On the Motion of an Elastic Body Rolling/Sliding on an Elastic Substrate

1995 ◽  
Vol 117 (2) ◽  
pp. 308-314 ◽  
Author(s):  
A. Spector ◽  
R. C. Batra
Keyword(s):  
Elastic Body ◽  
Frictional Force ◽  
Three Dimensional ◽  
The Body ◽  
Elastic Substrate ◽  
Linear Elastic ◽  
Linear Elastic Body ◽  
Body Rolling ◽  
Applied Forces ◽  
Two Phases

The three-dimensional evolutionary problem of rolling/sliding of a linear elastic body on a linear elastic substrate is studied. The inertial properties of the body regarded as rigid are accounted for. By employing an asymptotic analysis, it is shown that the process can be divided into two phases: transient and quasistationary. An expression for the frictional force as a function of the externally applied forces and moments, and inertial properties of the body is derived. For an ellipsoid rolling/sliding on a linear elastic substrate, numerical results for the frictional force distribution, slip/adhesion subareas, and the evolution of the slip velocity are given.

scholarly journals Growth estimates in linear elasticity with a sublinear body force without definiteness conditions on the elasticities

1984 ◽  
Vol 27 (2) ◽  
pp. 223-228 ◽  
Author(s):  
Franca Franchi
Keyword(s):  
Wave Equation ◽  
Body Force ◽  
Displacement Vector ◽  
Fundamental Solutions ◽  
Existence Results ◽  
The Body ◽  
Heat Diffusion ◽  
Initial Value ◽  
Linear Elastic ◽  
Linear Elastic Body

In this paper, we study the boundary-initial value problem for a linear elastic body ina bounded domain, when the body force depends on the displacement vector u in asublinear way.Recently, much attention has been given to nonlinear body forces not only to studythe fundamental solutions of the equations governing linear elastodynamics, see e.g.Kecs [3], but also to derive global non existence results in abstract problems with directapplications to nonlinear heat diffusion or to the nonlinear wave equation, see e.g. Ball[1], Levine and Payne [10].

The Physical Meaning of Astatic Equilibrium in Saint-Venant’s Principle for Linear Elasticity

1969 ◽  
Vol 36 (3) ◽  
pp. 392-396 ◽  
Author(s):  
C. A. Berg
Keyword(s):  
Stress Field ◽  
Elastic Body ◽  
Long Range ◽  
Small Volume ◽  
Boundary Surface ◽  
Small Region ◽  
Main Body ◽  
Linear Elastic ◽  
Loading System ◽  
Linear Elastic Body

When a boundary loading which is not only self-equilibrated but has the additional property that the loading system remains self-equilibrated when all the forces are rotated through an arbitrary angle about their points of application (astatic equilibrium), is applied to a small region of the surface of a linear elastic body, the long range stress field produced by the loading is in general of smaller order (with respect to the radius of the loaded segment of the boundary) than would be the long range stress field produced by a loading system which was merely self-equilibrating but which would not continue to be self-equilibrating if each force were rotated (von Mises [3], Sternberg [6]). The physical distinctions between astatic equilibrium loadings and merely self-equilibrated loadings, and the physical reasons why astatic equilibrium loadings produce smaller long range stresses, are examined. It is pointed out that astatic equilibrium loadings always produce zero mean deformation in a linear elastic body and that, therefore, if a small volume element, in the neighborhood of a small patch of the boundary surface subject to astatic equilibrium loading were considered as an isolated body, this small volume would undergo no mean deformation and would be easier to fit back into the main body than if it had been subject to merely self-equilibrated loading which would have caused mean deformation.

Determination of material properties of a linearly elastic peridynamic material

2021 ◽  
pp. 108128652110514
Author(s):  
Adair R Aguiar ◽  
Alan B Seitenfuss
Keyword(s):  
Linear Elasticity ◽  
Poisson Ratio ◽  
Three Dimensional ◽  
The Body ◽  
Free Energy Function ◽  
Equilibrium Solutions ◽  
Plane Shear ◽  
Linear Elastic ◽  
Classical Linear Elasticity

We investigate the properties of an isotropic linear elastic peridynamic material in the context of a three-dimensional state-based peridynamic theory, which considers both length and relative angle changes, and is based on a free energy function proposed in previous work that contains four material constants. To this end, we consider a class of equilibrium problems in mechanics to show that, in interior points of the body where deformations are smooth, the corresponding solutions in classical linear elasticity are also equilibrium solutions in peridynamics. More generally, we show that the equations of equilibrium are satisfied even when two of the four peridynamic constants are arbitrary. Pure torsion of a cylindrical shaft and pure bending of a cylindrical beam are particular cases of this class of problems and are used together with a correspondence argument proposed elsewhere to determine these two constants in terms of the elasticity constants of an isotropic material from the classical linear elasticity. One of the constants has a singularity in the Poisson ratio, which needs further investigation. Two additional experiments concerning bending of cylindrical beam by terminal load and anti-plane shear of a hollow cylinder, which do not belong to the previous class of problems, are used to validate these results.

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