Related papers: A mathematical model of network elastoplasticity
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…
We have studied experimentally and theoretically the response of randomly folded hyperelastic and elastoplastic sheets on the uniaxial compression loading and the statistical properties of crumpling networks. The results of these studies…
The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of…
Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
The history-dependent behaviors of classical plasticity models are often driven by internal variables evolved according to phenomenological laws. The difficulty to interpret how these internal variables represent a history of deformation,…
Underpinning the past decades of work on the design, initialization, and optimization of neural networks is a seemingly innocuous assumption: that the network is trained on a \textit{stationary} data distribution. In settings where this…
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…
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,…
This article is a description of elasticity theory for readers with mathematical background. The first sections are an abridgment of parts of the book by Marsden and Hughes, including a compact identification of the equations of motion as…
We study the problem of learning graph dynamics of deformable objects that generalizes to unknown physical properties. Our key insight is to leverage a latent representation of elastic physical properties of cloth-like deformable objects…
The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is {\it strong} near the threshold valence where the network…
We consider models for elastic liquids, such as solutions of flexible polymers. They introduce a relaxation time $\lambda$ into the system, over which stresses relax. We study the kinematics of the problem, and clarify the relationship…
The theory of mechanical response and stress transmission in disordered, jammed solids poses several open questions of how non-periodic networks -- apparently indistinguishable from a snapshot of a fluid -- sustain shear. We present a…
In a continuum description of materials, the stress tensor field $\bar{% \bar{\sigma}}$ quantifies the internal forces the neighbouring regions exert on a region of the material. The classical theory of elastic solids assumes that…
We study an elliptic-parabolic system of partial differential equations describing formation of biological network structures. The model takes into consideration the evolution of the permeability tensor under the influence of a diffusion…
The consolidation of suspended particulate matter under external forces such as pressure or gravity is of widespread interest. In this work, we derive a constitutive relation to describe the deformation of a {\it two-dimensional} strongly…
The elasticity of rubbery polymer networks has been considered to be entropy-driven. On the other hand, studies on single polymer chain mechanics have revealed that the elasticity of ultimately stretched polymer chains is dominated by the…