The phase field method for fracture integrates the Griffith theory and damage mechanics approach to predict crack initiation and propagation within one framework. It replaced the discrete representation of crack by diffusive damage and solved it based on a minimization of the global energy storage functional. As a result, no crack tracking topology is needed, and complex crack shapes can be captures without user intervention. However, it is also reported to have an inconsistency between the predicted fracture toughness and the material strength. Recently, a novel energetic degradation function was proposed in literature to handle this issue. This research does some further modifications to the global energy storage functional so that Newton's method can be directly used to solve the energy minimization. With the new energy form, direct implementation of the length-scale independent phase field method into finite element packages like LS-DYNA becomes possible. This paper presents the framework and details of implementing the length-scale independent phase field method into LS-DYNA through a user-defined element and material subroutine. Several numerical examples are presented to compare with the experiment crack shape. Most importantly, this paper is one of the first ones to quantitatively predict accurate force response compared to experiments. These examples verify the accuracy of the new energy form and implementation.
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Wu, J.Y.: A unified phase-field theory for the mechanics of damage and quasi-brittle failure. J. Mech. Phys. Solids 103, 72–99 (2017)
Francfort, G.A., Marigo, J.J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46, 1319–1342 (1998). https://doi.org/10.1016/S0022-5096(98)00034-9
Bourdin, B., Francfort, G.A., Marigo, J.-J.: Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48, 797–826 (2000)
Karma, A., Kessler, D.A., Levine, H.: Phase-field model of mode III dynamic fracture. Phys. Rev. Lett. 87, 45501-1-45501–4 (2001). https://doi.org/10.1103/PhysRevLett.87.045501
Miehe, C., Welschinger, F., Hofacker, M.: Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Int. J. Numer. Methods Eng. 83, 1273–1311 (2010). https://doi.org/10.1002/nme.2861
Borden, M.J., Hughes, T.J.R., Landis, C.M., et al.: A higher-order phase-field model for brittle fracture: formulation and analysis within the isogeometric analysis framework. Comput. Methods Appl. Mech. Eng. 273, 100–118 (2014)
Hofacker, M., Miehe, C.: A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns. Int. J. Numer. Methods Eng. 93, 276–301 (2013). https://doi.org/10.1002/nme.4387
Hesch, C., Weinberg, K.: Thermodynamically consistent algorithms for a finite-deformation phase-field approach to fracture. Int. J. Numer. Methods Eng. 99, 906–924 (2014). https://doi.org/10.1002/nme.4709
Verhoosel, C.V., de Borst, R.: A phase-field model for cohesive fracture. Int. J. Numer. Methods Eng. 96, 43–62 (2013). https://doi.org/10.1002/nme.4553
Liu, G., Li, Q., Msekh, M.A., et al.: Abaqus implementation of monolithic and staggered schemes for quasi-static and dynamic fracture phase-field model. Comput. Mater. Sci. 121, 35–47 (2016). https://doi.org/10.1016/j.commatsci.2016.04.009
Molnár, G., Gravouil, A.: 2D and 3D Abaqus implementation of a robust staggered phase-field solution for modeling brittle fracture. Finite Elem. Anal. Des. 130, 27–38 (2017). https://doi.org/10.1016/j.finel.2017.03.002
Emdadi, A., Fahrenholtz, W.G., Hilmas, G.E., et al.: A modified phase-field model for quantitative simulation of crack propagation in single-phase and multi-phase materials. Eng. Fract. Mech. 200, 339–354 (2018). https://doi.org/10.1016/j.engfracmech.2018.07.038
Nguyen, T.T., Yvonnet, J., Bornert, M., et al.: On the choice of parameters in the phase field method for simulating crack initiation with experimental validation. Int. J. Fract. 197, 213–226 (2016). https://doi.org/10.1007/s10704-016-0082-1
Wu, J.Y., Nguyen, V.P., Nguyen, C.T., et al.: Phase field modeling of fracture. Adv. Appl. Mech. Multi-scale Theory Comput. 52, 7–134 (2018)
Lorentz, E.: A nonlocal damage model for plain concrete consistent with cohesive fracture. Int. J. Fract. 207, 123–159 (2017). https://doi.org/10.1007/s10704-017-0225-z
Wu, J.Y.: Robust numerical implementation of non-standard phase-field damage models for failure in solids. Comput. Methods Appl. Mech. Eng. 340, 767–797 (2018a)
Hallquist, J.O.: LS-DYNA Theory Manual. Livermore Software Technology Corporation, Livermore (1998)
Abaqus, G.: Abaqus 6.11. Dassault Syst. Simulia Corp., Providence (2011)
Miehe, C., Hofacker, M., Welschinger, F.: A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Comput. Methods Appl. Mech. Eng. 199, 2765–2778 (2010). https://doi.org/10.1016/j.cma.2010.04.011
Linse, T., Hennig, P., Kästner, M., et al.: A convergence study of phase-field models for brittle fracture. Eng. Fract. Mech. 184, 307–318 (2017)
Tanné, E., Li, T., Bourdin, B., et al.: Crack nucleation in variational phase-field models of brittle fracture. J. Mech. Phys. Solids 110, 80–99 (2018)
Wu, J.Y.: A geometrically regularized gradient-damage model with energetic equivalence. Comput. Methods Appl. Mech. Eng. 328, 612–637 (2018b). https://doi.org/10.1016/j.cma.2017.09.027
Wu, J.Y., Nguyen, V.P.: A length scale insensitive phase-field damage model for brittle fracture. J. Mech. Phys. Solids. 119, 20–42 (2018). https://doi.org/10.1016/j.jmps.2018.06.006
Trunk, B.G.: Einfluss der Bauteilgrösse auf die Bruchenergie von Beton. [Ph.D. Thesis], ETH Zurich, 1999.
Gálvez, J.C., Elices, M., Guinea, G.V., et al.: Mixed mode fracture of concrete under proportional and nonproportional loading. Int. J. Fract. 94, 267–284 (1998). https://doi.org/10.1023/A:1007578814070
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Zhang, W., Tabiei, A. & French, D. A numerical implementation of the length-scale independent phase field method. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-020-01027-1
- Phase field method
- Length-scale independency
- Newton’s method