A SIMPLE FORMULATION OF A DILATANT JOINT ELEMENT GOVERNED BY COULOMB FRICTION

The paper considers a plane joint or interface element suitable for implementation into a standard non‐linear finite element code. Sliding of the joint is assumed to be governed by Coulomb friction, with a non‐associated flow rule and no cohesion. The constitutive equations are formulated in a manner appropriate for a backward difference discretization in time along the path of loading. It is shown that the backward difference assumption can lead to an explicit formulation in which no essential distinction need be drawn between opening and closing of the joint and sliding when the joint is closed. However, an inherent limitation of the dilatant Coulomb model becomes evident; the final formulation is internally consistent but does not describe reversed shear displacement in a physically reasonable way. Explicit equations for the consistent tangent stiffness and for the corrector step (or return algorithm) of the standard Newton—Raphson iterative algorithm are given. The equations have been implemented as a user element in the finite element code ABAQUS, and illustrative examples are given.