  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 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 heterogeneous structures: laminates,
wavy interfaces, and circular inclusions. In each case a non-dimensionalized
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.
