Contact between two bodies

Dynamic contact between two bodies (e.g., one sliding over the other) generates noise that is characteristic of the hardness of these bodies and of the physical and chemical properties of their interface. Moreover, the velocity of the sliding movement modifies the frequency band of the emitted acoustic waves. The sliding displacement of a finger at the surface of the skin for assessing its smoothness... 

FIGURE 3.1 Analysis procedure for force-distance curves with and without an adhesive force between the sample and the AFM probe (a) schematic of contact between two bodies when the applied force is positive (repulsive) (b) force-distance curve for the contact between probe and substrate without adhesive interaction (c) corresponding force-deformation plot (d) schematic of adhesive contact especiatly when the applied force is negative (attractive) (e) force-distance curve for adhesive contact (f) corresponding force-deformation plot. 

Ceramics are susceptible to contact damage and, thus, it is important to understand the stress fields that arise around contacts between two bodies. Consider the simple problem of a body being contacted by a linear force per unit thickness F, as illustrated in Fig. 4.22. The stress function for this problem can be expressed as x= CrOsinO, where C is a constant. From Eq. (4.27), the stress components are <7- =2Ccos 6/r, agg=a g=0. The constant C can be determined using statics for a force balance in the vertical direction, i.e.. 

Sealing by means of a threaded cormectirMi or a peti/hole connection Stiffness of a connection Plastic or elastic deformation at contact between two bodies... 

Adhesion and Triboelectricity. When dust particles move in an air stream confined by walls, the adhesive force may be increased as a result of electric charges generated by contact of the particles with the solid surface. The magnitude and sign of the charge can be determined [266,267] for the contact between two bodies under static conditions, but only for clean surfaces (see Section 15). Such calculations, however, are in any case difficult to carry out for real systems involving the movement of particles. 

Boundary condition can cause nonUnearity if they vary with displacement of the structure. Boundary condition is the load and the resistance to the deformation induced by the loads that represent the effects of the surrounding enviromnent on the model. Many of these nonlinear boundary conditions have a discontinuous character, which makes them some of the most severe nonlinearities in mechanics. Examples are frictional slip effects and contact between two bodies, such as an indenter and a coating. 

Scheme 5 Hertzian contact between two bodies with radius of curvature...

The model describing interaction between two bodies, one of which is a deformed solid and the other is a rigid one, we call a contact problem. After the deformation, the rigid body (called also punch or obstacle) remains invariable, and the solid must not penetrate into the punch. Meanwhile, it is assumed that the contact area (i.e. the set where the boundary of the deformed solid coincides with the obstacle surface) is unknown a priori. This condition is physically acceptable and is called a nonpenetration condition. We intend to give a mathematical description of nonpenetration conditions to diversified models of solids for contact and crack problems. Indeed, as one will see, the nonpenetration of crack surfaces is similar to contact problems. In this subsection, the contact problems for two-dimensional problems characterizing constraints imposed inside a domain are considered. 

Hertz [27] solved the problem of the contact between two elastic elliptical bodies by modeling each body as an infinite half plane which is loaded over a contact area that is small in comparison to the body itself. The requirement of small areas of contact further allowed Hertz to use a parabola to represent the shape of the profile of the ellipses. In essence. Hertz modeled the interaction of elliptical asperities in contact. Fundamental in his solution is the assumption that, when two elliptical objects are compressed against one another, the shape of the deformed mating surface lies between the shape of the two undeformed surfaces but more closely resembles the shape of the surface with the higher elastic modulus. This means the deformed shape after two spheres are pressed against one another is a spherical shape. 

Contact forces between two bodies have the same magnitude, the same line of action, and opposite direction. 

In collisions between two bodies the contact force and the duration of contact are usually unknown. However, the duration of contact is the same for both bodies, and the force on the first body is the negative of the force on the second body. Thus the net change in momentum is zero. This is called the principle of conservation of momentum. 

The mechanical properties of a material play an important role in powder flow and compaction by influencing particle-particle interaction and cohesion, that is to say, by influencing the true area of contact between particles. For example, Hertz [26] demonstrated that both the size and shape of the zone of contact followed simply from the elastic properties of a material. Clearly then, the true area of contact is affected by elastic properties. From the laws of elasticity, one can predict the area of contact between two elastic bodies. More recent work has demonstrated, however, that additional factors must be taken... 

Heat Exchange Between Two Bodies. Suppose that we take two bodies initially at equilibrium at temperatures 7h and Tq, where Tfi and 7c stand for a hot and a cold temperature, respectively. At time t = 0 we put them in contact and ask about the probability distribution of heat flow between them. In this case, no work is done between the two bodies and the heat transferred is equal to the energy variation of each of the bodies. Let Q be equal to the heat transferred from the hot to the cold body in one experiment. It can be shown [49] that in this case the total dissipation S is given by... 

The transfer of heat between two bodies requires a difference in their temperatures. The reversible transfer of heat between two bodies would require their temperatures to be the same. The question then arises of how we may reversibly add a quantity of heat to or remove a quantity of heat from a system over a temperature range. In order to do so we assume that we have an infinitely large number of heat reservoirs whose temperatures differ infinitesimally. Then, by bringing the system into thermal contact with these reservoirs successively and allowing thermal equilibrium to be obtained in each step, we approach a reversible process. 

When two elastic and frictionless spheres are brought into contact under compressional forces or pressures, deformation occurs. The maximum displacement and contact area depend not only on the compressional force but also on the elastic material properties and radii of the spheres. The contact between two elastic and frictionless spherical bodies under compression was first investigated by Hertz (1881) and is known as the Hertzian contact. 

Friction, a force acting between two bodies in contact, is parallel to the surface and opposite the motion (or tendency to move). By the second law, giving a mass of one kilogram (kg) an acceleration of 1 m/sec/sec requires a force of one Newton (N). However, if friction were 3 N, a force of 4 N must be applied to give the... 

Fig. 2.3 Temperature at the interface between two bodies 1 and 2 in contact with each other, a no contact resistance, b contact resistance according to (2.22)...

We will consider the two semi-infinite bodies shown in Fig. 2.24, which have different, but constant, initial temperatures d01 and d02- Their material properties Ax, a1 and A2, a2 are also different. At time t = 0 both bodies are brought into (thermal) contact with each other along the plane indicated by x = 0. After a very short period of time an average temperature is reached along the plane. Heat flows from body 1 with the higher initial temperature to body 2 which has a lower temperature. The transient conduction process described here serves as a model for the description of short-time contact between two (finite) bodies at different temperatures. Examples of this include the touching of different objects with a hand or foot and the short-time interaction of a heated metal body with a cooled object in reforming processes. 

Contact between two quiescent bodies (1) and (2) at the interface can exist (boundary condition of the 3rd kind)... 

One way to transfer energy from one body to another is to place two bodies at different temperatures in contact with each other. It is a universal experience that in such circumstances the internal jenergy of the hotter body will decrease and the internal energy of the colder body will increase. Therefore, energy must have flowed from one to tlJe other. The energy which flows directly between two bodies in contact because of a temperature difference we call heat. j... 

It is found by experiment that, at constant pressure or volume, the intermediate temperature at which two systems attain equilibrium on thermal contact is uniquely determined by their initial states. In addition, we find that, to a specified temperature of a suitably selected standard body of given initial temperature, there correspond unique temperature increments in all other systems of given initial states thermally contacted with the standard at constant p or v. These facts allow us to associate temperature changes produced by thermal contact between two systems with the transfer of a physical quantity heat between them and to assign to every system an extensive property called heat capacity. 

Equation (5.2) gives the contact area between an hemispherical tip and a plane surface for any externally vertically applied load larger than the pull off force. If equations (5.1)-(5.9) are helpful in understanding the contact between two elastic bodies, there arc not enough to describe the basic processes involved when a tip scans a surface. 

The dynamic interaction between two bodies may be described by a resultant force and moment. Thus, when bodies (i - 1) and i interact, whether through a joint or contact, a generalized force, f<, is exerted on body i by body (i - 1) and with a negative sign on body (i - 1). Its form is given in Equation 2.3. This force vector may be resolved in the dual basis defined above ... 

Heat Heat is defined as the energy that flows between two bodies that are at different temperatures. When two systems are in thermal contact (i.e., not insulated) energy flows from the system at a higher temperature to one at a lower temperature till the temperature becomes equal or thermal equilibrium is reached. This gives us a qualitative concept of heat. Once heat flows into a system, it appears in the system as an increase in its internal energy. 

Interface Surface that forms the boundary between two bodies of matter (liquid, solid, gas) or the area where two immiscible phases come in contact. 

Macroshock, or simply electric shock, describes simultaneous contact between the body surface and two electrical conductors at different potentials, and the physiological consequences of this contact. The two conductors maybe a hot conductor and ground, or two hot conductors, such as two of the phase wires in a three-phase power distribution system. 

A single chain at the compensation point Q has a quasi-ideal behavior. The size R scales like N, and the pair correlation function g r) decreases like 1 r (for r 7 ). However, the three-body repulsive interactions remain effective even at T = 6. Their effect (in three dimensions) is to introduce some correlation between the monomers. The probability of contact between two (or three) monomers is reduced by certain logarithmic factors. These factors could show up in certain measurements which are sensitive to local properties (e.g., specific heat) and possibly in certain optical properties. 

Solid Friction. Solid friction occurs when there is physical contact between two sohd bodies moving relative to each other. The type of motion divides solid friction into two categories, sliding and rolling friction. 

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