Abstract2018-05-24T12:52:58+00:00

Fourth order phase-field model for local max-ent approximants applied to crack propagation

Author (s): Amiri, F.; Millán, D.; Arroyo, M.; Silani, M.; Rabczuk, T.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 312
Pages: 254 – 275
Date: 2016

Abstract:
We apply a fourth order phase-field model for fracture based on local maximum entropy (LME) approximants. The higher order continuity of the meshfree LME approximants allows to directly solve the fourth order phase-field equations without splitting the fourth order differential equation into two second order differential equations. We will first show that the crack surface can be captured more accurately in the fourth order model. Furthermore, less nodes are needed for the fourth order model to resolve the crack path. Finally, we demonstrate the performance of the proposed meshfree fourth order phase-field formulation for 5 representative numerical examples. Computational results will be compared to analytical solutions within linear elastic fracture mechanics and experimental data for three-dimensional crack propagation.

  
  

Bibtex:

@article{Amiri2016254,
title = "Fourth order phase-field model for local max-ent approximants applied to crack propagation ",
journal = "Computer Methods in Applied Mechanics and Engineering ",
volume = "312",
number = "",
pages = "254 - 275",
year = "2016",
note = "Phase Field Approaches to Fracture ",
issn = "0045-7825",
doi = "http://dx.doi.org/10.1016/j.cma.2016.02.011",
url = "http://www.sciencedirect.com/science/article/pii/S0045782516300330",
author = "Fatemeh Amiri and Daniel Millán and Marino Arroyo and Mohammad Silani and Timon Rabczuk",
keywords = "Fracture",
keywords = "Local maximum entropy",
keywords = "Second order phase-field model",
keywords = "Fourth order phase-field model ",
abstract = "Abstract We apply a fourth order phase-field model for fracture based on local maximum entropy (LME) approximants. The higher order continuity of the meshfree \{LME\} approximants allows to directly solve the fourth order phase-field equations without splitting the fourth order differential equation into two second order differential equations. We will first show that the crack surface can be captured more accurately in the fourth order model. Furthermore, less nodes are needed for the fourth order model to resolve the crack path. Finally, we demonstrate the performance of the proposed meshfree fourth order phase-field formulation for 5 representative numerical examples. Computational results will be compared to analytical solutions within linear elastic fracture mechanics and experimental data for three-dimensional crack propagation. "
}