Γ-convergence for high order phase field fracture: continuum and isogeometric formulations

@article{Negri2020convergenceFH,
  title={$\Gamma$-convergence for high order phase field fracture: continuum and isogeometric formulations},
  author={Matteo Negri},
  journal={ArXiv},
  year={2020},
  volume={abs/1907.09814}
}
  • M. Negri
  • Published 23 July 2019
  • Mathematics
  • ArXiv
View PDF on arXiv
2 Citations

Figures from this paper

2 Citations

Conservational integrals of the fourth-order phase field model for brittle fracture via Noether theorem
A variational phase-field model For ductile fracture with coalescence dissipation
A novel phase-field model for ductile fracture is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence…

References

SHOWING 1-10 OF 44 REFERENCES
A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework
Anisotropic Mesh Adaptation for Crack Detection In Brittle Materials
TLDR
A modification of this variational model includes additional constraints via penalty terms to enforce the irreversibility of the fracture as well as the applied displacement field to numerically compute the time-evolving minimizing solution.
Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments
Phase-field description of brittle fracture in plates and shells
A continuum phase field model for fracture
Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations
The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by a…
An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS
TLDR
An adaptive space-time phase field formulation for dynamic fracture of brittle shells and the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.
A review on phase-field models of brittle fracture and a new fast hybrid formulation
In this contribution we address the issue of efficient finite element treatment for phase-field modeling of brittle fracture. We start by providing an overview of the existing quasi-static and…
Phase‐field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy
Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore,…
Quasi-Static Evolutions in Brittle Fracture Generated by Gradient Flows: Sharp Crack and Phase-Field Approaches
In this paper we will describe how gradient flows, in a suitable norm, are natural and helpful to generate quasi-static evolutions in brittle fracture. First, we will consider the case of a brittle…
...
...