Related papers: Size-dependent Elasticity in Materials
We consider the problem of an optimal distribution of soft and hard material for nonlinearly elastic planar beams. We prove that under gravitational force the optimal distribution involves no microstructure and is ordered, and we provide…
A Landau theory is constructed for the vulcanization transition in cross-linked polymer systems with spontaneous nematic ordering. The neo-classical theory of the elasticity of nematic elastomers is derived via the minimization of this…
We derive and study a simple 1D nonlinear model for Edge Localized Mode (ELM) cycles. The nonlinear dynamics of a resistive ballooning mode is modeled via a single nonlinear equation of the Ginzburg-Landau type with a radial frequency…
We introduce the entanglement gauge describing the combined effects of local operations and nonlocal unitary transformations on bipartite quantum systems. The entanglement gauge exploits the invariance of nonlocal properties for bipartite…
We present a Landau type theory for the non-linear elasticity of biopolymer gels with a part of the order parameter describing induced nematic order of fibers in the gel. We attribute the non-linear elastic behavior of these materials to…
With the eventual aim of describing flowing elasto-plastic materials, we focus on the elementary brick of such a flow, a plastic event, and compute the long-range perturbation it elastically induces in a medium submitted to a global shear…
We theoretically demonstrate the ability of electron beams to probe the nonlinear photonic response with nanometer spatial resolution, well beyond the capabilities of existing optical techniques. Although the interaction of electron beams…
We study the interaction of a liquid drop with an elastic beam in the case where bending effects dominate. We use a variational approach to derive equilibrium equations for the system in the presence of gravity and in the presence or…
The cytoskeleton of eukaryotic cells provides mechanical support and governs intracellular transport. These functions rely on the complex mechanical properties of networks of semiflexible protein filaments. Recent theoretical interest has…
We have reviewed recent developments of the theory of the impact for macroscopic elastic materials. This review includes (i) standard theories for the normal impact and the oblique impact, (ii) some typical approaches to simulate impact…
In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The…
With reference to spatially non-local nematic liquid crystals, we develop a theory of optical spatial solitons and modulational instability in anisotropic media with arbitrarily large birefringence. Asymmetric spatial profiles and…
A general model is formulated for elasto-plastic materials undergoing linear kinematic hardening to describe microstructure evolution associated with phase transformations. Using infinitesimal strain theory, the model is based on…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
We develop a quantum theory of electron confinement in metal nanofilms. The theory is used to compute the nonlinear response of the film to a static or low-frequency external electric field and to investigate the role of boundary conditions…
Nonlocality is important in realistic mathematical models of physical and biological systems when local models fail to capture the essential dynamics and interactions that occur over a range of distances. This review illustrates different…
We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids, via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale $\xi_E$, so that the…
We derive strain-gradient plasticity from a nonlocal phase-field model of dislocations in a plane. Both a continuous energy with linear growth depending on a measure which characterizes the macroscopic dislocation density and a nonlocal…
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a…
A theory for the prediction of the size dependence of torsional rigidities of nanosized structural elements is developed. It is shown that, to a very good approximation, the torsional rigidity (D) of a nanosized bar differs from the…