On the use of space-time finite elements in the solution of elasto-dynamic fracture problems

The use of a discontinuous Galerkin (DG) formulation for the solution of dynamic fracture problems in linear elastic media with and without cohesive zones is explored. The results are compared with closed-form as well as numerical solutions available from the literature. The effectiveness of the space-time finite element method in the study of dynamic fracture problems is demonstrated, especially in those cases in which dynamic fracture occurs along with time discontinuous loading.

[1]  J. Rice,et al.  A spectral method for three-dimensional elastodynamic fracture problems , 1995 .

[2]  Ted Belytschko,et al.  Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlinear continua , 1988 .

[3]  M. Gurtin,et al.  An introduction to continuum mechanics , 1981 .

[4]  F. Costanzo.  A continuum theory of cohesive zone models: deformation and constitutive equations , 1998 .

[5]  Xiaopeng Xu,et al.  Numerical simulations of fast crack growth in brittle solids , 1994 .

[6]  F. Costanzo,et al.  Steady growth of a crack with a rate and temperature sensitive cohesive zone , 2002 .

[7]  Morton E. Gurtin,et al.  Configurational Forces and the Dynamics of Planar Cracks in Three-Dimensional Bodies , 1997 .

[8]  Thomas J. R. Hughes,et al.  Space-time finite element methods for second-order hyperbolic equations , 1990 .

[9]  Xiaopeng Xu,et al.  Numerical simulations of dynamic crack growth along an interface , 1996 .

[10]  G. I. Barenblatt.  THE MATHEMATICAL THEORY OF EQUILIBRIUM CRACKS IN BRITTLE FRACTURE , 1962 .

[11]  M. Marder,et al.  Instability in lattice fracture. , 1993, Physical review letters.

[12]  T. Hughes,et al.  Space-time finite element methods for elastodynamics: formulations and error estimates , 1988 .

[13]  S. Aoki,et al.  Dynamic stress intensity factors using Ĵ-integral and finite element method , 1980 .

[14]  Francesco Costanzo,et al.  Proof of unconditional stability for a single-field discontinuous Galerkin finite element formulation for linear elasto-dynamics , 2005 .

[15]  H. Saunders,et al.  Advanced Fracture Mechanics , 1985 .

[16]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[17]  S. Atluri,et al.  Path-independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics , 1983 .

[18]  Michael Marder,et al.  Molecular dynamics of cracks , 1989, Comput. Sci. Eng..

[19]  S NguyenQ,et al.  A thermodynamic description of the running crack problem. , 1981 .

[20]  L. Freund,et al.  Computational methods based on an energy integral in dynamic fracture , 1985 .

[21]  Michael P Marder,et al.  Origin of crack tip instabilities , 1994, chao-dyn/9410009.

[22]  Philippe H. Geubelle,et al.  Numerical analysis of dynamic debonding under anti-plane shear loading , 1997 .

[23]  A. Needleman.  A Continuum Model for Void Nucleation by Inclusion Debonding , 1987 .

[24]  John W. Hutchinson,et al.  Dynamic Fracture Mechanics , 1990 .

[25]  Chien-Ching Ma,et al.  A dynamic crack model with viscous resistance to crack opening: Antiplane shear mode , 1990 .

[26]  N. Fleck,et al.  Dynamic crack growth across an interface , 1997 .

[27]  Morton E. Gurtin,et al.  Configurational forces and the basic laws for crack propagation , 1996 .

[28]  Francesco Costanzo,et al.  A continuum thermodynamic analysis of cohesive zone models , 1995 .

[29]  F. Costanzo.  An Analysis of 3D Crack Propagation using Cohesive Zone Models and the Theory of Configurational Forces , 2001 .

[30]  Swinney,et al.  Instability in the propagation of fast cracks. , 1992, Physical review. B, Condensed matter.

[31]  Jay Fineberg,et al.  Instability in dynamic fracture , 1999 .

[32]  M. Gurtin,et al.  On the energy release rate in elastodynamic crack propagation , 1980 .

[33]  James G. Boyd,et al.  Micromechanical analysis of a continuous fiber metal matrix composite including the effects of matrix viscoplasticity and evolving damage , 1994 .

[34]  D. S. Dugdale.  Yielding of steel sheets containing slits , 1960 .

[35]  Zhou,et al.  Dynamic crack processes via molecular dynamics. , 1996, Physical review letters.

[36]  K. Ravi-Chandar,et al.  On the role of the process zone in dynamic fracture , 1996 .

[37]  Francesco Costanzo,et al.  On the use of space-time finite elements in the solution of elasto-dynamic problems with strain discontinuities , 2002 .

[38]  Francesco Costanzo,et al.  A study of dynamic crack growth in elastic materials using a cohesive zone model , 1997 .