The Classification of Isotropic Points in Stress Fields

Isotropic points are significant features of any complicated two-dimensional field of stress and strain, for they are stable against perturbation. Around them the trajectories of principal stress or strain have three patterns, rather than the two usually recognized, the extra pattern being called monstar. The example of three-point bending of a beam illustrates how isotropic points can be born in pairs, one member of the pair necessarily having the monstar pattern, and how a point can subsequently change from one pattern to another. By making yet another distinction, one can divide isotropic points into six categories, in general. In the special case of statical equilibrium without body forces, the number of different categories for the isotropic points in a stress distribution reduces to four and there is a close analogy with the umbilic points of a surface, but for strain the number remains six.