Limit load theorems for the drucker-prager yield condition with a non-associated flow rule

Abstract

There exist a number of significant problems where the assumptions of limit and shakedown analysis, i.e. the bounding theorems, are not fully satisfied. Principal amongst such problems are those where the yield surface is convex but the flow rule is non-associated. This includes limit states in geomechanics where yield is pressure dependent but flow remains volume conserving. Coulomb friction between elastic bodies shows related behaviour. The paper explores the extent to which the classical limit theorems may be extended to the Drucker-Prager yield condition with a non-associated flow rule where the plastic strain rate involves no volume change. Bounds that correspond to the classical kinematic and static bounds are derived which defines a range within which consistent limit state solutions will exist, i.e. the limit state is not generally unique.