A block of material which yields according to Tresca's yield criterion, with yield stress 2c in uni-axial tension, is subjected to an initial principal stress state (σ ₁  σ ₂  σ ₃  ) = (3c/4, 3c/8, 3c/8). The stresses are then changed steadily, with fixed ratios of stress increments. Calculate the stress states at yield if the stress increment.

Fig. 3.27 Yield surface in principal effective stress space for undisturbed Mastemyr clay (proposed by Clausen, Graham, and Wood, 1984)

ratios (δσ ₁  ,δσ ₂  , δσ ₃  ) are

(a) (1,-1/2,-1/2);

(b) (-1/2, 1, -1/2);

(c) (-1/2, -1/2, 1);

(d) (0, 1, -1);

(e) (-1, 0, 1);

(f) (1, -1, 0).