Thermoelastic properties of microcracked polycrystals. Part I : Adequacy of Fourier-based methods for cracked elastic bodies

Jean-Baptiste Gasnier (1) , François Willot (1, 2) , Hervé Trumel (3) , Dominique Jeulin (1, 2) , Jacques Besson (2)

1 CMM - Centre de Morphologie Mathématique
2 CDM - Centre des Matériaux
3 CEA Le Ripault - CEA Le Ripault

This study is part of a work dedicated to predicting the overall thermoelastic properties of microcracked polycrystals. In the present part, the suitability of Fourier-based methods to estimate the mechanical response of a homogeneous body containing cracks is explored. The effect of the Green operator's discretization on the local elastic fields surrounding the crack's tip is investigated and compared with exact and finite elements solutions. The biases inherent to the Fourier method, namely the effects of grid discretization and crack orientation relative to the grid, are scrutinized. A way to quantify and overcome these biases is given, therefore providing a low resource demanding method to deal with thousands of microcracks embedded in a polycrystal, object of the companion paper.

Mots clés: Cracked media; Homogenization; Elasticity; Fourier-based Methods

Domaines: Matériaux

Jean-Baptiste Gasnier, François Willot, Hervé Trumel, Dominique Jeulin, Jacques Besson. Thermoelastic properties of microcracked polycrystals. Part I : Adequacy of Fourier-based methods for cracked elastic bodies. International Journal of Solids and Structures, 2018, 155, pp.248-256. ⟨10.1016/j.ijsolstr.2018.07.024⟩. ⟨hal-01932739v1⟩