A three-dimensional multi-scale computational homogenisation model was developed for the prediction of the nonlinear micro-mechanical response of the fibre-reinforced polymer composite. The two dominant damage mechanisms [1], i.e. matrix damage and fibre-matrix decohesion were considered and modelled using pressure dependent thermodynamically consistent paraboloidal yield criterion and cohesive elements respectively. A linear-elastic transversely isotropic materials model was used to model yarns within the representative volume element (RVE), the principal directions for which were calculated using a potential flow analysis along these yarns. A unified approach [2] was used to impose the RVE boundary conditions, which allows convenient switching between linear displacement, uniform traction and periodic boundary conditions. The developed computational model was implemented within the framework of the hierarchic finite element, which permits the use of arbitrary order of approximation leading to accurate results for relatively coarse meshes. Furthermore, the computational framework was designed to take advantage of distributed memory high-performance computing. The accuracy and efficiency of the developed computational framework were validated with multi-fibre multi-layer M2RVE and single layered plain weave textile composite RVE. In the case of M2RVE, each layer within laminate was represented by a cube with randomly distributed but axially aligned fibres of equal diameters. Elliptical cross sections and cubic splines were used respectively to model the cross sections and paths of the yarns within the textile RVE. The homogenised stress-strain response was validated against the experimental and reference results from the literature. Initiation and propagation of the fibre-matrix interfacial decohesion were also studied. Moreover, the developed computational framework was used to study the effect of fibre-matrix decohesion strength on the homogenised stress-strain response.

References

[1] C. González and J. LLorca. Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: microscopic mechanisms and modeling." Composites Science and Technology 67(13): 2795-2806, 2007.

[2] Z. Ullah, Ł. Kaczmarczyk, S. A. Grammatikos, M. C. Evernden and C. J. Pearce. Multi-scale computational homogenisation to predict the long-term durability of composite structures. Computers and Structures, 2015 (Under Review).