Related papers: Generic elasticity of thermal, under-constrained s…
Athermal (i.e. zero-temperature) under-constrained systems are typically floppy, but they can be rigidified by the application of external strain. Following our recently developed analytical theory for the athermal limit, here and in the…
We study the elasticity of thermalized spring networks under an applied bulk strain. The networks considered are sub-isostatic random-bond networks that, in the athermal limit, are known to have vanishing bulk and linear shear moduli at…
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…
The elastic response is studied of a single flexible chain grafted on a rigid plane and an ensemble of non-interacting tethered chains. It is demonstrated that the entropic theory of rubber elasticity leads to conclusions that disagree with…
Jammed packings of repulsive elastic spheres have emerged as a rich model system within which elastic properties of disordered glassy materials may be elucidated. Most of the work on these packings have focused on the case of vanishing…
The sol-gel transition is studied in two purely entropic models consisting of hard spheres in continuous three-dimensional space, with a fraction $p$ of nearest neighbor spheres tethered by inextensible bonds. When all the tethers are…
At zero temperature, spring networks with connectivity below Maxwell's isostatic threshold undergo a mechanical phase transition from a floppy state at small strains to a rigid state for applied shear strain above a critical strain…
Thermo-elasticity couples the deformation of an elastic (solid) body to its temperature and vice-versa. It is a solid-like property. Highlighting such property in liquids is a paradigm shift: it requires long-range collective interactions…
We study the elastic theory of amorphous solids made of particles with finite range interactions in the thermodynamic limit. For the elastic theory to exist one requires all the elastic coefficients, linear and nonlinear, to attain a finite…
It is known by now that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus which exists, all the higher order coefficients do not exist in the thermodynamic limit. Here we show that…
Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state-variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by…
We probe, using a model system, elastic and kinetic energies for sheared granular materials. For large enough $P/E_y$ (pressure/Young's modulus) and $P/\rho v^2$ ($P/$kinetic energy density) elastic dominates kinetic energy, and energy…
The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…
We present the general theory of Ising transitions in isotropic elastic media with vanishing thermal expansion. By constructing a minimal model with appropriate spin-lattice couplings, we show that in two dimensions near a continuous…
We study correlation properties of the generalized elastic model which accounts for the dynamics of polymers, membranes, surfaces and fluctuating interfaces, among others. We develop a theoretical framework which leads to the emergence of…
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the…
Many seemingly different macroscopic systems (magnets, ferroelectrics, CDW, vortices,..) can be described as generic disordered elastic systems. Understanding their static and dynamics thus poses challenging problems both from the point of…
In this article, we study a thermodynamically consistent thermo-visco-elastic model describing the balance of internal energy in a heat-conducting inelastic body. In the considered problem, the temperature dependence appears in both the…
We investigate a specific finite element model to study the thermoelastic behavior of an elastic body within the context of nonlinear strain-limiting constitutive relation. As a special subclass of implicit relations, the thermoelastic…
Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of contact…