Details
| Original language | English |
|---|---|
| Pages (from-to) | B589-B617 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 39 |
| Issue number | 4 |
| Publication status | Published - 2017 |
| Externally published | Yes |
Abstract
The purpose of this work is the development of a fully monolithic solution algorithm for quasi-static phase-field fracture propagation. Phase-field fracture consists of two coupled partial differential equations, and it is well known that the underlying energy functional is nonconvex and sophisticated algorithms are required. For the incremental, spatially discretized problem, we employ an adaptive error-oriented Newton algorithm which works as an inner loop within an inexact aug-mented Lagrangian iteration. The latter approach relaxes the crack irreversibility constraint, which is an inequality constraint in time. Six numerical tests and benchmarks are consulted to demon-strate the performance of the algorithmic techniques. Specifically, the fully monolithic approach is compared to a quasi-monolithic approach in which the phase-field is approximated through extrap-olation in the displacement equation. These comparisons are done in terms of certain quantities of interest and computational cost. Moreover, features such as crack nucleation, joining, branching, and fracture networks are addressed. Most examples are in two dimensions, but three-dimensional (3D) testing is provided as well. All findings are critically analyzed and point to open questions and future improvements.
Keywords
- Benchmark tests, Error-oriented Newton method, Inexact augmented Lagrangian, Phase-field fracture propagation
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Scientific Computing, Vol. 39, No. 4, 2017, p. B589-B617.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An error-oriented newton/inexact augmented Lagrangian approach for fully monolithic phase-field fracture propagation
AU - Wick, Thomas
N1 - Publisher Copyright: © 2017 SIAM. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017
Y1 - 2017
N2 - The purpose of this work is the development of a fully monolithic solution algorithm for quasi-static phase-field fracture propagation. Phase-field fracture consists of two coupled partial differential equations, and it is well known that the underlying energy functional is nonconvex and sophisticated algorithms are required. For the incremental, spatially discretized problem, we employ an adaptive error-oriented Newton algorithm which works as an inner loop within an inexact aug-mented Lagrangian iteration. The latter approach relaxes the crack irreversibility constraint, which is an inequality constraint in time. Six numerical tests and benchmarks are consulted to demon-strate the performance of the algorithmic techniques. Specifically, the fully monolithic approach is compared to a quasi-monolithic approach in which the phase-field is approximated through extrap-olation in the displacement equation. These comparisons are done in terms of certain quantities of interest and computational cost. Moreover, features such as crack nucleation, joining, branching, and fracture networks are addressed. Most examples are in two dimensions, but three-dimensional (3D) testing is provided as well. All findings are critically analyzed and point to open questions and future improvements.
AB - The purpose of this work is the development of a fully monolithic solution algorithm for quasi-static phase-field fracture propagation. Phase-field fracture consists of two coupled partial differential equations, and it is well known that the underlying energy functional is nonconvex and sophisticated algorithms are required. For the incremental, spatially discretized problem, we employ an adaptive error-oriented Newton algorithm which works as an inner loop within an inexact aug-mented Lagrangian iteration. The latter approach relaxes the crack irreversibility constraint, which is an inequality constraint in time. Six numerical tests and benchmarks are consulted to demon-strate the performance of the algorithmic techniques. Specifically, the fully monolithic approach is compared to a quasi-monolithic approach in which the phase-field is approximated through extrap-olation in the displacement equation. These comparisons are done in terms of certain quantities of interest and computational cost. Moreover, features such as crack nucleation, joining, branching, and fracture networks are addressed. Most examples are in two dimensions, but three-dimensional (3D) testing is provided as well. All findings are critically analyzed and point to open questions and future improvements.
KW - Benchmark tests
KW - Error-oriented Newton method
KW - Inexact augmented Lagrangian
KW - Phase-field fracture propagation
UR - http://www.scopus.com/inward/record.url?scp=85027714708&partnerID=8YFLogxK
U2 - 10.1137/16m1063873
DO - 10.1137/16m1063873
M3 - Article
AN - SCOPUS:85027714708
VL - 39
SP - B589-B617
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
SN - 1064-8275
IS - 4
ER -