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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 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.

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:
42 ENGINEERING; 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:https://doi.org/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:https://doi.org/10.1007/s00466-019-01807-y. https://www.osti.gov/servlets/purl/1603568.
@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}
}

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