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

Paul, Karsten; Zimmermann, Christopher; Mandadapu, Kranthi K.; Hughes, Thomas J.  R.; Landis, Chad M.; Sauer, Roger A.

doi:10.1007/s00466-019-01807-y

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

Journal Article · Tue Jan 21 00:00:00 EST 2020 · Computational Mechanics

DOI:https://doi.org/10.1007/s00466-019-01807-y· OSTI ID:1603568

Paul, Karsten ^[1]; Zimmermann, Christopher ^[1]; Mandadapu, Kranthi K. ^[2]; Hughes, Thomas J. R. ^[3]; Landis, Chad M. ^[3]; ^[1]

Aachen Univ. (Germany)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Univ. of Texas, Austin, TX (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: German Research Foundation (DFG); National Institutes of Health (NIH); US Department of the Navy, Office of Naval Research (ONR); USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1603568

Journal Information:: Computational Mechanics, Journal Name: Computational Mechanics Journal Issue: 4 Vol. 65; ISSN 0178-7675

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Kirchhoff-Love shells
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