Fracture is one of the most commonly encountered failure modes of engineering materials
and structures. Prevention of cracking-induced failure is, therefore, a major concern in …

This paper presents an overview of the theories and computer implementation aspects of
phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches …

Phase-field models, sometimes referred to as gradient damage or smeared crack models,
are widely used methods for the numerical simulation of crack propagation in brittle …

This paper presents a hybrid method for modeling hydraulic fracture propagation in an
unconventional shale formation with frictional and cemented natural fractures. The hybrid …

The phase field paradigm, in combination with a suitable variational structure, has opened a
path for using Griffith's energy balance to predict the fracture of solids. These so-called …

Computational modeling of the initiation and propagation of complex fracture is central to the
discipline of engineering fracture mechanics. This review focuses on two promising …

Heterogeneous materials with randomly distributed pores are ubiquitous, such as sintered
silver nanoparticles, concrete materials, 3D printed polymers, and natural bones. Recent …

Under a pure tensile loading, cracks in brittle, isotropic, and homogeneous materials often
propagate such that pure mode I kinematics are maintained at the crack tip. However …

Irreversible evolution is one of the central concepts as well as implementation challenges of
both the variational approach to fracture by Francfort and Marigo (1998) and its regularized …

This monograph is centered on mathematical modeling, innovative numerical algorithms
and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art …