Related papers: A mathematical model of network elastoplasticity
An elastic graph is a graph with an elasticity associated to each edge. It may be viewed as a network made out of ideal rubber bands. If the rubber bands are stretched on a target space there is an elastic energy. We characterize when a…
We present an edge-based framework for the study of geometric elastic network models to model mechanical interactions in physical systems. We use a formulation in the edge space, instead of the usual node-centric approach, to characterise…
We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity,…
Entangled networks are ubiquitous in tissues, polymers, and fabrics. However, their mechanics remain insufficiently understood due to the complexity of the topological constraints at the network level. Here, we develop a mathematical…
Many organisms have an elastic skeleton that consists of a closed shell of epithelial cells that is filled with fluid, and can actively regulate both elastic forces in the shell and hydrostatic pressure inside it. In this work we introduce…
We employ a mathematical model to analyze stress chains in thermoplastic elastomers (TPEs) with a microphase-separated spherical structure composed of triblock copolymers. The model represents stress chains during uniaxial and biaxial…
We propose a theoretical framework for dealing with a transient polymer network undergoing small deformations, based on the rate of breaking and re-forming of network crosslinks and the evolving elastic reference state. In this framework,…
Networks of elastic beams can deform either by stretching or bending of their members. The primary mode of deformation (bending or stretching) crucially depends on the specific details of the network architecture. In order to shed light on…
Under mechanical deformation, most materials exhibit both elastic and fluid (or plastic) responses. No existing formalism derived from microscopic principles encompasses both their fluid-like and solid-like aspects. We define the {\it…
The two approaches to analyzing the large strain behavior of rubbery networks are phenomenologically, using strain energy functions drawn from continuum mechanics, and molecular models, which apply statistical mechanics to compute the…
To go beyond the simple model for the fold as two flexible surfaces or faces linked by a crease that behaves as an elastic hinge, we carefully shape and anneal a crease within a polymer sheet and study its mechanical response. First, we…
We propose a three dimensional mechanical model of embryonic tissue dynamics. Mechanically coupled adherent cells are represented as particles interconnected with elastic beams which can exert non-central forces and torques. Tissue…
Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
This study presents a Eulerian theory to elucidate the molecular kinematics in polymer networks and their connection to continuum deformation, grounded in fundamental statistical physics and thermodynamics. Three key innovations are…
We numerically examine the nonlinear rubber elasticity of topologically constrained polymer networks. We propose a simple and effective model based on Graessley and Pearson's topological model (GP model) for describing the topological…
We consider a periodic lattice structure in $d=2$ or $3$ dimensions with unit cell comprising $Z$ thin elastic members emanating from a similarly situated central node. A general theoretical approach provides an algebraic formula for the…
We consider the impact of the elastomer network on the structure and fluctuations in the isotropic-genesis nematic elastomer, via a phenomenological model that underscores the role of network compliance. The model contains a…
We study the shapes of elastic membranes under the simultaneous exertion of tensile and compressive forces when the translational symmetry along the tension direction is broken. We predict a multitude of novel morphological phases in…
A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…
Statistical mechanics is an important tool for understanding polymer electroelasticity because the elasticity of polymers is primarily due to entropy. However, a common approach for the statistical mechanics of polymer chains, the Gaussian…