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 structural designs. Computational modeling of fracture constitutes an indispensable tool not only to predict the failure of cracking structures but also to shed insights into understanding the fracture processes of many materials such as concrete, rock, ceramic, metals, and biological soft tissues. This chapter provides an extensive overview of the literature on the so-called phase-field fracture/damage models (PFMs), particularly, for quasi-static and dynamic fracture of brittle and quasi-brittle materials, from the points of view of a computational mechanician. PFMs are the regularized versions of the variational approach to fracture which generalizes Griffith's theory for brittle fracture. They can handle topologically complex fractures such as initiation, intersecting, and branching cracks in both two and three dimensions with a quite straightforward implementation. One of our aims is to justify the gaining popularity of PFMs. To this end, both theoretical and computational aspects are discussed and extensive benchmark problems (for quasi-static and dynamic brittle/cohesive fracture) that are successfully and unsuccessfully solved with PFMs are presented. Unresolved issues for further investigations are also documented.

Phase-field modeling of fracture

Localisation studies have been carried out for an unconstrained, elasto-plastic, strain-softening Cosserat continuum. Because of the presence of an internal length scale in this continuum model a perfect convergence is found upon mesh refinement. A finite, constant width of the localisation zone and a finite energy dissipation are computed under static as well as under transient loading conditions. Because of the existence of rotational degrees-of-freedom in a Cosserat continuum additional wave types arise and wave propagation becomes dispersive. This has been investigated analytically and numerically for an elastic Cosserat continuum and an excellent agreement has been found between both solutions.

Localisation in a Cosserat continuum under static and dynamic loading conditions

An Introduction To Radiation Chemistry

Phase field and gradient enhanced damage models for quasi-brittle failure: A numerical comparative study

A polygonal XFEM with new numerical integration for linear elastic fracture mechanics

Modeling and simulation of quasi-brittle failure with continuous anisotropic stress-based gradient-enhanced damage models

The effects of carbonation conditions on the physical and microstructural properties of recycled concrete coarse aggregates

Mesoscopic modelling of masonry using weak and strong discontinuities

A novel constrained large time increment method for modelling quasi-brittle failure

Hysteretic behaviour of steel fibre RC coupled shear walls under cyclic loads: Experimental study and modelling

Bram Vandoren

Papers

Modeling and simulation of quasi-brittle failure with continuous anisotropic stress-based gradient-enhanced damage models

The effects of carbonation conditions on the physical and microstructural properties of recycled concrete coarse aggregates

Mesoscopic modelling of masonry using weak and strong discontinuities

A novel constrained large time increment method for modelling quasi-brittle failure

Hysteretic behaviour of steel fibre RC coupled shear walls under cyclic loads: Experimental study and modelling