Influence of the multiscale distribution of particles on elastic properties of concrete

Abstract

International audienceThe mechanical role of the shape of the aggregates, and their spatial distribution in concrete materials is examined. The effect on the macroscopic mechanical response as well as on the local stress fields are investigated by numerical means, making use of a recently developed Poisson-polyhedra model in which the aggregates have polyhedral shapes. Comparison is made with previous microstructure models of spheres. Full-field computations are carried out on large volume size using Fourier methods. The field maps are used to determine zones of highest stress. Furthermore, the scale separation hypothesis for the computation of the elastic properties is investigated using numerical calculations on various multiscale microstructures. Finally, numerical predictions for the elastic properties are compared to experimental measurements, and the results discussed

A review of nonlinear FFT-based computational homogenization methods

“…Moreover, FFT-based methods can be used to compute the effective viscosity of particle suspensions [309]. FFT-based computational techniques proved useful for studying the viscoelasticity of cement paste [310], mortar samples [311], cement [312] and concrete [313]. Furthermore, FFT-based techniques were used for studying explosive materials [314], secondary creep in a porous nuclear fuel [315], the thermal expansion of an energetic material [316], optical properties of deposit models for paint [317], dynamic recrystallization [318], to compute geodesics in two-dimensional media [182], fitting microstructure-property relationships [319], topology optimization [320] and for finding emerging microstructures associated to non-convex potentials [93,321].…”

Effective hyperelastic material parameters from microstructures constructed using the planar Boolean model

“…Stochastic models are often used to obtain statistically homogeneous microstructures, e.g., [12,23]. Statistically homogeneity is a necessary condition for identification of effective material properties; cf.…”

“…For each microstructure ensemble we identify the ensemble of macroscale parameters and compute the variances D 2 λ (δ) and D 2 μ (δ) of both apparent material parameters λ and μ. We then use a least-squares fit (12) to the variances, identifying as parameters the integral range δ 2 and the exponent α; see Fig. Note that, for the fit, we only use data points with small bias from the boundary conditions.…”

“…Also note that, e.g., for discs we use ensemble sizes n as given by n = 200•(64/δ) √ 2 ; see Table 2 and its caption. Using sufficiently large ensemble sizes will result in small relative margins of error for the apparent material parameters and allow a good fit in (12).…”

“…It is well known that the shape of the inclusions of the microstructures has an influence on the effective material properties of composite materials; cf. [12,44,68]. For each Boolean model, using different area fractions and using discs D and rectangles R 1 , R 3 , we construct 200 microstructures samples with δ = {64; 38.8; 23.4} for the given grain types.…”