Diffuse interface approach to brittle fracture

V. I. MARCONI; E. A. JAGLA

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

The American Physical Society

Año: 2005 vol. 71 p. 361101 - 361109

1063-651X

We present a continuum model for the propagation of cracks and fractures in brittle materials. The componentsof the strain tensor « are the fundamental variables. The evolution equations are based on a free energythat reduces to that of linear elasticity for small «, and accounts for cracks through energy saturation at largevalues of «. We regularize the model by including terms dependent on gradients of « in the free energy. Noadditional fields are introduced, and then the whole dynamics is perfectly defined. We show that the model isable to reproduce basic facts in fracture physics, like the Griffith?s dependence of the critical stress as a minusone-half power of the crack length. In addition, regularization makes the results insensitive to the numericalmesh used, something not at all trivial in crack modeling. We present an example of the application of themodel to predict the growth and curving of cracks in a nontrivial geometrical configuration.