Computational Physics Group

An adaptive spacetime discontinuous Galerkin method for cohesive models of elastodynamic fracture

R. Abedi¹, M.A. Hawker² , R.B. Haber¹ and K. Matous<sup>3

1</sup>Department 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.