A Phase Field Staggered Algorithm for Fracture Modeling in Heterogeneous Microstructure


Article Preview

The phase field approach to fracture modelling is based on a variational principle of the energy minimization as an extension of the Griffith’s brittle fracture theory. It introduces a scalar damage field, to differentiate between the fractured and intact material state. That way, it regularizes the sharp crack discontinuities and eliminates the need for the explicit tracking of the fracture surfaces. Moreover, the numerical implementation complexity is thus vastly reduced. In this contribution, the staggered phase field algorithm for the modelling of brittle fracture is implemented within the finite element program Abaqus. A common issue of the existing Abaqus implementations of the staggered phase field schemes is the computationally demanding fine incrementation of the loading applied, required to obtain an accurate solution. The computational time is reduced by imposing an appropriate convergence control paired with the Abaqus automatic time incrementation. Therefore, by taking advantage of the Abaqus computational efficiency, an accurate solution can be obtained for a moderate time step. The proposed model is verified on the symmetrically double notched tensile benchmark test. Compared to the existing implementations, it demonstrates an improvement in accuracy and the computational performance. Furthermore, a heterogeneous steel microstructure is analyzed displaying the model’s ability to solve crack nucleation and curvilinear crack paths.



Edited by:

Luis Rodríguez-Tembleque, Jaime Domínguez and Ferri M.H. Aliabadi




K. Seleš et al., "A Phase Field Staggered Algorithm for Fracture Modeling in Heterogeneous Microstructure", Key Engineering Materials, Vol. 774, pp. 632-637, 2018

Online since:

August 2018




* - Corresponding Author

[1] A. A., Griffith, Philos. Trans. Royal Soc. A. p.221 (1921).

[2] A.R. Ingraffea, V. Saouma, in: Engineering Application of Fracture Mechanics, edited by G.C. Sih, A. DiTommaso, Fracture mechanics of concrete: Structural application and numerical calculation, Springer, Dordrecht, (1985).

DOI: https://doi.org/10.1007/978-94-009-6152-4

[3] T. Belytschko, Y.Y. Lu, L. Gu, Eng Fract Mech., 51(2) (1995) 295-315.

[4] T. Belytschko, Y.Y. Lu, L. Gu, Int J Numer Meth Eng., 37(2) (1994) 229-256.

[5] G.L. Peng, Y.H. Wang, Applied Mechanics and Materials, 182-183 (2012) 1524-1528.

[6] M. Elices, G.V. Guinea, J. Gomez, J. Planas, Eng Fract Mech., 69(2) (2002) 137-163.

[7] N. Moes, T. Belytschko, Eng Fract Mech., 69(7) (2002) 813-833.

[8] J. Dolbow, N. Moes, T. Belytschko, Finite Elem Anal Des., 36(3-4) (2000) 235-260.

[9] R.H.J. Peerlings, L.H. Poh, M.G.D. Geers, Eng Fract Mech., 95 (2012) 2-12.

[10] F. Putar, J. Soric, T. Lesicar, Z. Tonkovic, Int J Solids Struct., 120 (2017) 171-185.

DOI: https://doi.org/10.1016/j.ijsolstr.2017.04.039

[11] S. Forest, J Eng Mech, 135(3) (2009) 117-131.

[12] D. Evangelia, L. Carl, S. Khemais, 19th International ESAFORM Conference on Material Forming (ESAFORM), Nantes, FRANCE, (2016).

[13] G. Molnar, A. Gravouil, Finite Elem Anal Des., 130 (2017) 27-38.

[14] M.J. Borden, C.V. Verhoosel, M.A. Scott, T.J.R. Hughes, C.M. Landis, Comput Methods Appl Mech Eng., volume 217 (2012) pp.77-95.

[15] F.P. Duda, A. Ciarbonetti, P.J. Sanchez, A.E. Huespe, Int J Plasticity, 65 (2015) 269-296.

[16] J. Reinoso, M. Paggi, C. Linder, Comput Mech, 59(6) (2017) 981-1001.

[17] M. Ambati, T. Gerasimov, L. De Lorenzis, Comput Mech, 55(5) (2015) 1017-1040.

[18] M. Ambati, R. Kruse, L. De Lorenzis, Comput Mech, 57(1) (2016) 149-167.

[19] B. Bourdin, G.A. Francfort, J.J. Marigo, J Mech Phys Solids., 48(4) (2000) 797-826.

[20] C. Miehe, M. Hofacker, F. Welschinger, Comput Methods Appl Mech Eng., 199(45-48) (2010) 2765-2778.

[21] G.W. Liu, Q.B. Li, M.A. Msekh, Z. Zuo, Comput. Mater. Sci., 121 (2016) 35-47.

[22] M. Hofacker, C. Miehe, Int. J. Fract., 178(1-2) (2012) 113-129.

[23] B. Bourdin, G.A. Francfort, J.J. Marigo, J Elasticity, 91(1-3) (2008) 5-148.

[24] M. Ambati, T. Gerasimov, L. De Lorenzis, Comput Mech., 55(2) (2015) 383-405.

[25] C. Miehe, F. Welschinger, M. Hofacker, Int J Numer Meth Eng. 83(10) (2010) 1273-1311.

DOI: https://doi.org/10.1002/nme.2861

Fetching data from Crossref.
This may take some time to load.