By J. C. Jaeger (auth.)
IN this monograph i've got tried to set out, in as elemen tary a sort as attainable, the elemental arithmetic of the theories of elasticity, plasticity, viscosity, and rheology, including a dialogue of the homes of the fabrics concerned and how within which they're idealized to shape a foundation for the mathe matical concept. there are lots of mathematical text-books on those topics, yet they're principally dedicated to tools for the answer of precise difficulties, and, whereas the current booklet could be considered as an creation to those, it's also in tended for the big category of readers comparable to engineers and geologists who're extra drawn to the distinctive research of rigidity and pressure, the houses of a few of the fabrics they use, standards for movement and fracture, etc, and whose curiosity within the concept is quite within the assumptions fascinated with it and how during which they impact the strategies than within the learn of specific difficulties. the 1st bankruptcy develops the research of pressure and pressure relatively totally, giving, specifically, an account of Mohr's repre sentations of tension and of finite homogeneous pressure in 3 dimensions. within the moment bankruptcy, at the behaviour of fabrics, the stress-strain family members for elasticity (both for isotropic and straightforward anisotropic substances), viscosity, plas ticity and a few of the easier rheological types are described.
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Extra info for Elasticity, Fracture and Flow: with Engineering and Geological Applications
A strain is called homogeneous if all straight lines remain straight lines after straining, and parallel straight lines remain parallel, though their direction may be altered. It follows by elementary geometry from this definition that similar and similarly situated figures at all points of the body are deformed in the same way, cf. Fig. 9 (c). This implies that the state of strain may be regarded as being the same allover the body. This is one reason for the name 'homogeneous' . There are two reasons for studying homogeneous strain: firstly, it will be shown in §§ 10, I I that in the general case there is a small region in which the strain is homogeneous surrounding any point, so that results proved for homogeneous strain apply in this region; secondly, while the strains occurring in engineering practice are usually infinitesimal, large strains do occur, occasionally in engineering and frequently in geology, and it is very desirable to have a detailed knowledge of their nature in a special case.
Sometimes the curve is initially linear and shows curvature only as C is approached, sometimes it has a small curvature throughout, but it may be roughly idealized by the straight line of Fig. 19 (d), ending abruptly in fracture with no significant amount of plastic deformation. A fact of the greatest importance for geology is that brittle materials such as rocks tend to become ductile when subjected to compression from all sides. 000 III fII £ Q. III o E ~ ~ 5000 bl') I C 4000 .. f2000 ~1000 10 20 E (O,o shortening) FIG.
By (5) and (6), A moves to the point A' such that P'A" =(I+EIIJ)X', A'A"=(ro+bllJlI)x', and B moves to the point B' such that P'B"=(I+EII)Y', B'B"=y'(bllJll-ro). , are negligible) that E(JJ is the extension of an element initially parallel to the x-axis, and Ell that of one initially parallel to the y-axis. "" corresponding to a shear of this amount as in § 6 (3). The three components of strain have been derived by differentiation from the two components of displacement so it might be expected that they are not independent.
Elasticity, Fracture and Flow: with Engineering and Geological Applications by J. C. Jaeger (auth.)