Smooth Limit Surfaces for Metals, Concrete, and Geotechnical Materials

A limit surface for engineering materials in terms of three invariants of stress is proposed in which the shape of the surface in the deviatoric plane is described as a function of mean pressure. The shape is triangular for small values of mean pressure and circular for large values. The surface contains no corners, intersects the tensile pressure axis at right angles, and asymptotically approaches a constant value for large values of mean pressure. Since the limit surface is smooth and convex, a scaled version is suitable for the yield surface of an associated plasticity theory with no special algorithm needed for corners. Traditional surfaces are obtained as special cases, and examples of fits to existing experimental data are given.