An extended isogeometric thin shell analysis based on Kirchhoff-Love theory

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

https://estudogeral.sib.uc.pt/bitstream/10316/27389/1/Element-wise%20fracture%20algorithm%20based%20on%20rotation%20of%20edges.pdf

Element-wise fracture algorithm based on rotation of edges

Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth

Efficient coarse graining in multiscale modeling of fracture

Strain smoothing in FEM and XFEM

In this paper, a h-adaptive methodology based on the polytopal meshes is proposed for capturing high stress gradients at the materials corners and the stress singularities at the vicinity of a crack tip. The adaptive refinement is based on the error indicator directly computed from the displacement solutions of the scaled boundary finite element method. Based on the error indicator, a polygon of n-sides which has an error exceeding a specified tolerance is subdivided recursively into $$(n+1)$$
 child polygons. The salient features of the proposed framework are: (a) circumvents a need for post-processing techniques for error estimation; (b) elements with hanging nodes are treated as polygons without a need for special treatment and (c) stress gradients and stress singularities are accurately captured due to the semi-analytical formulation. The robustness and the convergence properties of the proposed framework is demonstrated with three benchmark examples.

Nguyen-Xuan Hung

Papers

Strain smoothing in FEM and XFEM

An adaptive polytree approach to the scaled boundary boundary finite element method