Described are methods, systems, and apparatus, including computer program products for determining material constitutive relationships of fracture in a ductile material undergoing plastic deformation. A material pressure function is determined that describes dependence of a damage rule of at least a portion of the ductile material on pressure. A material azimuthal angle function is determined that describes dependence of the damage rule of the portion of the ductile material on principle stress. The damage rule of the portion of the ductile material is determined based on the material pressure function and the material azimuthal angle function. A weakening function of the portion of the ductile material is determined based on the damage rule. Material constitutive relationships of fracture in the portion of the ductile material are determined based on the weakening function and a matrix property of the ductile material.
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