Skip to main content

Elastoplastic Micromechanical Analysis of Fiber-Reinforced Composites with Defects


The objective of the present work is the computational micromechanical analysis of unidirectional fiber-reinforced composites, considering defects. The micromechanical model uses refined beam theories based on the Carrera unified formulation (CUF) and involves using the component-wise (CW) approach, resulting in a high-fidelity model. Defects are introduced in the representative volume element (RVE) in the form of matrix voids by modifying the material properties of a certain quantity of the Gauss points associated with the matrix. The quantity of Gauss points thus modified is based on the required void volume fraction, and the resulting set is prescribed a material property with negligible stiffness to model voids. Two types of void distribution are considered in the current work—randomly distributed voids within the matrix and voids clustered in a region of the RVE. The current study investigates the influence of the volume fraction of voids present in the matrix and their distribution throughout the RVE domain on the macroscale mechanical response. Material nonlinearity is considered for the matrix phase. Numerical assessments are performed to investigate the influence of the volume fraction and the distribution of the voids on the macroscopic response.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11


  1. Jeong, H.: Effects of voids on the mechanical strength and ultrasonic attenuation of laminated composites. J. Compos. Mater. 31(3), 276–292 (1997)

    Article  Google Scholar 

  2. Prakash, R.: Non-destructive testing of composites. Composites 11(4), 217–224 (1980)

    Article  Google Scholar 

  3. Stone, D.E.W., Clarke, B.: Ultrasonic attenuation as a measure of void content in carbon-fibre reinforced plastics. Non-Destr. Test. 8(3), 137–145 (1975)

    Article  Google Scholar 

  4. Hsu, D.K.: Ultrasonic measurements of porosity in woven graphite polyimide composites. In: Review of Progress in Quantitative Nondestructive Evaluation, pp. 1063–1068. Springer, New York (1988)

    Chapter  Google Scholar 

  5. Huang, H., Talreja, R.: Effects of void geometry on elastic properties of unidirectional fiber reinforced composites. Compos. Sci. Technol. 65(13), 1964–1981 (2005)

    Article  Google Scholar 

  6. Rao, M.V., Mahajan, P., Mittal, R.K.: Effect of architecture on mechanical properties of carbon/carbon composites. Compos. Struct. 83(2), 131–142 (2008)

    Article  Google Scholar 

  7. Shigang, A., Daining, F., Rujie, H., Yongmao, P.: Effect of manufacturing defects on mechanical properties and failure features of 3D orthogonal woven C/C composites. Compos. B Eng. 71, 113–121 (2015)

    Article  Google Scholar 

  8. Seon, G., Makeev, A., Nikishkov, Y., Lee, E.: Effects of defects on interlaminar tensile fatigue behavior of carbon/epoxy composites. Compos. Sci. Technol. 89, 194–201 (2013)

    Article  Google Scholar 

  9. Vajari, D.A., González, C., Llorca, J., Legarth, B.N.: A numerical study of the influence of microvoids in the transverse mechanical response of unidirectional composites. Compos. Sci. Technol. 97, 46–54 (2014)

    Article  Google Scholar 

  10. Carrera, E., Cinefra, M., Petrolo, M., Zappino, E.: Finite Element Analysis of Structures Through Unified Formulation. Wiley, New York (2014)

    Book  Google Scholar 

  11. Kaleel, I., Petrolo, M., Waas, A.M., Carrera, E.: Computationally efficient, high-fidelity micromechanics framework using refined 1D models. Compos. Struct. 181, 358–367 (2017)

    Article  Google Scholar 

  12. Carrera, E., Petrolo, M., Nagaraj, M.H., Delicata, M.: Evaluation of the influence of voids on 3D representative volume elements of fiber-reinforced polymer composites using CUF micromechanics. Compos. Struct. 254, 112833 (2020)

    Article  Google Scholar 

  13. Kaleel, I., Petrolo, M., Waas, A.M., Carrera, E.: Micromechanical progressive failure analysis of fiber-reinforced composite using refined beam models. J. Appl. Mech. 85(2), (2018)

  14. Carrera, E., Petrolo, M.: Refined beam elements with only displacement variables and plate/shell capabilities. Meccanica 47(3), 537–556 (2012)

    MathSciNet  Article  Google Scholar 

  15. Xia, Z., Zhang, Y., Ellyin, F.: A unified periodical boundary conditions for representative volume elements of composites and applications. Int. J. Solids Struct. 40(8), 1907–1921 (2003)

    Article  Google Scholar 

  16. Sun, C.T., Vaidya, R.S.: Prediction of composite properties from a representative volume element. Compos. Sci. Technol. 56(2), 171–179 (1996)

    Article  Google Scholar 

  17. Carrera, E., Kaleel, I., Petrolo, M.: Elastoplastic analysis of compact and thin-walled structures using classical and refined beam finite element models. Mech. Adv. Mater. Struct. 26(3), 274–286 (2019)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to M. Petrolo.

Ethics declarations

Conflict of interest

On behalf of all the authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Nagaraj, M.H., Kaleel, I., Carrera, E. et al. Elastoplastic Micromechanical Analysis of Fiber-Reinforced Composites with Defects. Aerotec. Missili Spaz. 101, 53–59 (2022).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Micromechanics
  • Defect modeling
  • Higher-order theories
  • CUF