Related papers: Stress in Rotating Disks and Cylinders
A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on…
In classical continuum theory, Volterra's principle [1, 2] is a long-known method to solve linear rheological (viscoelastic) problems derived from the corresponding elastic ones. Here, we introduce and present another approach that is…
In this paper we study the wedge disclination within the elastoplastic defect theory. Using the stress function method we found exact analytical solutions for all characteristic fields of a straight wedge disclination in a cylinder. The…
We provide a derivation of the Foppl-von Karman equations for the shape of and stresses in an elastic plate with residual strains. These might arise from a range of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage…
This note provides a MATLAB code to determine the critical strain associated with the onset of dynamic recrystallization. The code takes a closed-form constitutive model and derives the critical strain by solving $\partial^2 \theta /…
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…
The paper gives an introduction to rate equations in nonlinear continuum mechanics which should obey specific transformation rules. Emphasis is placed on the geometrical nature of the operations involved in order to clarify the different…
The nature of an instability that controls the transition from static to dynamical friction is studied in the the context of an array of frictional disks that are pressed from above on a substrate. In this case the forces are all explicit…
The paper considers the general case of incompressible non-classical elasticity with small deformations and rotations. The thermodynamic stability is analysed for free energy density with three rotational degrees of freedom. Although the…
The classical alpha-disc model assumes that the turbulent stress scales linearly with -- and responds instantaneously to -- the pressure. It is likely, however, that the stress possesses a non-negligible relaxation time and will lag behind…
Relativistic kinematics is usually considered only as a manifestation of pseudo-Euclidean (Lorentzian) geometry of space-time. However, as it is explicitly stated in General Relativity, the geometry itself depends on dynamics, specifically,…
Taking the cue from experiments on actin growth on spherical beads, we formulate and solve a model problem describing the accretion of an incompressible elastic solid on a rigid sphere due to attachment of diffusing free particles. One of…
We study a technique for verification of stress and pressure computations on boundaries in flow simulations. We utilize existing experiments to provide validation of the simulations. We show that this approach can reveal critical flaws in…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
The Kelvin problem of an isotropic elastic space subject to a concentrated load is solved in a manner that exploits the problem's built-in symmetries so as to determine in the first place the unique balanced and compatible stress field.
The paper is concerned with comparative analysis of differential and integral formulations for boundary value problems in nonlocal elasticity. For the sake of simplicity, the focus is on an antiplane problem for a half-space for an…
Surface tension is a prominent factor for the deformation of solids at micro-/nano-scale. This paper investigates the effects of surface tension on the two-dimensional contact problems of an elastic layer bonded to the rigid substrate.…
In this paper we construct a solution of the two-dimensional problem of the elasticity theory (plane deformation) on pressing of the flat stamp in the rectangular plate by using the symbolic method and the exact solution of the harmonic…
Using classical description of spin degrees of freedom, we extend recent formulation of the perfect-fluid hydrodynamics for spin-polarized fluids to the case including dissipation. Our work is based on the analysis of classical kinetic…
A backward stable numerical calculation of a function with condition number $\kappa$ will have a relative accuracy of $\kappa\epsilon_{\text{machine}}$. Standard formulations and software implementations of finite-strain elastic materials…