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This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling…
Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter $\epsilon$ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying…
Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In…
Fracture mechanics is crucial for many fields of engineering, as precisely predicting failure of structures and parts is required for efficient designs. The simulation of failure processes is, from a mechanical and a numerical point of…
Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We…
The phase-field method has become popular for the numerical modeling of fluid-filled fractures, thanks to its ability to represent complex fracture geometry without algorithms. However, the algorithm-free representation of fracture geometry…
Phase-field models are a leading approach for realistic fracture problems. They treat the crack as a second phase and use gradient terms to smear out the crack faces, enabling the use of standard numerical methods for simulations. This…
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 phase field fracture methods have gained significant…
The phase-field model for fracture, despite its popularity and ease of implementation comes with its set of computational challenges. They are the non-convex energy functional, variational inequality due to fracture irreversibility, the…
The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…
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 approach to modeling fracture uses a diffuse damage field to represent a crack. This addresses the singularities that arise at the crack tip in computations with sharp interface models, mollifying some of the difficulties…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
The $\xi$-based spatially adaptive three-field variable phase-field model for quasi-static anti-plane crack propagation is introduced. A dynamically optimized regularization length is integrated to improve computational efficiency and…
The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…
Recently, the phase field method has been increasingly used for brittle fractures in soft materials like polymers, elastomers, and biological tissues. When considering finite deformations to account for the highly deformable nature of soft…
While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the…
The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The…
We present a phase field formulation for fracture in functionally graded materials (FGMs). The model builds upon homogenization theory and accounts for the spatial variation of elastic and fracture properties. Several paradigmatic case…
The simulation of crack initiation and propagation in an elastic material is difficult, as crack paths with complex topologies have to be resolved. Phase-field approach allows to simulate crack behavior by circumventing the need to…