  Fracture is a ubiquitous phenomenon in most composite engineering structures,
and is often the responsible mechanism for catastrophic failure. Over the past
several decades, many approaches have emerged to model and predict crack
failure. The phase field method for fracture uses a surrogate damage field to
model crack propagation, eliminating the arduous need for explicit crack
meshing. In this work a novel numerical framework is proposed for implementing
hybrid phase field fracture in heterogeneous composite materials. The proposed
method is based on the "reflux-free" method for solving, in strong form, the
equations of linear elasticity on a block-structured adaptive mesh refinement
(BSAMR) mesh. The use of BSAMR enables highly efficient and scalable
regridding, facilitates the use of temporal subcycling for explicit time
integration, and allows for ultra-high refinement at crack boundaries with
minimal computational cost. The method is applied to a variety of simple
composite structures: laminates, wavy interfaces, and circular inclusions. In
each case a nondimensionalized parameter study is performed to identify regions
of behavior, varying both the geometry of the problem and the relative fracture
energy release rate. In the laminate and wavy interface cases, regions of
delamination and fracture correspond to simple analytical predictions. For the
circular inclusions, the modulus ratio of the inclusion is varied as well as
the delamination energy release rate and the problem geometry. In this case, a
wide variety of behaviors was observed, including deflection, splitting,
delamination, and pure fracture.
