  A mechanical model is introduced for predicting the initiation and evolution
of complex fracture patterns without the need for a damage variable or law. The
model, a continuum variant of Newton's second law, uses integral rather than
partial differential operators where the region of integration is over finite
domain. The force interaction is derived from a novel nonconvex strain energy
density function, resulting in a nonmonotonic material model. The resulting
equation of motion is proved to be mathematically well-posed. The model has the
capacity to simulate nucleation and growth of multiple, mutually interacting
dynamic fractures. In the limit of zero region of integration, the model
reproduces the classic Griffith model of brittle fracture. The simplicity of
the formulation avoids the need for supplemental kinetic relations that dictate
crack growth or the need for an explicit damage evolution law.
