Diffuse interface approach to brittle fracture

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 71, Issue 3, 2005, Pages

  Marconi, V I ^a   Jagla, E A ^a  

^a ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSE INTERFACE TECHNIQUES; LINEAR ELASTICITY; PHASE FIELD MODELS; SOLID-SOLID TRANSFORMATIONS;

CRACKS; ELASTICITY; EQUATIONS OF MOTION; FREE ENERGY; MATERIALS SCIENCE; MATHEMATICAL MODELS; PROBLEM SOLVING; TENSORS;

BRITTLE FRACTURE;

EID: 41349093713     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.036110     Document Type: Article

References (21)

1. H. Emmerich, The Diffuse Interface Approach in Condensed Matter (Springer, Berlin, 2003); L.-Q. Chen, Annu. Rev. Mater. Sci. 32, 113 (2002).
2. H. Emmerich, The Diffuse Interface Approach in Condensed Matter (Springer, Berlin, 2003); L.-Q. Chen, Annu. Rev. Mater. Sci. 32, 113 (2002).
3. I. S. Aranson, V. A. Kalatsky, and V. M. Vinokur, Phys. Rev. Lett. 85 118 (2000).
4. A. Karma, D. A. Kessler, and H. Levine, Phys. Rev. Lett. 87, 045501 (2001).
5. L. O. Eastgate, J. P. Sethna, M. Rauscher, T. Cretegny, C.-S. Chen, and C. R. Myers, Phys. Rev. E 65, 036117 (2002).
6. The theory presented by Y. M. Jin, Y. U. Wang, and A. G. Khachaturyan [Philos. Mag. 83, 1587 (2003)] uses a phase field of tensorial nature, and then is close to the one we present here. However, it seems to be applicable only when there is a finite number of cleavage planes in the material.
7. A. Karma and A. E. Lobkovsky, Phys. Rev. Lett. 92, 245510 (2004); H. Henry and H. Levine, ibid 93, 105504 (2004).
8. A. Karma and A. E. Lobkovsky, Phys. Rev. Lett. 92, 245510 (2004); H. Henry and H. Levine, ibid 93, 105504 (2004).
9. K. Kassner, Ch. Misbah, J. Müller, J. Kappey, and P. Kohlert, Phys. Rev. E 63, 036117 (2001).
10. E. A. Brener and R. Spatschek, Phys. Rev. E 67, 016112 (2003).
11. That is why we prefer to call our approach a diffuse interface one. We reserve the term "phase field model" for cases where there are additional fields.
12. j), and then in its present form our formalism does not properly describe problems in which finite relative rotations of different parts of the body occur.
13. T. Lookman, S. R. Shenoy, K. O. Rasmussen, A. Saxena, and A. R. Bishop, Phys. Rev. B 67, 024114 (2003); S. R. Shenoy, T. Lookman, A. Saxena, and A. R. Bishop, ibid. 60, R12 537 (1999).
14. T. Lookman, S. R. Shenoy, K. O. Rasmussen, A. Saxena, and A. R. Bishop, Phys. Rev. B 67, 024114 (2003); S. R. Shenoy, T. Lookman, A. Saxena, and A. R. Bishop, ibid. 60, R12 537 (1999).
15. S. Kartha, J. A. Krumhansl, J. P. Sethna, and L. K. Wickham, Phys. Rev. B 52, 803 (1995).
16. D. S. Chandrasekharaiah and L. Debnath, Continuum Mechanics (Academic, San Diego, 1996).
17. 3, and enforce the compatibility condition by using a Lagrange multiplier. Notwithstanding, it should be mentioned that another possibility is to use only two truly independent variables, expressing explicitly the third one in terms of the other two using the compatibility equation (3). In that case we would obtain a nonlocal, long range interaction between the two independent variables, as explained in Refs. [11,12]
18. We expect that the exact form of the expression we use to interpolate between the quadratic dependence at low ε and the constant value at large ε captures in the macroscopic model some relevant details of the material at the microscopic scale (see Ref. [17]).
19. E. E. Gdoutos, Problems of Mixed Mode Crack Propagation (Martinus Nijhoff Publishers, Leiden, 1984).
20. M. J. Buehler, F. F. Abraham, and H. Gao, Nature (London) 426, 141 (2003).
21. E. A. Jagla, Phys. Rev. E 69, 056212 (2004).