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11. For a small displacement, the angle of rotation, θ = α/2, is used, unlike for large deformations, where the general Eq. 10 is applicable. It is possible to find such shear conditions where no rotation occurs. This case, called pure shear, is based on the definition of θij from Eq. 12. θij = 0 if all differences of the displacement gradients equal zero. For the simple shear, this condition has the following form: du1/dx2 = du2/dx1. A geometrical image of pure shear is drawn in Fig. 6. In pure shear, the diagonal AB of the small square (at some point) moves, due to deformation, into new position A*B*, parallel to its initial position, and the diagonal OM does not change its position at all, being only extended to OM*.
France, 1827. D. Poisson (1781-1840) − French mathematician and physicist, an author of fundamental works in the field of mathematical analysis and the theory of elasticity. D. Poisson, Mémoire sur l'équilibre et le mouvement des corps élastiques, Mém. Acad. Sci. Inst. France, 1829. L. Cauchy, Sur les équations differentielles d'équilibrium ou de mouvement pour le points matériels, Ex. , 1829. Some authors try to distinguish between “strain” and “deformation”. The College Dictionary has the following definition: “strain is a deformation of a body or a structure as a result of an applied force”.
However, there are at least three important principal exceptions. 1. A central physical problem exists in explanation of macro-observations of the molecular structure of matter. One would like to understand what happens to a molecule or how intermolecular interactions occur; then going through micro-volumes containing numerous molecules and averaging molecular phenomena, one would come to the macro properties of a body. 2. In some applications we use “zero” size. If geometrical shapes under consideration have sharp angles and the size at the corner of any angle (formally) equals zero, extrapolation of calculations results in such “zero” volume and sometimes leads to infinite values, and this is out of the realm of physical meaning.
Popular Mechanics (May 2004)
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