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In both cases, some degree of concavity of the yield surface becomes permissible when the elastic constants change radically with plastic deformation but is not likely to occur. When it appears again, the word "convexity" will be understood to include this limited concavity possibility. Similarly, the inability of soil to carry appreciable tension can be duplicated in the imagined metal by taking the yield stress and workhardening in tension as zero or as sm all in comparison with the corresponding quantities in compression.

An equilibrium state of stress may exist which is perfectly safe and yet the soil may progress toward failure. The lower bound theorem of limit analysis does not hold directly or in an extended manner for work-hardening. Unfortunately also, the basic principle of the upper bound theorem is inapplicable in general because there is no way of computing the energy dissipation from the state of the material and the plastic strain alone. The normal pressure on the plane of sliding, or the value of p, is needed in addition and is not known in the usual statically indeterminate problem.

A) Comparison Areal diffieulty does arise in eon- on of Fig. 7 a and Flg. 7 b Isotropie stressneetion with the limiting radial line hardening eurves with yield eurve [22] found by unloading along q = 0 and then whieh separates the stable region of addlng <1, (cf. Fig. 3); b) Loading path E" showing volume expansion and behavior from the ineipient unstable Edrop in stress as plastie deformation or the forbidden. The idea of isotropie proeeeds. hardening eould be extended beyond the radial line limit by drawing a set of limiting COULOMB lines of the eonventional c-q; type whieh also move outward in proportion to the eonsolidation pressure as shown dotted in Fig.