Multiscale computational homogenisation of 3D textile-based fiber reinforced polymer composites

Zahur Ullah, Lukasz Kaczmarczyk, Edward Archer, AT McIlhagger, Eileen Harkin-Jones

Research output: Contribution to conferenceOtherpeer-review


This paper presents a multiscale computational homogenisation approach for the calculation of homogenised
structural level mechanical properties of 3D textile/woven based fiber reinforced polymer (FRP) composites. Textile
or woven composites, in which interlaced fibres are used as reinforcement, are a class of FRP composites which
provide flexibility of design and functionality and are used in many engineering applications, including ships,
aircrafts, automobiles, civil structures and prosthetics [1]. The more recently developed 3D-textile composites,
consisting of 3D arrangements of yarns in a polymer matrix, allow weaving of near-net-shape and complex structures
as compared to the traditional 2D-textile composites. In addition, these 3D-textile composites provide high throughthickness
mechanical properties, lower manufacturing cost and improved impact and delamination resistance. The
macro or structural level mechanical properties of these composites are rooted in their underlying complicated and
heterogeneous micro structures. The heterogeneous microstructure of these composites requires a detailed multiscale
computational homogenisation, which results in the macroscopic constitutive behaviour based on their
microscopically heterogeneous representative volume elements (RVE). Elliptical cross sections and cubic splines are
used respectively to model the cross sections and paths of the yarns within these RVEs. The RVE geometry along
with other input parameters, e.g. material properties and boundary conditions, are modelled in CUBIT/Trelis using a
parameterised Python script.

The multiscale computational homogenisation scheme, with a unified imposition of RVE boundary conditions, is
implemented in MoFEM (Mesh Oriented Finite Element Method) [2], which allows convenient switching between
linear displacement, uniform traction and periodic boundary conditions. MoFEM utilises hierarchic basis functions
[3], which permits the use of arbitrary order of approximation leading to accurate results for relatively coarse meshes.
The matrix and yarns within the RVEs are modelled by considering isotropic and transversely isotropic materials
models respectively. The principal direction of the yarns required for the transversely isotropic material model is
calculated using a computationally inexpensive potential flow analysis along these yarns. Furthermore, the
computational framework is designed to take advantage of distributed memory high-performance computing. The
implementation and performance of the computational tool is demonstrated with a variety of 2.5D and 3D woven
based FRP composites including 3D orthogonal interlock, 3D orthogonal layer-to-layer interlock, 3D orthogonal
through-the-thickness angle interlock, 2.5D layer-to-layer angle interlock and 2.5D layer-layer angle interlock [4].

[1] Z. Ullah, Ł. Kaczmarczyk, S. A. Grammatikos, M. C. Evernden and C. J. Pearce (2016). Multi-scale
computational homogenisation to predict the long-term durability of composite structures. Computers and Structures, 181 . pp. 21-31.
[3] Ł. Kaczmarczyk, Z. Ullah, K. Lewandowski, X. Meng, X. -Y. Zhou, I. Athanasiadis, I and C. J. Pearce (2017). MoFEM-v0.6.20. Zenodo.
[3] M. Ainsworth and J. Coyle (2003). Hierarchic finite element bases on unstructured tetrahedral meshes.
International Journal for Numerical Methods in Engineering, 58 (14): 2103–2130,
[4] Y. Rahali, M. Assidi, I. Goda, A. Zghal, and J. F. Ganghoffer (2016). Computation of the effective mechanical properties including nonclassical moduli of 2.5 D and 3D interlocks by micromechanical approaches. Composites Part B: Engineering, 98, 194-212.
Original languageEnglish
Publication statusPublished (in print/issue) - 11 Jun 2018
Event6th European Conference on Computational Mechanics (ECCM 6)
7th European Conference on Computational Fluid Dynamics (ECFD 7)
- Glasgow, United Kingdom
Duration: 11 Jun 201815 Jun 2018


Conference6th European Conference on Computational Mechanics (ECCM 6)
7th European Conference on Computational Fluid Dynamics (ECFD 7)
Abbreviated titleECCM 6 and ECFD 7
Country/TerritoryUnited Kingdom
Internet address


  • Fiber reinforced polymer composites
  • 3D textile/woven composites
  • Finite element analysis
  • Multiscale computational homogenization


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