An adaptive
spacetime discontinuous Galerkin method for cohesive
models of elastodynamic fracture
R. Abedi1, M.A. Hawker2 ,
R.B. Haber1 and K. Matous3
1Department of Mechanical Science and
Engineering
University of Illinois at Urbana-Champaign
Urbana, IL 61801, U.S.A.
2C&I Engineering
Louisville, KY 40218, U.S.A.
3Computational Science and Engineering
University of Illinois at Urbana-Champaign
Urbana, IL 61801, U.S.A.
Abstract
This paper describes an adaptive numerical framework for
cohesive fracture models based on a spacetime
discontinuous Galerkin (SDG) method for elastodynamics
with elementwise momentum balance. Discontinuous basis
functions and jump conditions written with respect to
target traction values simplify the implementation of
cohesive traction–separation laws in the SDG framework; no
special cohesive elements or other algorithmic devices are
required. We use unstructured spacetime grids in a
h-adaptive
implementation to adjust simultaneously the spatial and
temporal resolutions. Two independent error indicators
drive the adaptive refinement. One is a dissipation-based
indicator that controls the accuracy of the solution in
the bulk material; the second ensures the accuracy of the
discrete rendering of the cohesive law. Applications of
the SDG cohesive model to elastodynamic fracture
demonstrate the effectiveness of the proposed method and
reveal a new solution feature: an unexpected
quasi-singular structure in the velocity response.
Numerical examples demonstrate the use of adaptive
analysis methods in resolving this structure, as well as
its importance in reliable predictions of fracture
kinetics.
Acknowledgment
The authors gratefully acknowledge the contributions of
Shuo-Heng Chung, Scott Miller, Jeff Erickson,Yong Fan,
Michael Garland, Jayandran Palaniappan, Laxmikant Kale,
Shripad Thite, Aaron Becker and Yuan Zhou to this work.
Support from the Center for Process Simulation and Design
(CPSD) and the Center for Simulation of Advanced Rockets
(CSAR) at the University of Illinois is gratefully
acknowledged. The U.S. National Science Foundation
supports research in CPSD via grant NSF DMR 01-21695. The
CSAR research program is supported by the U.S. Department
of Energy through the University of California under
subcontract B341494.
© 2009 Notre Dame and Dr.
Karel Matous