Related papers: Nonsmooth geometry and collapse of flexible struct…
Geometrically frustrated elastic ribbons exhibit, in many cases, significant changes in configuration depending on the relation between their width and thickness. We show that the existence of such a transition, and the scaling at which it…
Topologically interlocked material systems are two-dimensional assemblies of unit elements from which no element can be removed from the assembly without disassembly of the entire system. Consequently, such tile assemblies are able to carry…
In many applications of Structural Engineering the following question arises: given a set of forces $\mathbf{f}_1,\mathbf{f}_2,\dots,\mathbf{f}_N$ applied at prescribed points $\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_N$, under what…
The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction…
Kinetic simulations have demonstrated that three-dimensional reconnection in collisionless regimes proceeds through the formation and interaction of magnetic flux ropes, which are generated due to the growth of tearing instabilities at…
Soft adhesive contacts are ubiquitous in nature and are increasingly used in synthetic systems, such as flexible electronics and soft robots, due to their advantages over traditional joining techniques. While methods to study the failure of…
The localized loading of an elastic sheet floating on a liquid bath occurs at scales from a frog sitting on a lily pad to a volcano supported by the Earth's tectonic plates. The load is supported by a combination of the stresses within the…
Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden non-spatial symmetries can occur…
The stress-strain relationship of biological soft tissues affected by Marfan's syndrome is believed to be non-convex. More specifically, Haughton and Merodio recently proposed a strain-energy density leading to localized strain softening,…
In this Thesis we investigate properties of stability, rigidity and unitarity of the string landscape in ten and lower dimensions. The dissertation explores these aspects by intertwining a detailed analysis of string vacua, with and without…
Geometric frustration results from a discrepancy between the locally favored arrangement of the constituents of a system and the geometry of the embedding space. Geometric frustration can be either non-cumulative, which implies an extensive…
In this paper, we analyze the effect of geometrical constraint on the conformational properties of an infinitely long linear semiflexible polymer chain confined in-between two constraints under good solvent condition in two dimensions. The…
Nonlinear elastic responses of short and stiff polyelectrolytes are investigated by dynamic simulations on a single molecule level. When a polyelectrolyte condensate undergoes a mechanical unfolding, two types of force-extension curves,…
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…
In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…
Solids deform and fluids flow, but soft glassy materials, such as emulsions, foams, suspensions, and pastes, exhibit an intricate mix of solid and liquid-like behavior. While much progress has been made to understand their elastic (small…
We use numerical simulations to show how noninteracting hard particles binding to a deformable elastic shell may self-assemble into a variety of linear patterns. This is a result of the nontrivial elastic response to deformations of shells.…
Shearing stresses can change the volume of a material via a nonlinear effect known as shear dilatancy. We calculate the elastic dilatancy coefficient of soft sphere packings and random spring networks, two canonical models of marginal…
Nonlinear elastic theory studies the elastic constants of a material (such as Young's modulus or bulk modulus) as a power series in the applied load. The inverse bulk modulus K, for example depends on the compression P: $ {1/ K(P)} = c_0 +…
Bending the edge of a thin elastic material promotes rigidity far from its clamped boundary. However, this curvature-induced rigidity can be overwhelmed by gravity or other external loading, resulting in elastic buckling and large…