Unique Critical State Hyperplasticity

Abstract

Over the last 30 years there has been considerable interest in the extension of the modifed Cam Clay constitutive model to include anisotropic material behaviour. Many formulations have been proposed that allow the elliptical yield (or bounding) surface to rotate off the hydrostatic axis, thereby introducing anisotropy. Several of these extensions have included one or more inner yield surfaces that produce inelastic behaviour within the outer surface. However, a Lode angle dependency (LAD), essential for reproducing the behaviour of particulate media, has not been introduced in a satisfactory way in the existing models. Rotating a LAD yield surface has presented challenges for earlier workers, such as maintaining convexity of that surface and uniqueness of the Critical State (CS) cone for differing degrees of anisotropy [1]. This paper overcomes the above difficulties by presenting a two surface anisotropic hyperplasticity model that includes a deviatoric section with a dependency on both (i) the Lode angle and (ii) the intermediate principal stress whilst maintaining a convex yield surface and a unique CS cone for any degree of anisotropy. The model is derived from free-energy and dissipation functions which provide the hyperelasticity law, yield function and direction of plastic flow without any additional assumptions [2]. Through the use of a target anisotropic hardening law, as proposed by Wheeler et al. [3], the model allows for a unique level of CS anisotropy, in agreement with recent findings from discrete element analyses [4]. An efficient implicit backward Euler stress integration algorithm and derivation of the algorithmic consistent tangent (for both small strain and finite deformation analysis) allows the model to be used in practical boundary value simulations.