A new algorithm to generate representative volume elements of composites with cylindrical or spherical fillers

Abstract

A new algorithm to generate random spatial distributions of cylindrical fibres and spheres is developed based on a constrained optimization formulation. All filler particles are generated simultaneously within the specimen domain; subsequently their position is iteratively perturbed to remove particle overlapping. The algorithm is able to achieve volume fractions of up to 0.8 in the case of circular cylindrical fibres of equal diameter; the method can be applied to any statistical distribution of fibre diameters. The spatial distribution of fibres and spheres is analysed by plotting spatial statistical metrics; it is shown that the microstructures generated are spatially random and similar to those observed in real fibre composites. The algorithm is employed to effectively predict the transversely isotropic elastic, damping and plastic properties of a unidirectional fibre composite by analysis of an RVE of smaller size than previously reported.

Measurements and predictions of the viscoelastic properties of a composite lamina and their sensitivity to temperature and frequency

“…Virtual microstructures of UD composited were generated using an algorithm based on optimization techniques and previously proposed by the authors [29]. In brief, this algorithm allows randomly placing a number of fibres, of arbitrary shape, in a stochastic volume element (SVE) of square crosssection in the isotropic plane.…”

“…We measured the viscoelastic response of the constituents and that of the UD plates along different directions and at different temperatures and frequencies. We then construct random RVEs of the ply microstructure employing a previously developed algorithm [27,29,30] which guarantees effectively random arrangements of fibres and perform Monte Carlo analyses in the commercial FE solver ABAQUS/standard. The numerical predictions are validated by the measurements and are compared to a number of existing theoretical models, in order to rank their effectiveness.…”

Representative volume elements for the simulation of isotropic composites highly filled with monosized spheres

“…Therefore, alternative approaches have also been developed such as rate-dependent densification algorithm (Jodrey and Tory, 1985) or "drop and roll" algorithm (Visscher and M. Bolsterli, 1972) which are rather dedicated to analysis of spheres close packing (Torquato et al, 2000). A more recent approach suggests to start from a Poisson distribution of spheres and exploit an optimization formulation to improve particle localization while enforcing a non-overlapping constraint (Pathan et al, 2017). However the final volume fraction reached hardly exceeds 40%.…”

An efficient method to generate random distribution of fibers in continuous fiber reinforced composites

“…Therefore, we can use the coefficient of variation which defines as Equation to compare the randomness of the distribution. where σ and μ are mean and SD, respectively. We extracted this coefficient for a generated microstructures with δ = 50 and ϕ f = 65%, compared to those reported by Pathan and listed in Table . At such volume fraction, the proposed algorithm achieves a relatively high coefficient of variation compared with other algorithms, indicating decent randomness of the generated microstructures.…”