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Elastic properties and internal states of isotropic sphere packings are studied by numerical simulations. Several numerical protocols to assemble dense configurations are compared. One, which imitates experiments with lubricated contacts,…
We extend stochastic thermodynamics by relaxing the two assumptions that the Markovian dynamics must be linear and that the equilibrium distribution must be a Boltzmann distribution. We show that if we require the second law to hold when…
This is the second paper devoted to energetic rigidity, in which we apply our formalism to examples in two dimensions: underconstrained random regular spring networks, vertex models, and jammed packings of soft particles. Spring networks…
Within the framework of continuum mechanics, the full description Of joint motion of elastic bodies and compressible viscous fluids with taking into account thermal effects is given by the system consisting of the mass, momentum, and energy…
We study the elastic response of concentrated suspensions of rigid wire frame particles to a step strain. These particles are constructed from infinitely thin, rigid rods of length $L$. We specifically compare straight rod-like particles to…
The deformation problem for a transversely isotropic elastic layer bonded to a rigid substrate and coated with a very thin elastic layer made of another transversely isotropic material is considered. The leading-order asymptotic models (for…
A second-gradient elastic (SGE) material is identified as the homogeneous solid equivalent to a periodic planar lattice characterized by a hexagonal unit cell, which is made up of three different linear elastic bars ordered in a way that…
Experimental testing on dry woven fabrics exhibits a complex set of evidences that are difficult to be completely described using classical continuum models. The aim of this paper is to show how the introduction of energy terms related to…
An indentation experiment involves five variables: indenter shape, material behavior of the substrate, contact size, applied load and indentation depth. Only three variable are known afterwards, namely, indenter shape, plus load and depth…
The entropy of a polymer confined in a curved surface and the elastic free energy of a membrane consisting of polymers are obtained by scaling analysis. It is found that the elastic free energy of the membrane has the form of the in-plane…
Clapeyron's Theorem in classical linear elasticity provides a way to explicitly express the energy stored in an equilibrium configuration in terms of the work of the forces applied on the boundary. We derive several new integral relations…
In our earlier paper [9], it is proved that a homogeneous rigid, traction or impedance condition on one or two intersecting line segments together with a certain zero point-value condition implies that the solution to the Lam\'e system must…
Critically elastic materials - those that are rigid with a single state of self-stress - can be generated from parent systems with two states of self-stress by the removal of one of many constraints. We show that the elastic moduli of the…
Fundamental solutions for two- and three-dimensional linear isotropic size-dependent couple stress elasticity are derived, based upon the decomposition of displacement fields into dilatational and solenoidal components. While several…
We consider the elastic energy of a hanging drape -- a thin elastic sheet, pulled down by the force of gravity, with fine-scale folding at the top that achieves approximately uniform confinement. This example of energy-driven pattern…
A method to derive homogeneous effective constitutive equations for periodically layered elastic media is proposed. The crucial and novel idea underlying the procedure is that the coefficients of the dynamic effective medium can be…
A method is presented to calculate from first principles the higher-order elastic constants of a solid material. The method relies on finite strain deformations, a density functional theory approach to calculate the Cauchy stress tensor,…
Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived…
Elastic constants are among the most fundamental and important properties of solid materials, which is why they are routinely characterized in both experiments and simulations. While conceptually simple, the treatment of elastic constants…
A question of some fundamental importance is whether a given assembly of frictional granules (say sand or powder) will exhibit stress autocorrelations with long-range anisotropic decay as determined by the elastic Green's function. In…