  A continuum model of fracture that describes, in principle, the propagation
and interaction of arbitrary distributions of cracks and voids with evolving
topology without a fracture criterion is developed. It involves a 'law of
motion' for crack-tips, primarily as a kinematical consequence coupled with
thermodynamics. Fundamental kinematics endows the crack-tip with a topological
charge. This allows the association of a kinematical conservation law for the
charge, resulting in a fundamental evolution equation for the crack-tip field,
and in turn the crack field. The vectorial crack field degrades the elastic
modulus in a physically justified anisotropic manner. The mathematical
structure of this conservation law allows an additive 'free' gradient of a
scalar field in the evolution of the crack field. We associate this naturally
emerging scalar field with the porosity that arises in the modeling of ductile
failure. Thus, porosity-rate gradients affect the evolution of the crack-field
which, then, naturally degrades the elastic modulus, and it is through this
fundamental mechanism that spatial gradients in porosity growth affects the
strain-energy density and stress carrying capacity of the material - and, as a
dimensional consequence related to fundamental kinematics, introduces a
length-scale in the model. The key hypothesis of this work is that brittle
fracture is energy-driven while ductile fracture is stress-driven; under
overall shear loadings where mean stress vanishes or is compressive, shear
strain energy can still drive shear fracture in ductile materials.
