamming transition between solid-like and fluid-like states. In this thesis, we investigate jamming in granular media by studying granular packings at various distances from the transition. In numerical model systems of spherical particles, the jamming transition has many features of a critical transition. Using the linear response of such packings to external perturbations, we shed new light on their critical behavior. We analyze various scaling relations in terms of the non-affine deformations of the packing, and identify a diverging length scale that determines beyond what scale these systems can be treated as a continuum. This length scale and various other properties are determined primarily by the number of contacts between grains in the system. In the second half of the thesis we investigate force networks in granular media using the recently developed Force Network Ensemble. We discuss the analytical properties of the ensemble, and apply it to study granular media under shear stress, identifying upper bounds on the shear stress that cohesionless granular media can sustain. Show less
