Braid group, knot theory, and statistical mechanics by M. L. Ge, C. N. Yang

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By M. L. Ge, C. N. Yang

Yang C.N., Ge M.L. (eds.) Braid crew, knot thought, and statistical mechanics (WS, 1989)(ISBN 9971508281)(331s)

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Example text

Mohr's graphical construction is quick and simple, however, and one diagram can give the stresses on any desired plane. 5) 2 which is the equation for a circle of radius{1(σχ — ay) + i xy}112 with centre at the point [%(σχ + ay), 0]. This is the basis for the geometrical representation of the state of stress at a point devised by Mohr. The circle is plotted with reference to axes of normal stress σ as abscissa and shear stress τ as ordinate. The sign convention used on the circle will be normal stress positive to the right and negative to the left of the origin.

In the x direction there is ε^ and in the y and z _νσν (σ) Stress FIG. *-£(«,+%> t4

The strain which occurs perpendicular to the direction of a stress is termed lateral or transverse strain and is found to be of opposite sign and pro­ portional, in the elastic range, to the strain in the direction of the stress. The ratio of lateral to longitudinal strain is called Poisson's ratio and will be given the symbol v. It is important to remember C O N C E P T S OF D E F O R M A T I O N AND STRAIN 47 that lateral strain does not imply that there is also stress in the lateral direction.

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