Research Papers

A Phase-Field Damage Model for Orthotropic Materials and Delamination in Composites

[+] Author and Article Information
Bensingh Dhas

Computational Mechanics Laboratory,
Department of Civil Engineering Indian
Institute of Science,
Bangalore 560012, India
e-mail: bensingh@civil.iisc.ernet.in

Md. Masiur Rahaman

Computational Mechanics Laboratory,
Department of Civil Engineering Indian
Institute of Science,
Bangalore 560012, India
e-mail: masiur@civil.iisc.ernet.in

Kiran Akella

Scientist Research & Development
Establishment (Engineers),
Defense Research and Development
Pune 411006, India
e-mail: kiranakella@rde.drdo.in

Debasish Roy

Computational Mechanics Laboratory,
Department of Civil Engineering Indian
Institute of Science,
Bangalore 560012, India
e-mail: royd@civil.iisc.ernet.in

J. N. Reddy

Advanced Computational Mechanics Laboratory,
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843-3123
e-mail: jnreddy@tamu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 2, 2017; final manuscript received November 16, 2017; published online November 28, 2017. Editor: Yonggang Huang.

J. Appl. Mech 85(1), 011010 (Nov 28, 2017) (8 pages) Paper No: JAM-17-1550; doi: 10.1115/1.4038506 History: Received October 02, 2017; Revised November 16, 2017

A phase-field damage model for orthotropic materials is proposed and used to simulate delamination of orthotropic laminated composites. Using the deviatoric and hydrostatic tensile components of the stress tensor for elastic orthotropic materials, a degraded elastic free energy that can accommodate damage is derived. The governing equations follow from the principle of virtual power and the resulting damage model, by its construction, conforms with the physical relevant condition of no matter interpenetration along the crack faces. The model also dispenses with the traction separation law, an extraneous hypothesis conventionally brought in to model the interlaminar zones. The model is assessed through numerical simulations on delaminations in mode I, mode II, and another such problem with multiple initial notches. The present method is able to reproduce nearly all the features of the experimental load displacement curves, allowing only for small deviations in the softening regime. Numerical results also show forth a superior performance of the proposed method over existing approaches based on a cohesive law.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Whitney, J. M. , and Nuismer, R. J. , 1974, “ Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations,” J. Compos. Mater., 8(3), pp. 253–265. [CrossRef]
Irwin, G. R. , 1957, “ Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate,” ASME J. Appl. Mech., 24(3), pp. 361–364.
Rice, J. R. , 1968, “ A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,” ASME J. Appl. Mech., 35(2), pp. 379–386. [CrossRef]
Hellen, T. , 1975, “ On the Method of Virtual Crack Extensions,” Int. J. Numer. Methods Eng., 9(1), pp. 187–207. [CrossRef]
Parks, D. M. , 1974, “ A Stiffness Derivative Finite Element Technique for Determination of Crack Tip Stress Intensity Factors,” Int. J. Fract., 10(4), pp. 487–502. [CrossRef]
Verhoosel, C. V. , and Borst, R. , 2013, “ A Phase-Field Model for Cohesive Fracture,” Int. J. Numer. Methods Eng., 96(1), pp. 43–62. [CrossRef]
May, S. , Vignollet, J. , and de Borst, R. , 2015, “ A Numerical Assessment of Phase-Field Models for Brittle and Cohesive Fracture: Γ-Convergence and Stress Oscillations,” Eur. J. Mech. -A/Solids, 52, pp. 72 –84. [CrossRef]
Simo, J. C. , Oliver, J. , and Armero, F. , 1993, “ An Analysis of Strong Discontinuities Induced by Strain-Softening in Rate-Independent Inelastic Solids,” Comput. Mech., 12(5), pp. 277–296. [CrossRef]
Belytschko, T. , and Gracie, R. , 2007, “ On Xfem Applications to Dislocations and Interfaces,” Int. J. Plasticity, 23(10), pp. 1721–1738. [CrossRef]
Oliver, J. , Huespe, A. , Pulido, M. , and Chaves, E. , 2002, “ From Continuum Mechanics to Fracture Mechanics: The Strong Discontinuity Approach,” Eng. Fract. Mech., 69(2), pp. 113–136. [CrossRef]
Huespe, A. E. , Needleman, A. , Oliver, J. , and Sánchez, P. J. , 2009, “ A Finite Thickness Band Method for Ductile Fracture Analysis,” Int. J. Plasticity, 25(12), pp. 2349–2365. [CrossRef]
Huespe, A. , Needleman, A. , Oliver, J. , and Sánchez, P. , 2012, “ A Finite Strain, Finite Band Method for Modeling Ductile Fracture,” Int. J. Plasticity, 28(1), pp. 53–69. [CrossRef]
Rahaman, M. M. , Deepu, S. , Roy, D. , and Reddy, J. , 2015, “ A Micropolar Cohesive Damage Model for Delamination of Composites,” Compos. Struct., 131, pp. 425–432. [CrossRef]
Bazant, Z. P. , and Pijaudier-Cabot, G. , 1988, “ Nonlocal Continuum Damage, Localization Instability and Convergence,” ASME J. Appl. Mech., 55(2), pp. 287–293. [CrossRef]
Frémond, M. , and Nedjar, B. , 1996, “ Damage, Gradient of Damage and Principle of Virtual Power,” Int. J. Solids Struct., 33(8), pp. 1083–1103. [CrossRef]
Alfano, G. , and Crisfield, M. , 2001, “ Finite Element Interface Models for the Delamination Analysis of Laminated Composites: Mechanical and Computational Issues,” Int. J. Numer. Methods Eng., 50(7), pp. 1701–1736. [CrossRef]
Škec, L. , Jelenić, G. , and Lustig, N. , 2015, “ Mixed-Mode Delamination in 2D Layered Beam Finite Elements,” Int. J. Numer. Methods Eng., 104(8), pp. 767–788. [CrossRef]
Aranson, I. , Kalatsky, V. , and Vinokur, V. , 2000, “ Continuum Field Description of Crack Propagation,” Phys. Rev. Lett., 85(1), pp. 118–121. [CrossRef] [PubMed]
Lemaitre, J. , 1986, “ Local Approach of Fracture,” Eng. Fract. Mech., 25(5–6), pp. 523–537. [CrossRef]
Spatschek, R. , Brener, E. , and Karma, A. , 2011, “ Phase Field Modeling of Crack Propagation,” Philos. Mag., 91(1), pp. 75–95. [CrossRef]
Hakim, V. , and Karma, A. , 2009, “ Laws of Crack Motion and Phase-Field Models of Fracture,” J. Mech. Phys. Solids, 57(2), pp. 342–368. [CrossRef]
Da Silva, M. N. , Duda, F. P. , and Fried, E. , 2013, “ Sharp-Crack Limit of a Phase-Field Model for Brittle Fracture,” J. Mech. Phys. Solids, 61(11), pp. 2178–2195. [CrossRef]
Fried, E. , and Gurtin, M. E. , 2003, “ The Role of the Configurational Force Balance in the Nonequilibrium Epitaxy of Films,” J. Mech. Phys. Solids, 51(3), pp. 487–517. [CrossRef]
Karma, A. , and Lobkovsky, A. E. , 2004, “ Unsteady Crack Motion and Branching in a Phase-Field Model of Brittle Fracture,” Phys. Rev. Lett., 92(24), p. 245510. [CrossRef] [PubMed]
Henry, H. , and Levine, H. , 2004, “ Dynamic Instabilities of Fracture Under Biaxial Strain Using a Phase Field Model,” Phys. Rev. Lett., 93(10), p. 105504. [CrossRef] [PubMed]
Bourdin, B. , Francfort, G. A. , and Marigo, J.-J. , 2000, “ Numerical Experiments in Revisited Brittle Fracture,” J. Mech. Phys. Solids, 48(4), pp. 797–826. [CrossRef]
Miehe, C. , Welschinger, F. , and Hofacker, M. , 2010, “ Thermodynamically Consistent Phase-Field Models of Fracture: Variational Principles and Multi-Field Fe Implementations,” Int. J. Numer. Methods Eng., 83(10), pp. 1273–1311. [CrossRef]
Francfort, G. A. , and Marigo, J.-J. , 1998, “ Revisiting Brittle Fracture as an Energy Minimization Problem,” J. Mech. Phys. Solids, 46(8), pp. 1319–1342. [CrossRef]
Griffith, A. A. , 1921, “ The Phenomena of Rupture and Flow in Solids,” Philos. Trans. R. Soc. London. Ser. A, 221(582–593), pp. 163–198. [CrossRef]
Gurtin, M. E. , 1996, “ Generalized Ginzburg-Landau and Cahn-Hilliard Equations Based on a Microforce Balance,” Phys. D: Nonlinear Phenom., 92(3–4), pp. 178–192. [CrossRef]
Duda, F. P. , Ciarbonetti, A. , Sánchez, P. J. , and Huespe, A. E. , 2015, “ A Phase-Field/Gradient Damage Model for Brittle Fracture in Elastic–Plastic Solids,” Int. J. Plasticity, 65, pp. 269–296. [CrossRef]
Coleman, B. D. , and Noll, W. , 1963, “ The Thermodynamics of Elastic Materials With Heat Conduction and Viscosity,” Archive Rational Mech. Anal., 13(1), pp. 167–178. [CrossRef]
Borden, M. J. , Hughes, T. J. , Landis, C. M. , and Verhoosel, C. V. , 2014, “ A Higher-Order Phase-Field Model for Brittle Fracture: Formulation and Analysis Within the Isogeometric Analysis Framework,” Comput. Methods Appl. Mech. Eng., 273, pp. 100–118. [CrossRef]
Miehe, C. , Hofacker, M. , and Welschinger, F. , 2010, “ A Phase Field Model for Rate-Independent Crack Propagation: Robust Algorithmic Implementation Based on Operator Splits,” Comput. Methods Appl. Mech. Eng., 199(45), pp. 2765–2778. [CrossRef]
Farrell, P. , and Maurini, C. , 2017, “ Linear and Nonlinear Solvers for Variational Phase-Field Models of Brittle Fracture,” Int. J. Numer. Methods Eng., 109(5), pp. 648–667. [CrossRef]
De Morais, A. , De Moura, M. , Marques, A. , and De Castro, P. , 2002, “ Mode-I Interlaminar Fracture of Carbon/Epoxy Cross-Ply Composites,” Compos. Sci. Technol., 62(5), pp. 679–686. [CrossRef]
Turon, A. , Camanho, P. P. , Costa, J. , and Dávila, C. , 2006, “ A Damage Model for the Simulation of Delamination in Advanced Composites Under Variable-Mode Loading,” Mech. Mater., 38(11), pp. 1072–1089. [CrossRef]
Robinson, P. , Besant, T. , and Hitchings, D. , 2000, “ Delamination Growth Prediction Using a Finite Element Approach,” Eur. Struct. Integrity Soc., 27, pp. 135–147. [CrossRef]


Grahic Jump Location
Fig. 1

Geometry and the boundary conditions for the DCB test

Grahic Jump Location
Fig. 2

Load versus the crack opening displacement for DCB test. The experimental data is taken from [36]. Predictions of load displacement curve based on decohesion elements [37] are also presented for comparison.

Grahic Jump Location
Fig. 3

Geometry and the boundary conditions for the ENF test

Grahic Jump Location
Fig. 4

Comparison of the load displacement curve obtained from present methodology, decohesion element [37] and experiment [36]

Grahic Jump Location
Fig. 5

Mesh convergence study for ENF test

Grahic Jump Location
Fig. 6

Geometry and the boundary conditions for multidelamination problem

Grahic Jump Location
Fig. 7

Contour of phase-field parameter plotted on the deformed shape of the multidelamination specimen for a crack mouth opening displacement of about 25 mm. Notice the lamina bridging the two precracks is still intact.

Grahic Jump Location
Fig. 8

Load-displacement curve for multidelamination problem. The experimental data is from Robinson et al. [38] while the interface element-based simulation data are from Alfano and Crisfield [16].



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In