On stress-strain relations for isotropic rigid perfectly plastic solids

J. L. Dais
1969 Quarterly of Applied Mathematics  
Sufficient conditions under which principal directions of stress and strain rate must coincide are established rigorously. It is the coincidence of these directions which permits a proper interpretation of principal strain rate components in principal stress space. Introduction. A rigid perfectly plastic solid is characterized by a "yield" or "limit" surface /( where a',-is the stress deviator tensor) then normality requires that for some scalar X, ei; = X(3//3o-i,) = XaJ,-; coincidence of
more » ... coincidence of principal directions of stress and strain rate is then immediate since the principal axes of the stress and stress deviator tensors coincide. More generally, if / is a function of stress invariants which is differentiable in the components of cr" then the principal directions of cr"-and d//d cr2 > c3 . Deformation occurs by simple shearing in the direction of the shear stress vector T if the magnitude r of T reaches a critical value k. Since the planes of maximum shearing, called slip planes, are orthogonal, the simple
doi:10.1090/qam/99825 fatcat:yvhqd354qreotou7hedzitvz5i