Research

Jamming

The properties of granular materials, in particular sand, are a constant source of fascination for children and adults alike. One can literally see the excitation in the eyes of the children, when making their first "hands-on" experience with sand, they realize that the seemingly stable and solid sand can also flow through their fingers and drop to the floor like a liquid. At some other time they might make the quite opposite experience that sand, when put in a funnel does not, as it should, flow through the opening and drive the wheel attached underneath, but rather stays at rest in a jammed state. This "fascination sand" persists over the years, such that parents may think it to be a rather pleasant educational duty to help their children bake a cake of sand.
For the scientist this fascination may arise through the apparent contradiction between the indeformability of the individual grains and the fragility of the assembly as a whole. This means that small changes in the loading conditions (e.g. by changing the inclination angle of the support) can lead to large scale structural rearrangements ("avalanches") or even to the complete fluidization of the material.
This transition between the solid and the flowing state, the transition between jammed and unjammed material, can be triggered in various ways. If one applies a shear stress, which is small and below a certain threshold ("yield-stress"), the material will respond as an elastic solid. Increasing the stress above the yield-stress, the particles will unjam and start to flow. Without external drive, an (un)jamming transition can also occur for decreasing particle volume fraction below a critical value. This special point, which has many properties of a true critical point, has been given the name "point J".

We use computer simulations to study the microscopic dynamics of a driven assembly of soft particles near the jamming transition. We observe superdiffusive, spatially heterogeneous, and collective particle motion over a characteristic scale which displays a surprising non-monotonic behavior across the transition. As a result, we establish a connection between single particle dynamics and collective particle motion, which allows us to develop an intuitive and appealing picture of jamming as the consequence of the diverging size of rigid particle clusters.

Elasticity of fiber bundles

Fibers constitute elemental building blocks of a broad range of biological and human-made structures. At one extreme, oriented fibers are used to enhance tensile mechanical strength while maintaining bending compliance, such as in muscle or skin. Synthetic counterparts are rope or cable and reinforced membranous structures such as tires and fabrics. At the other extreme of mechanical function, fibers are used to enhance bending stiffness via bundling or layering. Slender fiber bundles abound in cellular processes and consist typically of either filamentous actin or microtubules. In each case, the cell uses specific crosslinking proteins to align and crosslink constituent F-actin and/or microtubule fibers, thereby dramatically enhancing structural bending stiffness. Technologically important synthetic counterparts are single-walled carbon nanotube bundles crosslinked either reversibly by weak van der Waals interactions or irreversibly by electron beam irradiation.

Depending on the degree of mechanical coupling induced by intervening crosslinks, the bending stiffness can be varied dramatically from "decoupled bending", in which constituent filaments bend independently, to "fully-coupled bending", in which the bundle behaves like a homogeneous elastic rod. These intriguing mechanical properties can be understood in terms of the wormlike bundle model , which describes bundles as an assembly of semiflexible filaments interconnected by crosslinking proteins. Unlike the standard wormlike chain model, the wormlike bundle model exhibits a state- dependent bending stiffness that derives from a generic competition between the bending and twist stiffness of individual filaments and their relative motion mediated by the stiffness of the crosslinkers.

Mechanics of fiber networks

Fibrous and cellular materials are ubiquitious in nature as well as many areas of technology. Prominent examples from biology are bone, wood or the cytoskeleton of cells. Due to microstructural randomness the elastic properties of these biomaterials result from a subtle interplay between the architecture of the network and the elastic properties of its building blocks. In these networks highly non-affine deformations as well as inhomogeneous distribution of stresses have been found. Few is known, however, about the actual nature of the deformations present and the expression ``non-affine'' is only used to signal the absence of affine deformations.

In this project we focus on a particular class of heterogeneous networks composed of crosslinked elastic fibers. These systems have been suggested as model systems for studying the mechanical properties of paper sheets or biological networks of semiflexible polymers. Our approach combines computer simulations and theoretical concepts. For example, we have been able to formulate a self-consistent effective medium theory ("floppy-mode theory"), to calculate the network elasticity.
Within this theoretical framework the calculation of the network elastic modulus is reduced to the description of a "test" filament in an array of pinning sites. The coupling strength to these sites represents the elastic modulus of the network and has to be calculated self-consistently.

Very recently, we have generalized the formalism to composite networks of filaments with different stiffnesses. The cell cytoskeleton, built up from microtubules, actin filaments and intermediate filaments, is just one striking example of a biologically relevant composite network.
Combining theory with network MC-simulations we can reveal a non-trivial relationship between the mechanical behavior and the relative fraction of stiff polymer: when there are few stiff polymers, non-percolated stiff "inclusions" are protected from large deformations by an encompassing floppy matrix, while at higher fractions of stiff material the stiff network is independently percolated and dominates the mechanical response.