Modares Mechanical Engineering

Modares Mechanical Engineering

Implementation of the phase-field method for brittle fracture and application to porous structures

Authors
Mohammad Mousavion 1
Mohammad Mashayekhi 2
Mostafa Jamshidian 3
Hojjat Badnava 4
1 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
2 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, IRAN
3 Assistant Professor, Department of Mechanical Engineering, Isfahan University of Technology
4 Department of Mechanical Engineering, Behbahan Khatam Alanbia University of Technology, Khuzestan, Iran
Abstract
Recently, the phase field approach has gained popularity as a versatile tool for simulating crack propagation. The purpose of this study is to employ the capabilities of the phase field method for crack growth modeling in complex structures such as porous media. The phase field method does not need predefined cracks and it can simulate curvilinear crack path. This goal is accomplished by replacing the sharp discontinuities with a scalar damage phase field parameter representing the diffuse crack topology. To simulate brittle fracture in this study, the equations of elastic displacement field and fracture phase field are first introduced. Afterwards, using the weak form of the equations, the staggered solution of the equations is performed. To implement the equations in the finite element method, the Abaqus software with User Element Subroutine (UEL) is used. Given that the bone structure is somehow a porous structure, a representative volume element of the bone is selected for phase field simulation. In order to verify the developed model, the tensile test of the single edge notched specimen has been simulated. Subsequently, crack propagation in a porous media with different porosities under tensile loading was simulated. The simulation results illustrate the capability of the phase field method in predicting crack growth in geometrically complex structures. In addition, the load-carrying capacity or the strength of the porous structure continuously decreases with increasing porosity and noteworthy is that such a strength is suddenly decreased around a critical porosity value.
Keywords
Phase field method
Brittle fracture
Porous structures
finite element method

Subjects

[1] A. A Griffith, The phenomena of rupture and flow in solids, Philosophical transactions of the royal society of london. Series A, containing papers of a mathematical or physical character, Vol. 221, pp. 163-198, 1921.
[2] G. R. Irwin, Onset of fast crack propagation in high strength steel and aluminum alloys, Naval research lab Washington DC, 1956.
[3] V. L. Ginzburg, L. D. Landau, On the theory of superconductivity, Zh. eksp. teor. Fiz, Vol. 20, pp. 1064-1082, 1950.
[4] B. Bourdin, G. A. Francfort, J. J. Marigo, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, Vol. 48, No. 4, pp. 797-826, 2000.
[5] J. Dolbow, T. Belytschko, A finite element method for crack growth without remeshing, International journal for numerical methods in engineering, Vol. 46, No. 1, pp. 131-150, 1999.
[6] N. Moës, A. Gravouil, T. Belytschko, Non‐planar 3D crack growth by the extended finite element and level sets-Part I: Mechanical model, International Journal for Numerical Methods in Engineering, Vol. 53, No. 11, pp. 2549-2568, 2002.
[7] G. L. Peng, Y. H. Wang, A Node Split Method for Crack Growth Problem, Applied Mechanics and Materials, Vol. 182, pp. 1524-1528, 2012.
[8] C. Miehe, M. Hofacker, F. Welschinger, A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Computer Methods in Applied Mechanics and Engineering, Vol. 199, No. 45, pp. 2765-2778, 2010.
[9] M. A. Msekh, J. M. Sargado, M. Jamshidian, P. M. Areias, T. Rabczuk, Abaqus implementation of phase-field model for brittle fracture, Computational Materials Science, Vol. 96, pp. 472-484, 2015.
[10] M. J. Borden, C. V. Verhoosel, M. A. Scott, T. J. Hughes, C. M. Landis, A phase field description of dynamic brittle fracture, Computer Methods in Applied Mechanics and Engineering, Vol. 217, pp. 77-95, 2012.
[11] C. Miehe, L. M. Schänzel, Phase field modeling of fracture in rubbery polymers. Part I: Finite elasticity coupled with brittle failure, Journal of the Mechanics and Physics of Solids, Vol. 65, pp. 93-113, 2014.
[12] S. May, J. Vignollet, R. De Borst, A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-convergence and stress oscillations, European Journal of Mechanics-A/Solids, Vol. 52, pp. 72-84, 2015.
[13] M. A. Msekh, M. Silani, M. Jamshidian, P. Areias, X. Zhuang, G. Zi, P. He, T. Rabczuk, Predictions of J integral and tensile strength of clay/epoxy nanocomposites material using phase field model, Composites Part B: Engineering, Vol. 93, pp. 97-114, 2016.
[14] H. Badnava, M. A. Msekh, E. Etemadi, and T. Rabczuk, An h-adaptive thermo-mechanical phase field model for fracture, Finite Elements in Analysis and Design, Vol. 138, pp. 31-47, 2018.
[15] V. Bousson, F. Peyrin, C. Bergot, M. Hausard, A. Sautet, J. D. Laredo, Cortical Bone in the Human Femoral Neck: Three‐Dimensional Appearance and Porosity Using Synchrotron Radiation, Journal of Bone and Mineral Research, Vol. 19, No. 5, pp. 794-801, 2004.
[16] T. L. Norman, D. Vashishth, D. Burr, Fracture toughness of human bone under tension, Journal of biomechanics, Vol. 28, No. 3, pp. 309313-311320, 1995.
[17] P. K. Zysset, X. E. Guo, C. E. Hoffler, K. E. Moore, S. A. Goldstein, Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur, Journal of biomechanics, Vol. 32, No. 10, pp. 1005-1012, 1999.
Modares Mechanical Engineering
Volume 18, Issue 7
November 2018
Pages 217-225