@article{LegatiukWeiszPatrault,
  author    = {Legatiuk, Dmitrii and Weisz-Patrault, Daniel},
  title     = {Coupling of Complex Function Theory and Finite Element Method for Crack Propagation Through Energetic Formulation: Conformal Mapping Approach and Reduction to a Riemann-Hilbert Problem},
  series = {Computational Methods and Function Theory},
  volume    = {2021},
  journal   = {Computational Methods and Function Theory},
  publisher = {Springer},
  address   = {Heidelberg},
  doi       = {10.1007/s40315-021-00403-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210805-44763},
  pages     = {1 -- 23},
  abstract  = {In this paper we present a theoretical background for a coupled analytical-numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical-numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann-Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{Hanna,
  author    = {Hanna, John},
  title     = {Computational Modelling for the Effects of Capsular Clustering on Fracture of Encapsulation-Based Self-Healing Concrete Using XFEM and Cohesive Surface Technique},
  series = {Applied Sciences},
  volume    = {2022},
  journal   = {Applied Sciences},
  number    = {Volume 12, issue 10, article 5112},
  publisher = {MDPI},
  address   = {Basel},
  doi       = {10.3390/app12105112},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220721-46717},
  pages     = {1 -- 17},
  abstract  = {The fracture of microcapsules is an important issue to release the healing agent for healing the cracks in encapsulation-based self-healing concrete. The capsular clustering generated from the concrete mixing process is considered one of the critical factors in the fracture mechanism. Since there is a lack of studies in the literature regarding this issue, the design of self-healing concrete cannot be made without an appropriate modelling strategy. In this paper, the effects of microcapsule size and clustering on the fractured microcapsules are studied computationally. A simple 2D computational modelling approach is developed based on the eXtended Finite Element Method (XFEM) and cohesive surface technique. The proposed model shows that the microcapsule size and clustering have significant roles in governing the load-carrying capacity and the crack propagation pattern and determines whether the microcapsule will be fractured or debonded from the concrete matrix. The higher the microcapsule circumferential contact length, the higher the load-carrying capacity. When it is lower than 25\% of the microcapsule circumference, it will result in a greater possibility for the debonding of the microcapsule from the concrete. The greater the core/shell ratio (smaller shell thickness), the greater the likelihood of microcapsules being fractured.},
  subject      = {Beton},
  language  = {en}
}