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3 Spectral Analysis of Finite Dimensional Operators
A great number of engineering problems can be viewed as an input to output map**, as shown in Fig. 3.1, where the system represents the law for the...
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Nonequilibrium Dynamics of Anisotropic Fluids
In Chap. 9 we summarized methods for analyzing the equilibrium statistics of physical system, using Monte Carlo methods. While at equilibrium complex...
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Connection between Different Levels of Description
One of the major issues raised by the Boltzmann equation is the problem of the reduced description. Equations of hydrodynamics constitute a closet...
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10 Slip or Temperature Dependent Frictional Contact
The frictional contact problems which have been described up to now contained a constant friction coefficient, although, as was described in Sect....
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14 Conclusions, Remarks and Future Directions
This monograph shows clearly that the branch of the Mathematical Theory of Contact Mechanics which deals with quasistatic processes has made an...
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2 Evolution Equations, Contact and Friction
Contact processes take place on the surface, and, therefore, are described by boundary conditions. However, these are the boundaries or surfaces of...
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1 Stability of Two Rubber Balloons
Rubber balloons, that usually adorn children’s parties, can also enchant the scientist. Indeed, there is much more than fun and games to be had with...
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Chapter 3 Rough Terrain Motion Planning
Motion planning algorithms for mobile robots in rough terrain must explicitly consider the effects of robot-terrain interaction. This differs from...
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Chapter 1 Introduction
Mobile robots are increasingly being employed in rough, outdoor terrain for applications such as forestry, mining, search and rescue, and hazardous...
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5 A Detailed Representative Problem
In the previous three chapters various constitutive laws for the behaviour of the material and different contact conditions were described in some...
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7 Elastic Contact
Existence results for the problem of quasistatic contact between an elastic material and a reactive foundation were first obtained in [18] and [19]....
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12 Contact with Damage
We describe new results dealing with contact problems for materials that may undergo internal damage, resulting from strains and stresses which lead...
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8 Viscoelastic Contact
We describe results for contact problems involving viscoelastic materials. It will be seen that adding viscosity to the models leads to a substantial...
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9 Viscoplastic Contact
We describe contact problems for viscoplastic materials in which once the stress reaches the so-called yield limit the deformation becomes...
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4 Thermodynamic Derivation
In this chapter we present a short review of thermodynamic principles and potentials and describe their use in derivation of general thermomechanical...
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2 Kinetic Theory of Rubber
We start by considering an elastic bar of any solid material, be it steel, aluminium, wood - or rubber. The bar is fixed to the bottom at one end and...
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8 Many Balloons – The Emergence of a Pseudoelastic Hysteresis
The hysteresis represented in Fig. 7.9 for an inflation-deflation process of two communicating balloons is only the beginning. Figure 8.1 shows the...
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5 Stability of a Single Balloon
We recall the pressure-radius characteristic given in (3.24) and its graph which is represented by the solid curve of Fig. 3.4. We assume the elastic...
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11 History of Rubber and Its Use
Despite its spectacular properties rubber was not much good for anything before the latter part of the 19th century. To be sure the Aztecs had used...
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Vibrations of X-Braced Portal Frames
Because of devastation of structures due to earthquake and wind force, increasing attention has been paid to dynamic responses of braced structures...