Hierarchical finite element based multiscale computational homogenisation of coupled hygro- mechanical analysis for fibre-reinforced polymers

Zahur Ullah, L. Kaczmarczyk, C. J. Pearce

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This paper presents a multiscale computational homogenisation of the coupled hygro- mechanical analysis of the fibre-reinforced polymers (FRPs). This is ongoing research work for the development of a computational framework to predict the long-term durability of these materials for use in the construction industry. Textile or woven composites, in which interlaced fibres are used as reinforcement, is a class of FRPs which provides full flexibility of design and functionality due to the mature textile manufacturing industry and is commonly used in many engineering applications, including ships, aircrafts, automobiles, civil structures and prosthetics [1]. During their service life textile composites are exposed to different hygrothermal environmental conditions in addition to mechanical loading, which leads to matrix plasticisation and degradation of fibres/matrix interfaces [2]. Therefore, understanding of moisture transport mechanisms and their effect on the mechanical performance of these materials are vital for predicting their long-term durability.The heterogeneous microstructure of textile composites requires a detailed multiscale computational homogenisation. The use of multiscale computational homogenisation results in the macroscopic constitutive behaviour of the structures based on its microscopically heterogeneous representative volume element (RVE). A plain weave textile composite RVE is considered in this case, consisting of matrix and yarns embedded in the matrix. These yarns are modeled with elliptical cross section and cubic spline paths. An automated parameterised RVE geometry along with material properties, boundary conditions and meshes are generated in CUBIT with Python scrip, which allows rapid generation of different types of composites.The multiscale computational homogenisation framework is implemented in our group’s FE software, MoFEM (Mesh Oriented Finite Element Method). A unified approach is used to impose the RVE boundary conditions, which allows convenient switching between displacement, traction and periodic boundary conditions [3]. The effect of moisture concentration on Young’s modulus and moisture induced swelling are considered in the model. The final resultant nonlinear discretised system of equations is solved using the Newton–Raphson method. Matrix and yarns are considered as isotropic and transversely isotropic materials respectively. The required principal directions of the yarns for the transversely isotropic material model are calculated from a computationally inexpensive potential flow analysis along these yarns. Furthermore, the computational framework utilises the flexibility of hierarchic basis functions [2], which permits the use of arbitrary orders of approximation leading to very accurate results for relatively coarse meshes. Convergence studies based on hierarchical finite element analysis is also performed to show the effectiveness of the developed approach. The developed code is based on distributed memory parallel programming and is tested on high performance computer facilities. The implementation and performance of the developed computational tool are demonstrated with numerical examples.
Original languageEnglish
Title of host publicationUnknown Host Publication
Publisher18th International Conference on Composite Structures
Number of pages1
Publication statusAccepted/In press - 15 Jun 2015
Event18th International Conference on Composite Structures (ICCS 18) - Lisbon, Portugal
Duration: 15 Jun 2015 → …


Conference18th International Conference on Composite Structures (ICCS 18)
Period15/06/15 → …

Bibliographical note

Reference text: [1] T. W. Chua. Multi–scale modeling of textile composites. Master’s thesis, Department of Mechanical Engineering, Technische Universiteit Eindhoven, January 2011.
[2] X. Tang, J. D. Whitcomb, Y. Li and H. –j. Sue. Micromechanics modeling of moisture diffusion in woven composites. Composites Science and Technology, 65(6), 817–826, 2005.
[3] Ł. Kaczmarczyk, C. J. Pearce, and N. Bićanić. Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization. International Journal for Numerical Methods in Engineering, 74(3):506–522, 2008.
[4] M. Ainsworth and J. Coyle. Hierarchic finite element bases on unstructured tetrahedral meshes. International Journal for Numerical Methods in Engineering, 58 (14): 2103– 2130, 2003.


  • Multiscale computational homogenisation
  • Hygro-mechanical analysis
  • Fibre reinforced polymer
  • Textile composites
  • Transverse isotropy.


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