Related papers: A strain tensor that couples to the Madelung stres…
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…
Comparison of a few simple models of fluid and solid membranes illustrates how shear stresses can arise from a bending energy through a coupling between curvature and surface stresses, a feature incidental to the fluid or solid nature of…
Usual introductions of the concept of motion are not well adapted to a subsequent, strictly tensorial, theory of elasticity. The consideration of arbitrary coordinate systems for the representation of both, the points in the laboratory, and…
A soft solid is said to be initially stressed if it is subjected to a state of internal stress in its unloaded reference configuration. Developing a sound mathematical framework to model initially stressed solids in nonlinear elasticity is…
The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids {\bf 57}, 762 (2009)]. For a class of simple axisymmetric…
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…
Electromagnetic properties of a simple polarisable medium may be parameterised in terms of a constitutive tensor whose properties can in principle be determined by experiments in non-inertial (accelerating) frames and in the presence of…
Regarding a recent dispute about the symmetry of the stress tensor of fluids, more considerations are presented. The usual proofs of this symmetry are reviewed, and contradictions between this symmetry and the mechanism of gas viscosity are…
We revisit the results of Zamolodchikov and others on the deformation of two-dimensional quantum field theory by the determinant $\det T$ of the stress tensor, commonly referred to as $T\overline T$. Infinitesimally this is equivalent to a…
We derive the membrane elastic stress and torque tensors using the standard Helfrich model and a direct variational method in which the edges of a membrane are infinitesimally translated and rotated. We give simple expressions of the stress…
The form of the stress tensor is investigated in smooth, dense granular flows which are generated in split-bottom shear geometries. We find that, within a fluctuation fluidized spatial region, the form of the stress tensor is directly…
The stress-gradient theory has a third order tensor as kinematic degree of freedom, which is work-conjugate to the stress gradient. This tensor was called micro-displacements just for dimensional reasons. Consequently, this theory requires…
We prove that the stress tensor, tau^{ab}, of a molecular system with arbitrary, short-range interactions can be point-wisely expressed as the functional derivative of the partition function with respect to the local deformation tensor. In…
Stress tensors are derived for the multiparticle collision dynamics algorithm, a particle-based mesoscale simulation method for fluctuating fluids, resembling those of atomistic or molecular systems. Systems with periodic boundary…
The constitutive relation of the quasi-static deformation on two dimensional packed samples of polygons is calculated using molecular dynamic simulations. The stress values at which the system remains stable are bounded by a failure…
Accurate and robust models for the pressure strain correlation are an essential component for the success of Reynolds Stress Models in turbulent flow simulations. However replicating the non-local action of pressure using only local tensors…
We propose a thermodynamically based approach for constructing effective rate-type constitutive relations describing finite deformations of metamaterials. The effective constitutive relations are formulated as \emph{second-order} in time…
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…
Accurate and robust models for the pressure strain correlation are an essential component for the success of Reynolds Stress Models in turbulent flow simulations. However replicating the non-local action of pressure using only local tensors…
According to the classical theory of elasticity, a plate subjected to a bending moment always deflects with symmetric tensile and compressive strains in its two sides, without overall deformation perpendicular to the bending moment. Here,…