Granular Elasticity without the Coulomb Condition

A self-contained elastic theory is derived which accounts both for mechanical yield and shear-induced volume dilatancy. Its two essential ingredients are thermodynamic instability and the dependence of the elastic moduli on compression.

Figure 1

Compression $\delta$ versus pressure $P$ (left) and shear $u_s$ (right). Stability is maintained only where the lines are solid.

Figure 2

Plots of ${\varphi }_1$ (solid lines) and ${\varphi }_2-{\varphi }_1$ (dashed lines) as functions of $a$ for $\nu =0.2,0.3,0.4$ (denoted as 1, 2, 3).