skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on January 21, 2021

Title: An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

Abstract

Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1-continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.

Authors:
 [1];  [1];  [2];  [3];  [3]; ORCiD logo [1]
  1. Aachen Univ. (Germany)
  2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  3. Univ. of Texas, Austin, TX (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); US Department of the Navy, Office of Naval Research (ONR); National Institutes of Health (NIH); German Research Foundation (DFG)
OSTI Identifier:
1603568
Grant/Contract Number:  
[AC02-05CH11231; N00014-17-1-2119; N00014-13-1-0500; N00014-17-1-2039; R01-GM110066]
Resource Type:
Accepted Manuscript
Journal Name:
Computational Mechanics
Additional Journal Information:
[ Journal Volume: 65; Journal Issue: 4]; Journal ID: ISSN 0178-7675
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
phase fields; brittle fracture; isogeometric analysis; adaptive local refinement; LR NURBS; nonlinear finite elements; Kirchhoff-Love shells

Citation Formats

Paul, Karsten, Zimmermann, Christopher, Mandadapu, Kranthi K., Hughes, Thomas J. R., Landis, Chad M., and Sauer, Roger A. An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS. United States: N. p., 2020. Web. doi:10.1007/s00466-019-01807-y.
Paul, Karsten, Zimmermann, Christopher, Mandadapu, Kranthi K., Hughes, Thomas J. R., Landis, Chad M., & Sauer, Roger A. An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS. United States. doi:10.1007/s00466-019-01807-y.
Paul, Karsten, Zimmermann, Christopher, Mandadapu, Kranthi K., Hughes, Thomas J. R., Landis, Chad M., and Sauer, Roger A. Tue . "An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS". United States. doi:10.1007/s00466-019-01807-y.
@article{osti_1603568,
title = {An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS},
author = {Paul, Karsten and Zimmermann, Christopher and Mandadapu, Kranthi K. and Hughes, Thomas J. R. and Landis, Chad M. and Sauer, Roger A.},
abstractNote = {Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C1-continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.},
doi = {10.1007/s00466-019-01807-y},
journal = {Computational Mechanics},
number = [4],
volume = [65],
place = {United States},
year = {2020},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on January 21, 2021
Publisher's Version of Record

Save / Share:

Works referenced in this record:

A review on phase-field models of brittle fracture and a new fast hybrid formulation
journal, December 2014

  • Ambati, Marreddy; Gerasimov, Tymofiy; De Lorenzis, Laura
  • Computational Mechanics, Vol. 55, Issue 2
  • DOI: 10.1007/s00466-014-1109-y

Phase-field modeling of fracture in linear thin shells
journal, February 2014


Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments
journal, August 2009

  • Amor, Hanen; Marigo, Jean-Jacques; Maurini, Corrado
  • Journal of the Mechanics and Physics of Solids, Vol. 57, Issue 8
  • DOI: 10.1016/j.jmps.2009.04.011

A phase-field description of dynamic brittle fracture
journal, April 2012

  • Borden, Michael J.; Verhoosel, Clemens V.; Scott, Michael A.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 217-220
  • DOI: 10.1016/j.cma.2012.01.008

Numerical experiments in revisited brittle fracture
journal, April 2000

  • Bourdin, B.; Francfort, G. A.; Marigo, J-J.
  • Journal of the Mechanics and Physics of Solids, Vol. 48, Issue 4
  • DOI: 10.1016/S0022-5096(99)00028-9

A time-discrete model for dynamic fracture based on crack regularization
journal, November 2010

  • Bourdin, Blaise; Larsen, Christopher J.; Richardson, Casey L.
  • International Journal of Fracture, Vol. 168, Issue 2
  • DOI: 10.1007/s10704-010-9562-x

A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method
journal, June 1993

  • Chung, J.; Hulbert, G. M.
  • Journal of Applied Mechanics, Vol. 60, Issue 2
  • DOI: 10.1115/1.2900803

Revisiting brittle fracture as an energy minimization problem
journal, August 1998


A phase-field formulation for dynamic cohesive fracture
journal, May 2019

  • Geelen, Rudy J. M.; Liu, Yingjie; Hu, Tianchen
  • Computer Methods in Applied Mechanics and Engineering, Vol. 348
  • DOI: 10.1016/j.cma.2019.01.026

An optimization-based phase-field method for continuous-discontinuous crack propagation: A phase-field method for continuous-discontinuous crack propagation
journal, July 2018

  • Geelen, Rudy J. M.; Liu, Yingjie; Dolbow, John E.
  • International Journal for Numerical Methods in Engineering, Vol. 116, Issue 1
  • DOI: 10.1002/nme.5911

On penalization in variational phase-field models of brittle fracture
journal, September 2019

  • Gerasimov, T.; De Lorenzis, L.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 354
  • DOI: 10.1016/j.cma.2019.05.038

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture
journal, May 2018

  • Gerasimov, Tymofiy; Noii, Nima; Allix, Olivier
  • Advanced Modeling and Simulation in Engineering Sciences, Vol. 5, Issue 1
  • DOI: 10.1186/s40323-018-0105-8

A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach
journal, June 2015

  • Heister, Timo; Wheeler, Mary F.; Wick, Thomas
  • Computer Methods in Applied Mechanics and Engineering, Vol. 290
  • DOI: 10.1016/j.cma.2015.03.009

A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns: A PHASE FIELD MODEL OF DYNAMIC FRACTURE
journal, July 2012

  • Hofacker, M.; Miehe, C.
  • International Journal for Numerical Methods in Engineering, Vol. 93, Issue 3
  • DOI: 10.1002/nme.4387

Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
journal, October 2005

  • Hughes, T. J. R.; Cottrell, J. A.; Bazilevs, Y.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 39-41
  • DOI: 10.1016/j.cma.2004.10.008

Phase-Field Model of Mode III Dynamic Fracture
journal, July 2001


Virtual crack closure technique: History, approach, and applications
journal, March 2004


A continuum phase field model for fracture
journal, December 2010


On degradation functions in phase field fracture models
journal, October 2015


Existence of Solutions to a Regularized Model of Dynamic Fracture
journal, July 2010

  • Larsen, Christopher J.; Ortner, Christoph; SÜLi, Endre
  • Mathematical Models and Methods in Applied Sciences, Vol. 20, Issue 07
  • DOI: 10.1142/S0218202510004520

A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
journal, November 2010

  • Miehe, Christian; Hofacker, Martina; Welschinger, Fabian
  • Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 45-48
  • DOI: 10.1016/j.cma.2010.04.011

Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations
journal, August 2010

  • Miehe, C.; Welschinger, F.; Hofacker, M.
  • International Journal for Numerical Methods in Engineering, Vol. 83, Issue 10
  • DOI: 10.1002/nme.2861

A finite element method for crack growth without remeshing
journal, September 1999


Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis
journal, March 1999


A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method
journal, January 2011

  • Radovitzky, R.; Seagraves, A.; Tupek, M.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 1-4
  • DOI: 10.1016/j.cma.2010.08.014

An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching
journal, October 1984

  • Ravi-Chandar, K.; Knauss, W. G.
  • International Journal of Fracture, Vol. 26, Issue 2
  • DOI: 10.1007/BF01157550

High-accuracy phase-field models for brittle fracture based on a new family of degradation functions
journal, February 2018

  • Sargado, Juan Michael; Keilegavlen, Eirik; Berre, Inga
  • Journal of the Mechanics and Physics of Solids, Vol. 111
  • DOI: 10.1016/j.jmps.2017.10.015

On the theoretical foundations of thin solid and liquid shells
journal, August 2016


A stabilized finite element formulation for liquid shells and its application to lipid bilayers
journal, February 2017

  • Sauer, Roger A.; Duong, Thang X.; Mandadapu, Kranthi K.
  • Journal of Computational Physics, Vol. 330
  • DOI: 10.1016/j.jcp.2016.11.004

Phase field approximation of dynamic brittle fracture
journal, June 2014

  • Schlüter, Alexander; Willenbücher, Adrian; Kuhn, Charlotte
  • Computational Mechanics, Vol. 54, Issue 5
  • DOI: 10.1007/s00466-014-1045-x

Fluid Films with Curvature Elasticity
journal, December 1999

  • Steigmann, D. J.
  • Archive for Rational Mechanics and Analysis, Vol. 150, Issue 2
  • DOI: 10.1007/s002050050183