Mesh-objective two-scale finite element analysis of damage and failure in ceramic matrix composites

  • Pascal Meyer
  • Anthony M WaasEmail author
Research Article
Part of the following topical collections:
  1. Integrated Computational Engineering of Composites


A mesh-objective two-scale finite element approach for analyzing damage and failure of fiber-reinforced ceramic matrix composites is presented here. The commercial finite element software suite Abaqus is used to generate macroscopic models, e.g., structural-level components or parts of ceramic matrix composites (CMCs), coupled with a second finite element code which pertains to the sub-scale at the fiber-matrix interface level, which is integrated seamlessly using user-generated subroutines and referred to as the integrated finite element method (IFEM). IFEM calculates the reaction of a microstructural sub-scale model that consists of a representative volume element (RVE) which includes all constituents of the actual material, e.g., fiber, matrix, and fiber/matrix interfaces, details of packing, and nonuniformities in properties. The energy-based crack band theory (CBT) is implemented within IFEM’s sub-scale constitutive laws to predict micro-cracking in all constituents included in the model. The communication between the micro- and macro-scale is achieved through the exchange of strain, stress, and stiffness tensors. Important failure parameters, e.g., crack path and proportional limit, are part of the solution and predicted with a high level of accuracy. Numerical predictions are validated against experimental results.


Multi-scale analysis Crack band Ceramic matrix composites Finite elements 



The authors are grateful to the Aerospace Engineering Department at the University of Michigan for the continued support of the research studies presented here.


  1. 1.
    Kanoute P, Boso DP, Chaboche JL, Schrefler BA (2009) Multiscale methods for composites: a review. Arch Comput Methods Eng 16: 31–75.CrossRefGoogle Scholar
  2. 2.
    Heinrich C, Waas AM (2013) Investigation of progressive damage and fracture in laminated composites using the smeared crack approach. CMC-Computers Mater Continua 35: 155–181.Google Scholar
  3. 3.
    Yuan Z, Fish J (2008) Towards realization of computational homogenization in practice. IJNME 73: 361–380.CrossRefGoogle Scholar
  4. 4.
    Ghosh S, Kyunghoon L, Moorthy S (1995) Multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method. Int J Solids Struct 32: 27–62.CrossRefGoogle Scholar
  5. 5.
    Key CT, Garnich MR, Hansen AC (2004) Progressive failure predictions for rib-stiffened panels based on multicontinuum technology. Composite Struct 65: 357–366.CrossRefGoogle Scholar
  6. 6.
    Bacarreza O, Aliabadi MH, Apicella A (2012) Multi-scale failure analysis of plain-woven composites. J Strain Anal 47: 379–388.CrossRefGoogle Scholar
  7. 7.
    Jirásek M (1998) Nonlocal models for damage and fracture: comparison of approaches. Int J Solids Struct 35: 4133–4145.CrossRefGoogle Scholar
  8. 8.
    Aboudi J, Pindera MJ, Arnold SM (2001) Linear thermoelastic higher-order theory for periodic multiphase materials. J Appl Mech 68: 697–707.CrossRefGoogle Scholar
  9. 9.
    Pineda EJ, Bednarcyk BA, Waas AM, Arnold SM (2013) Progressive failure of a unidirectional fiber-reinforced composite using the method of cells: discretization objective computational results. IJSS 50: 1203–1216.Google Scholar
  10. 10.
    Feyel F, Chaboche JL (2000) Fe 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. Comput Methods Appl Mech Eng 183: 309–330.CrossRefGoogle Scholar
  11. 11.
    Ladevèze P, Nouy A (2003) On a multiscale computational strategy with time and space homogenization for structural mechanics. Comput Methods Appl Mech Eng 192: 3061–3087.CrossRefGoogle Scholar
  12. 12.
    Michel JC, Moulinec H, Suquet P (1999) Effective properties of composite materials with periodic microstructure: a computational approach. Comput Methods Appl Mech Eng 172: 109–143.CrossRefGoogle Scholar
  13. 13.
    Smit RJM, Brekelmans WAM, Meijer JEH (1998) Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling. Comput Methods Appl Mech Eng 155: 181–192.CrossRefGoogle Scholar
  14. 14.
    Baz̆ant ZP (1983) Crack band theory for fracture of concrete. Mater Struct 16: 155–177.Google Scholar
  15. 15.
    Abaqus (2008) Abaqus User’s Manual. Dassault Systèmes Simulia Corp, Providence, RI. version 6.11 edition.Google Scholar
  16. 16.
    Chandrupatla TR, Belegundu AD (2002) Introduction to finite elements in engineering. Pearson Education Inc., Upper Saddle River, NJ.Google Scholar
  17. 17.
    Heinrich C, Aldridge M, Kieffer J, Waas AM, Shahwan K (2012) The influence of the representative volume element (RVE) size on the homogenized response of cured fiber composites. Model Simul Mater Sci Eng 20. doi:10.1088/0965-0393/20/7/075007.CrossRefGoogle Scholar
  18. 18.
    Xia Z, Zhang Y, Ellyin F (2003) A unified periodical boundary conditions for representative volume elements of composites and applications. Int J Solids Struct 40: 1907–1921.CrossRefGoogle Scholar
  19. 19.
    Corman GS, Luthra KL (2005) Silicon melt infiltrated ceramic composites (HiPerComp) In: Handbook of ceramic composites, 99–115.. Kluwer Academic Publisher, Boston, MA.CrossRefGoogle Scholar
  20. 20.
    Pineda EJ, Waas AM (2012) Modelling progressive failure of fibre reinforced laminated composites: mesh objective calculations. Aeronaut J 116: 1221–1246.CrossRefGoogle Scholar
  21. 21.
    Baz̆ant ZP, Cedolin L (1991) Stability of structures: elastic, inelastic, fracture and damage theories. Oxford University Press, New York.Google Scholar
  22. 22.
    Pineda EJ, Bednarcyk BA, Waas AM, Arnold SM (2013) On multiscale modeling using the generalized method of cells: preserving energy dissipation across disparate length scales. Comput Mater Continua 35: 119–154.Google Scholar

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© Meyer and Waas. 2015

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Aeronautics and AstronauticsUniversity of WashingtonSeattle,WA 98195 - 2400USA

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