Related papers: Predicting the mechanical properties of spring net…

We study the elastic properties of thermal networks of Hookean springs. In the purely mechanical limit, such systems are known to have vanishing rigidity when their connectivity falls below a critical, isostatic value. In this work we show…

For various engineering and industrial applications it is desirable to realize mechanical systems with broadly adjustable elasticity to respond flexibly to the external environment. Here we discover a topology-correlated transition between…

Two approaches to incorporate heterogeneity in discrete models are compared. In the first, standard approach, the heterogeneity is dictated by geometrical structure of the discrete system. In the second approach, the heterogeneity is…

We study the elastic properties of phantom networks of Gaussian and nearly-Gaussian springs. We show that the stress tensor of a Gaussian network coincides with the conductivity tensor of an equivalent resistor network, while its elastic…

Nonlinearities and instabilities in mechanical structures have shown great promise for embedding advanced functionalities. However, simulating structures subject to nonlinearities can be challenging due to the complexity of their behavior,…

Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. To understand the response of such a network as a function of the prestrain, we consider…

We introduce a mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton. This discrete model involves a regular array of pre-stressed protein filaments that exhibit resistance to enthalpic stretching, joined at…

Disordered network materials abound in both nature and synthetic situations while rigorous analysis of their nonlinear mechanical behaviors still is very challenging. The purpose of this paper is to connect the mathematical framework of…

We employ a matrix-based solver for the linear rheology of fluid-immersed disordered spring networks to reveal four distinct dynamic response regimes. One regime - completely absent in the known vacuum response - exhibits coupled fluid flow…

Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for…

Athermal models of disordered fibrous networks are highly useful for studying the mechanics of elastic networks composed of stiff biopolymers. The underlying network architecture is a key aspect that can affect the elastic properties of…

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber reinforced materials are also common in technology. An important characteristic of such materials is their…

The most profound effect of disorder on the elastic response of solids is the nonaffinity of local displacements whereby the atoms (particles, network junctions) do not simply follow the macroscopic strain, as they do in perfect crystals,…

Hooke's law states that the forces or stresses experienced by an elastic object are proportional to the applied deformations or strains. The number of coefficients of proportionality between stress and strain, i.e., the elastic moduli, is…

We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams stiff polymers easily deform in bending,…

Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous and, although the importance of force distributions for structural…

Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…

In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational…

We study the dynamics of a single semiflexible filament coupled to a Hookean spring at its boundary. The spring produces a fluctuating tensile force on the filament, whose value depends on the filament's instantaneous end-to-end length. The…

We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…