13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- The brutal formation of cracks of finite length at crack nucleation, observed in the simulations, challenges the limits of the quasi static formulation. Therefore, a dynamic version of the phase field model, where dynamic equations of motion replace the static equilibrium condition (Eq. 3), is currently being worked on. Within the context of the present work, especially the impact of the dynamic effects on the crack nucleation behavior of the phase field model is of interest. Another open task for future work is the influence of material inhomogeneities, such as inclusions or pores, on the effective fracture strength of the phase field model. References [1] I.S. Aranson, V.A. Kalatsky, V.M. Vinokur, Continuum field description of crack propagation. Phys Rev Let, 85/1 (2000) 118–121. [2] L.O. Eastgate, J.P. Sethna, M. Rauscher, T. Cretegny, C.-S. Chen, C.R. Myers, Fracture in mode I using a conserved phase-field model. Phys Rev E, 65/3 (2002) 036117. [3] A. Karma, A.E. Lobkovsky, Unsteady crack motion and branching in a phase-field model of brittle fracture. Phys Rev Let, 92/24 (2004) 245510. [4] H. Henry, H. Levine, Dynamic instabilities of fracture under biaxial strain using a phase field model. Phys Rev Let, 93/10 (2004) 105504. [5] V. Hakim, A. Karma, Crack path prediction in anisotropic brittle materials. Phys Rev Let, 95/23 (2005) 235501. [6] F. Corson, M. Adda-Bedia, H. Henry, E. Katzav, Thermal fracture as a framework for quasistatic crack propagation. Int J Fract, 158 (2009) 1–14. [7] B. Bourdin, G.A. Francfort, J.-J. Marigo, Numerical experiments in revisited brittle fracture. J Mech Phys Solid, 48/4 (2000) 797–826. [8] C. Kuhn, R. Müller, A continuum phase field model for fracture. Eng Fract Mech, 77/18 (2010) 3625–3634. [9] C. Miehe, F. Welschinger, M. Hofacker, Thermodynamically consistent phasefield models for fracture: Variational principles and multi-field FE implementations. Int J Numer Meth Eng, 83/10 (2010) 1273–1311. [10] M.J. Borden, C.V. Verhoosel, M.A. Scott, T.J.R. Hughes, C.M. Landis, A phase-field description of dynamic brittle fracture. Comput Meth Appl Mech Eng, 217–220 (2012) 77– 95. [11] V. Hakim, A. Karma, Laws of crack motion and phase-field models of fracture. J Mech Phys Solid, 57/2 (2009) 342–368. [12] C. Kuhn, R. Müller. On an energetic interpretation of a phase field model for fracture. PAMM, 11/1 (2011) 159–160. [13] H. Amor, J.-J. Marigo, C. Maurini, N.K. Pham, Stability analysis and numerical implementation of non-local damage models via a global variational approach, in: WCCM8 - ECCOMAS 2008, 2008. [14] K. Pham, H. Amor, J.-J. Marigo, C. Maurini, Gradient damage models and their use to approximate brittle fracture. Int J Damage Mech, 20/4 (2011) 618–652. [15] K. Pham, J.-J. Marigo, and C. Maurini, The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models. J Mech Phys Solid, 59/6 (2011) 1163–1190. [16] A. Benallal, J.-J. Marigo, Bifurcation and stability issues in gradient theories with softening. Modell Simul Mater Sci Eng, 15/1 (2007) 283–295.
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