singularities
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Better energies for low-dimensional elastic systems under combined bending and stretching
We present new kinematic bending measures and quadratic energies for isotropic elastic plates and shells, with certain desirable features not present in commonly employed models in mechanics and soft matter. These are justified both by simple physical arguments related to the through-thickness variation in strain, and through a detailed reduction from a three-dimensional energy quadratic in stretch. The measure of plate bending is a dilation-invariant surface tensor that couples stretch and curvature in a natural extension of primitive generalized bending strains for straight rods. The extension to naturally-curved rods and shells, for which the pure stretching of a curved rest configuration is not a dilation, contrasts with previous ad hoc postulated forms. Our results provide a clean basis for simple models of low-dimensional elastic systems, and should enable more accurate probing of the structure of singularities in soft sheets and membranes.
Flow singularities in soft materials: from thermal motion to active molecular stresses
The motion of passive or active agents in soft materials generates long ranged deformation fields with signatures informed by hydrodynamics and the properties of the soft matter host. These signatures are even more complex when the soft matter host itself is an active material. Measurement of these fields reveals mechanics of the soft materials and hydrodynamics central to understanding self-organization. In this talk, I first introduce a new method based on correlated displacement velocimetry, and use the method to measure flow fields around particles trapped at the interface between immiscible fluids. These flow fields, decomposed into interfacial hydrodynamic multipoles, including force monopole and dipole flows, provide key insights essential to understanding the interface’s mechanical response. I then extend this method to various actomyosin systems to measure local strain fields around myosin molecular motors. I show how active stresses propagate in 2d liquid crystalline structures and in disordered networks that are formed by the actin filaments. In particular, the response functions of contractile and stable gels are characterized. Through similar analysis, I also measure the retrograde flow fields of stress fibers in single cells to understand subcellular mechanochemical systems.
Endless forms most beautiful: how to program materials using geometry, topology and singularities
The dream of programmable matter is to create materials whose physical properties (shape, moduli, response to perturbations, etc.) can be changed on the fly. For many years, my group has been thinking about how to program flat sheets that fold up into three dimensional shapes, most recently by exploiting the principles of origami design. Unfortunately, a combinatorial explosion of folding pathways makes robust folding particularly challenging. In this talk, I will discuss how this pluripotency arises from the topology of the configuration space. This suggests a broader understanding of a larger class of materials spanning from folding forms to spring networks to mechanical structures that perform computational logic.
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