Abstract
A three-dimensional multi-scale computational homogenisation framework is developed for the prediction of nonlinear micro/meso-mechanical response of the fibre-reinforced polymer (FRP) composites. Two dominant damage mechanisms, i.e. matrix elasto-plastic response and fibre–matrix decohesion are considered and modelled using a non-associative pressure dependent paraboloidal yield criterion and cohesive interface elements respectively. A linear-elastic transversely isotropic material model is used to model yarns/fibres within the representative volume element (RVE). A unified approach is used to impose the RVE boundary conditions, which allows convenient switching between linear displacement, uniform traction and periodic boundary conditions. The computational model is implemented within the framework of the hierarchic finite element, which permits the use of arbitrary orders of approximation. Furthermore, the computational framework is designed to take advantage of distributed memory high-performance computing. The accuracy and performance of the computational framework are demonstrated with a variety of numerical examples, including unidirectional FRP composite, a composite comprising a multi-fibre and multi-layer RVE, with randomly generated fibres, and a single layered plain weave textile composite. Results are validated against the reference experimental/numerical results from the literature. The computational framework is also used to study the effect of matrix and fibre–matrix interfaces properties on the homogenised stress–strain responses.
Highlights
Compared to conventional materials, fibre-reinforced polymer (FRP) composites can offer exceptional physical and chemical properties, making them ideal for a variety of engineering applications, including aerospace, marine, automotive industry, civil structures and prosthetics [1, 2, 3]
Multi-scale computational homogenisation (CH) provides an accurate modelling framework to simulate the behaviour of FRP composites and determine the macro-scale homogenised response, based on the physics of an underlying, microscopically heterogeneous, representative volume element (RVE) [4, 5, 6, 7, 8, 9, 3]
The pressure dependent, Drucker-Prager yield criterion was used to model matrix plasticity and both fibre breakage and fibrematrix interfacial decohesion were modelled with cohesive interface elements
Summary
Fibre-reinforced polymer (FRP) composites can offer exceptional physical and chemical properties (including high strength, low specific weight, fatigue and corrosion resistance, low thermal expansion and high dimension stability), making them ideal for a variety of engineering applications, including aerospace, marine, automotive industry, civil structures and prosthetics [1, 2, 3]. Each lamina was modelled as a cube with randomly distributed but axially aligned fibres, generated using a fibres randomisation algorithm in DIGIMAT FE [16] Both cross [0/90]ns and angle [±45]ns (where the subscript ns represents n layers with the same sequence and symmetric about the mid plane) GFRP composites were considered with in-plane shear loading and results of stress-strain behaviour were validated against the experimental results. A statistically proven random distribution algorithm proposed by the same authors in [22] was used to randomly generate UD fibres within the RVEs. Similar to previous studies, fibres were modelled as linearelastic and isotropic material and fibre-matrix decohesion was modelled with cohesive interface elements. Results of the RVE strain fields and homogenised stress-strain response were validated against the experimental results and found in a good agreement These numerical simulations, described above, of FRP composite behaviour are limited to specific RVE type (2D or 3D, UD or woven/textile) or loading scenarios (normal or shear).
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