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Research Papers

Failure Prediction of Unidirectional Composites Undergoing Large Deformations1

[+] Author and Article Information
Jacob Aboudi

Faculty of Engineering,
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: aboudi@eng.tau.ac.il

Konstantin Y. Volokh

Faculty of Civil Engineering,
Technion-Israel Institute of Technology,
Haifa 32000, Israel
e-mail: cvolokh@technion.ac.il

To Professor Alan Needleman, keen and always engaging.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 25, 2014; final manuscript received April 8, 2015; published online June 3, 2015. Assoc. Editor: Vikram Deshpande.

J. Appl. Mech 82(7), 071004 (Jul 01, 2015) (15 pages) Paper No: JAM-14-1391; doi: 10.1115/1.4030351 History: Received August 25, 2014; Revised April 08, 2015; Online June 03, 2015

In previous publications, strain-energy functions with limiters have been introduced for the prediction of onset of failure in monolithic isotropic hyperelastic materials. In the present investigation, such enhanced strain-energy functions whose ability to accumulate energy is limited have been incorporated with a finite strain micromechanical analysis. As a result, macroscopic constitutive equations have been established which are capable to predict the onset of loss of static stability in a hyperelastic phase of composite materials undergoing large deformations. The details of the micromechanical analysis, based on a tangential formulation, for composites with periodic microstructure are presented. The derived micromechanical analysis includes the capability to model a possible imperfect bonding between the composite’s constituents and to provide the field distribution in the composite. The micromechanical method is verified by comparison with analytical and finite difference solutions for porous hyperelastic materials that are valid in some special cases. Results are given for a rubberlike matrix characterized by softening hyperelasticity, reinforced by unidirectional nylon fibers. The response of the composite to various types of loadings is presented up to the onset of loss of static stability at a location within the hyperelastic rubber constituent, and initial failure envelopes are shown.

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References

Christensen, R. M., 2013, The Theory of Materials Failure, Oxford University Press, Oxford, UK.
Gosse, J. H., and Christensen, R. M., 2001, “Strain Invariant Failure Criteria for Polymers in Composite Materials,” AIAA Paper No. 2001-1184. [CrossRef]
Humphrey, J. D., 2002, Cardiovascular Solid Mechanics, Springer, New York.
Aboudi, J., Arnold, S. M., and Bednarcyk, B. A., 2013, Micromechanics of Composite Materials: A Generalized Multiscale Analysis Approach, Elsevier, Oxford, UK.
Volokh, K. Y., 2013, “Review of the Energy Limiters Approach to Modeling Failure of Rubber,” Rubber Chem. Technol., 86(3), pp. 470–487. [CrossRef]
Volokh, K. Y., 2010, “On Modeling Failure of Rubber-Like Materials,” Mech. Res. Commun., 37(8), pp. 684–689. [CrossRef]
Volokh, K. Y., 2010, “Comparison of Biomechanical Failure Criteria for Abdominal Aortic Aneurysm,” J. Biomech., 43(10), pp. 2032–2034. [CrossRef] [PubMed]
Aboudi, J., and Pindera, M.-J., 2004, “High-Fidelity Micromechanical Modeling of Continuously Reinforced Elastic Multiphase Materials Undergoing Finite Deformation,” Math. Mech. Solids, 9(6), pp. 599–628. [CrossRef]
Aboudi, J., 2009, “Finite Strain Micromechanical Analysis of Rubber-Like Matrix Composites Incorporating the Mullins Damage Effect,” Int. J. Damage Mech., 18(1), pp. 5–29. [CrossRef]
Ogden, R. W., 1984, Non-Linear Elastic Deformations, Ellis Horwood, Chichester, UK.
Holzapfel, G. A., 2000, Nonlinear Solid Mechanics, Wiley, New York.
Volokh, K. Y., 2014, “On Irreversibility and Dissipation in Hyperelasticity With Softening,” ASME J. Appl. Mech., 81(7), p. 074501. [CrossRef]
Wang, J., Duan, H. L., Zhang, Z., and Huang, Z. P., 2005, “An Anti-Interpenetration Model and Connections Between Interphase and Interface Models in Particle-Reinforced Composites,” Int. J. Mech. Sci., 47(4–5), pp. 701–718. [CrossRef]
Jafari, A. H., Abeyaratne, R., and Horgan, C. O., 1984, “The Finite Deformation of a Pressurized Circular Tube for a Class of Compressible Materials,” J. Appl. Math. Phys. (ZAMP), 35(2), pp. 227–246. [CrossRef]
Haughton, D. M., 1987, “Inflation and Bifurcation of Thick-Walled Compressible Elastic Spherical Shells,” IMA J. Appl. Math., 39(3), pp. 259–272. [CrossRef]
Blatz, P. J., and Ko, W. L., 1962, “Application of Finite Elastic Theory to the Deformation of Rubbery Materials,” Trans. Soc. Rheol., 6(1), pp. 223–251. [CrossRef]
Horgan, C. O., 1995, “On Axisymmetric Solutions for Compressible Nonlinearly Elastic Solids,” J. Appl. Math. Phys. (ZAMP), 46, pp. S107–S125. [CrossRef]
Horgan, C. O., 2001, “Equilibrium Solutions for Compressible Nonlinearly Elastic Material,” Nonlinear Elasticity: Theory and Applications, R. W.Ogden and Y.Fu, eds., Cambridge University Press, Cambridge, UK, pp. 135–159.
Hashin, Z., and Rosen, B. W., 1964, “The Elastic Moduli of Fiber-Reinforced Materials,” ASME J. Appl. Mech., 31(2), pp. 223–232. [CrossRef]
Chung, D. T., Horgan, C. O., and Abeyaratne, R., 1986, “The Finite Deformation of Internally Pressurized Hollow Cylinders and Spheres for a Class of Compressible Elastic Materials,” Int. J. Solids Struct., 22(12), pp. 1557–1570. [CrossRef]
Hamdi, A., Nait Abdelaziz, M., Ait Hocine, N., Heuillet, P., and Benseddiq, N., 2006, “A Fracture Criterion of Rubber-Like Materials Under Plane Stress Conditions,” Polym. Test., 25(8), pp. 994–1005. [CrossRef]
Yeoh, O. H., 1990, “Characterization of Elastic Properties of Carbon Black Filled Rubber Vulcanizates,” Rubber Chem. Technol., 63(5), pp. 792–805. [CrossRef]
Assaad, M., and Arnold, S. M., 1999, “An Analysis of the Macroscopic Tensile Behavior of a Nonlinear Nylon Reinforced Elastomeric Composite System Using MAC/GMC,” NASA Glenn Research Center, Cleveland, OH, Paper No. NASA/TM-1999-209066.
Gasser, T. C., Ogden, R. W., and Holzapfel, G. A., 2006, “Hyperelastic Modelling of Arterial Layers With Distributed Collagen Fibre Orientations,” J. R. Soc. Interface, 3(6), pp. 15–35. [CrossRef] [PubMed]
Kim, H. S., 2009, “Nonlinear Multiscale Anisotropic Material and Structural Models for Prosthetic and Native Aortic Heart Valves,” Ph.D. dissertation, Georgia Institute of Technology, Atlanta, GA.
Kim, H. S., Haj-Ali, R., and Aboudi, J., 2010, “Nonlinear Micromechanical Modeling Approach for Anisotropic Hyperelastic Tissue Materials,” 1st International Conference on Advances in Interaction and Multiscale Mechanics, Jeju, South Korea, May 31–June 2.
Balakhovsky, K., Jabareen, M., and Volokh, K., 2014, “Modeling Rupture of Growing Aneurysms,” J. Biomech., 47(3), pp. 653–658. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

(a) A schematic representation of the stress T1 and strain-energy ψ variation of a hyperelastic material with energy limiter. (b) A multiphase composite with doubly periodic microstructures defined with respect to global initial coordinates in the plane X2-X3. (c) The repeating unit cell is defined with respect to local initial coordinates in the plane Y2-Y3. (d) A characteristic subcell (βγ) in which a local initial system of coordinates (Y¯2(β),Y¯3(γ)) is introduced the origin of which is located at the center.

Grahic Jump Location
Fig. 2

(a) The response of the monolithic Ogden harmonic material to simple tension in the two-direction. (b) The macroscopic response of porous Ogden material subjected to a biaxial loading. Comparison between the HFGMC, exact CCA, and finite difference solutions for φ→∞. (c) The macroscopic response of porous Ogden material subjected to a biaxial loading. Comparison between the HFGMC and finite difference solutions for φ = 5 MPa and m = 10.

Grahic Jump Location
Fig. 3

(a) The response of the monolithic JAH harmonic material to simple tension in the two-direction. (b) The macroscopic response of porous Ogden material subjected to a biaxial loading. Comparison between the HFGMC, exact CCA, and finite difference solutions for φ→∞. (c) The macroscopic response of porous JAH material subjected to a biaxial loading. Comparison between the HFGMC and finite difference solutions for φ = 1 MPa and m = 10.

Grahic Jump Location
Fig. 4

(a) The response of the monolithic Blatz and Ko material to simple tension in the two-direction. (b) The macroscopic response of porous Blatz and Ko material subjected to a biaxial loading. Comparison between the HFGMC, exact CCA, and finite difference solutions for φ→∞. (c) The macroscopic response of porous Blatz and Ko material subjected to a biaxial loading. Comparison between the HFGMC and finite difference solutions for φ = 0.2 MPa and m = 10.

Grahic Jump Location
Fig. 5

The response of the monolithic matrix described by Eq. (56) to simple tension in the one-direction. (a) Piola–Kirchhoff stress T1 and (b) strain-energy ψ.

Grahic Jump Location
Fig. 6

(a) Stress–deformation gradient response of the nylon/rubberlike composite to uniaxial stress loading in the fibers direction and (b) the induced deformation gradient in the transverse direction. (c) Stress–deformation gradient response of the composite to uniaxial stress loading in the transverse direction and (d) the induced deformation gradient in the other transverse direction. (e) The distribution in the repeating unit cell 0≤Y2/H≤1,0≤Y3/L≤1 of the strain-energy ψ when ψ = ψc = 63.1 MPa.

Grahic Jump Location
Fig. 7

(a) Stress–deformation gradient response of the unreinforced matrix caused by the application of a biaxial loading. (b) Macroscopic axial stress and (c) transverse stress against deformation gradient of the nylon/rubberlike composite. The composite is subjected to equal axial and transverse loading while keeping all other global stress components equal to zero.

Grahic Jump Location
Fig. 8

Biaxial loading of nylon/rubberlike composite. (a) Initial failure envelope in the plane F¯11 - F¯22. (b) Initial failure envelope in the plane T¯11 - T¯22.

Grahic Jump Location
Fig. 9

Stress–deformation gradient response of the nylon/rubberlike composite to biaxial loading in both transverse directions

Grahic Jump Location
Fig. 10

Axial response to off-axis unidirectional nylon/rubberlike composite. The rotation θ around three-direction denotes the angle between the fibers (oriented in the one-direction) and loading (applied in the X-direction).

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Fig. 11

Nylon/rubberlike composite in the presence of imperfect bonding of rN = rT = 5×10-6 m/MPa. (a) Stress–deformation gradient response of the nylon/rubberlike composite to uniaxial stress loading in the fibers direction and (b) the induced deformation gradient in the transverse direction. (c) Stress–deformation gradient response of the composite to uniaxial stress loading in the transverse direction and (d) the induced deformation gradient in the other transverse direction.

Grahic Jump Location
Fig. 12

Biaxial loading of nylon/rubberlike composite in the presence of imperfect bonding of rN = rT = 5×10-6 m/MPa. (a) Initial failure envelope in the plane F¯11-F¯22. (b) Initial failure envelope in the plane T¯11-T¯22.

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