- Numerical studies of the ductile-brittle transition are described that are based on incorporating physically based models of the competing fracture mechanisms into the material's constitutive relation. An elasticviscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Cleavage is modeled in terms of attaining a temperature and strain rate independent critical value of the maximum principal stress over a specified material region of the order of one or two grain sizes. Various analyses of ductile-brittle transitions carried out within this framework are discussed. The specimens considered include the Charpy V-notch test and cracked specimens under mode I or mode II loading conditions. The fracture mode transition emerges as a natural outcome of the initial-boundary value problem solution.