Constitutive dual potentials in classical plasticity

Abstract

Inseveral branches of solid mechanics the constitutive relations and their inverses are expressible as tensor gradients of Legendre potentials. Exceptionally the response of classical rigid/plastic materials has never been shown to admit dual potentials of any kind. This is remedied here when the yield surface is convex and the normality flow-rule applies. The sought-for potentials are nonlinear homogeneous functions of first degree: one governs the magnitude of Cauchy stress at yield and the other the magnitude of Eulerian strain-rate via a work-equivalence norm. The duality is not of Legendre type but reflects a correspondence based on polar reciprocity. The geometrical background is developed ab initio and the construction is illustrated by several examples