Elastostatic field distributions in polycrystals and cracked media

Abstract

This work addresses the problem of the reconstruction of the local fields distribution occurring in heterogeneous linear elastic solids. The constitutive heterogeneities are crystals and cracks. Through comparisons with FFT computations, it is shown that self-consistent estimates together with an assumption of normal distribution at the phase scale provide an accurate description of the elastostatic field histograms in polycrystals without cracks. In the case of inter and transgranular cracks, full-field FFT simulations indicate that the field histograms present van Hove singularities. Their natures are determined analytically in the low-density regime, in the case of an homogeneous medium containing cracks.

Morphological characterization and elastic response of a granular material

“…The former also presents the most narrow stress histogram. The histograms of the stress field in both the grains and wax present asymmetric distribution tails close to powerlaws, features which are consistent with results obtained in elasticity for polycrystals (Willot et al, 2020).…”

A review of nonlinear FFT-based computational homogenization methods

“…FFT-based computational homogenization methods have been used in concurrent multi-scale simulation [217,226,322,323] and in connection to stochastic FEM [324]. They served as the basis for investigating field statistics [325][326][327][328] and as a reference for mean-field estimates [329][330][331]. FFT-based methods for higherorder homogenization were reported for strain gradient materials [332,333] as well as to calculate the elastic moduli of beams and plates [334].…”

Periodic smoothing splines for FFT-based solvers

“…It should be noted that this smoother, if applied as a post-treatment of the solution fields, will add an extra regularity to the fields which will become C 1 . This may lead to unphysical features of the stress field in cases where it naturally presents singularities such as in the presence of cracks [42,43]. Hereafter we will restrict ourselves to the case m = 1 because higher-order splines may induce (i) too much regularity to the fields and (ii) several inflection points which are not desired because the smooth field can exceed the initial interval of values and leads to unphysical values (such as negative material properties in the case of pre-smoothing).…”