We present a theory with a structure that enables analyses of ductile fracture under any type of loading. The theory builds on the standard concept of homogeneous yielding that underlies Gurson-like models and further proceeds from the concept of unhomogeneous yielding on a (yield) system that depends on the spatial distribution of voids. Depending on the desired level of refinement in analysis, a given simulation employs one or more yield systems with the isotropic limit being reached for an infinite number of systems. We illustrate the predictive capabilities of the theory by considering simulations of three-dimensional crack initiation and growth in a round notched bar, a shear specimen and a compression pin.