Mechanics of deformable bodies

From this kind of continuum mechanics one can move further towards the domain of almost pure mathematics until one reaches the field of rational mechanics, which harks back to Joseph Lagrange s (1736-1813) mechanics of rigid bodies and to earlier mathematicians such as Leonhard Euler (1707-1783) and later ones such as Augustin Cauchy (1789-1857), who developed the mechanics of deformable bodies. The preeminent exponent of this kind of continuum mechanics was probably Clifford Truesdell in Baltimore. An example of his extensive writings is A First Course in... 

Mechanics is the physical science that deals with the effects of forces on the state of motion or rest of solid, liquid, or gaseous bodies. The field may he divided into the mechanics of rigid bodies, the mechanics of deformable bodies, and the mechanics of fluids. 

Sommerfeld, A., Mechanics of Deformable Bodies, 1964 English translation Academic Press, New York, 1964. 

A. Sommerfield, Mechanics of Deformable Bodies (includes discussion of the perfect analogy between hydrodynamics and electrodynamics ). 

As demonstrated by the foregoing two formulations, some problems taken from mechanics can be formulated by using only Newton s laws of motion these are called mechanically determined problems. The dynamics of rigid bodies in the absence of friction, statically determined problems of rigid bodies, and mechanics of ideal fluids provide examples of this class. Some other mechanics problems, however, require knowledge beyond Newton s laws of motion. These are called mechanically undetermined problems. The dynamics of rigid bodies with friction and the mechanics of deformable bodies provide examples of this class. 

The fracture mechanics (in a narrow sense) is usually associated with the mechanics of deformable bodies containing macroscopic cracks. These cracks are presented as mathematical cuts. The principal problem of fracture mechanics is to find conditions of stability of the system "cracked body - loading" with respect to the crack growth. 

Classical lamination theory consists of a coiiection of mechanics-of-materials type of stress and deformation hypotheses that are described in this section. By use of this theory, we can consistentiy proceed directiy from the basic building block, the lamina, to the end result, a structural laminate. The whole process is one of finding effective and reasonably accurate simplifying assumptions that enable us to reduce our attention from a complicated three-dimensional elasticity problem to a SQlvable two-dimensinnal merbanics of deformable bodies problem. 

In a study on the mechanism of deformation of metals, Gaugh and Wood wrote The properties of the solid state are baffling in the extreme. As a matter of fact, the deformation of solid bodies represents a very difficult chapter of applied physics. It is well known that all natural phenomena in which the effects of forces acting between the atoms and molecules interfere are very difficult to deal with quantitatively. Even the theory of real gases which show a departure from the ideal behaviour has not yet been completely mastered. Is it then surprising that the theory of the liquid and particularly that of the solid state is entwined with a great deal of obstacles and difficulties ... 

Balankin, A. S. (1992). Fractal Mechanics of Deformable Mediums and Solid Bodies Fracmre Topology DoWady AN, 322(5), 869-874. 

Adhesion is the interaction that develops between two dissimilar bodies when they are contacted. Adhesion is thus a multidisciplinary science dealing with the chemistry and physics of surfaces and interfaces as well as the mechanics of deformation and fracture of adhesive joints. In this overview, these various aspects of adhesion are discussed. We begin by describing the general types of adhesive bonds. This is followed by sections on solid surfaces and their characterization, interfacial properties, surface treatment, and finally a discussion of the mechanics of adhesive joints. 

Rabotnov Yu.N. (1979) Mechanics of a deformed solid body. Nauka, Moscow (in Russian). 

A rigid body is one that does not deform. True rigid bodies do not exist in nature however, the assumption of rigid body behavior is usually an acceptable accurate simplification for examining the state of motion or rest of structures and elements of structures. The rigid body assumption is not useful in the study of structural failure. Rigid body mechanics is further subdivided into the study of bodies at rest, stalks, and the study of bodies in motion, dynamics. 

The application of force to a stationary or moving system can be described in static, kinematic, or dynamic terms that define the mechanical similarity of processing equipment and the solids or liquids within their confines. Static similarity relates the deformation under constant stress of one body... 

The application of force to a stationary or moving system can be described in static, kinematic, or dynamic terms that define the mechanical similarity of processing equipment and the solids or liquids within their confines. Static similarity relates the deformation under constant stress of one body or structure to that of another it exists when geometric similarity is maintained even as elastic or plastic deformation of stressed structural components occurs [53], In contrast, kinematic similarity encompasses the additional dimension of time, while dynamic similarity involves the forces (e.g., pressure, gravitational, centrifugal) that accelerate or retard moving masses in dynamic systems. The inclusion of tune as another dimension necessitates the consideration of corresponding times, t and t, for which the time scale ratio t, defined as t = t It, is a constant. 

In contrast to the disapline of mechanics, wherein the responses of bodies to unbalanced forces are of concern, rheology concerns balanced forces which do not change the center of gravity of the body. Since rheology involves deformation and flow, it is concerned primarily with the evaluation... 

At first we have deliberately focused on the applied (technological) importance of the study of melt behavior under extension since the theoretical importance of the analysis of melt extension for polymer physics and mechanics can be regarded as already generally recognized. The scientific success and recognition of melt extension stems, we believe, from several fundamental causes, major of which are as follows. The geometrical pattern of deformation (shear, twisting, tension, etc.) is not very important for mechanics of the usual solid bodies since there is a well-known and multiply verified connection (linear Hooke s mechanics) between the main (if... 

Microscopically, the skin is a multilayered organ composed of many histological layers. It is generally subdivided into three layers the epidermis, the dermis, and the hypodermis [1]. The uppermost nonviable layer of the epidermis, the stratum corneum, has been demonstrated to constitute the principal barrier to percutaneous penetration [2,3]. The excellent barrier properties of the stratum corneum can be ascribed to its unique structure and composition. The viable epidermis is situated beneath the stratum corneum and responsible for the generation of the stratum corneum. The dermis is directly adjacent to the epidermis and composed of a matrix of connective tissue, which renders the skin its elasticity and resistance to deformation. The blood vessels that are present in the dermis provide the skin with nutrients and oxygen [1]. The hypodermis or subcutaneous fat tissue is the lowermost layer of the skin. It supports the dermis and epidermis and provides thermal isolation and mechanical protection of the body. 

In this chapter, two simple cases of stereomechanical collision of spheres are analyzed. The fundamentals of contact mechanics of solids are introduced to illustrate the interrelationship between the collisional forces and deformations of solids. Specifically, the general theories of stresses and strains inside a solid medium under the application of an external force are described. The intrinsic relations between the contact force and the corresponding elastic deformations of contacting bodies are discussed. In this connection, it is assumed that the deformations are processed at an infinitely small impact velocity and for an infinitely long period of contact. The normal impact of elastic bodies is modeled by the Hertzian theory [Hertz, 1881], and the oblique impact is delineated by Mindlin s theory [Mindlin, 1949]. In order to link the contact theories to collisional mechanics, it is assumed that the process of a dynamic impact of two solids can be regarded as quasi-static. This quasi-static approach is valid when the impact velocity is small compared to the speed of the elastic... 

Plastic deformation is defined as the permanent distortion of a body under stress. The stress at which the material deforms plastically is called the yield stress or yield point. This deformation can occur via a number of mechanisms ... 

Tensile and shear forces are not the only types of loads that can result in deformation. Compressive forces may as well. For example, if a body is subjected to hydrostatic pressure, which exists at any place in a body of fluid (e.g. air, water) owing to the weight of the fluid above, the elastic response of the body would be a change in volume, but not shape. This behavior is quantified by the bulk modulus, B, which is the resistance to volume change, or the specific incompressibihty, of a material. A related, but not identical property, is hardness, H, which is defined as the resistance offered by a material to external mechanical action (plastic deformation). A material may have a high bulk modulus but low hardness (tungsten carbide, B = 439 GPa, hardness = 30 GPa). 

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