Abstract
A multiscale model based on the fast Fourier transform (FFT) is applied to study the nonlinear mechanical behavior of Callovo-Oxfordian (COx) argillite, a typical heterogeneous clayey rocks. COx argillite is modeled as a three-phase composite with a clay matrix and two types of mineral inclusions. The macroscopic mechanical behavior of argillite samples with different mineralogical compositions are satisfactorily predicted by unified local constitutive models and material parameters. Moreover, the numerical implementation of the FFT-based nonlinear homogenization is easier than direct homogenization, such as the FEM-based homogenization, because it automatically satisfies the periodic boundary condition.
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Abbreviations
- \( E_{ij,} \text{ }\varSigma_{ij} \) :
-
Macroscopic strain and stress tensor
- \( \varepsilon_{ij} (\varvec{y}),\sigma_{ij} (\varvec{y}),u_{i} (\varvec{y}) \) :
-
Microscopic strain tensor, stress tensor and displacement vector
- \( \Upomega_{x} ,\Upomega_{y} \) :
-
Macroscopic and microscopic domain
- \( C_{ijkl}^{0} \) :
-
Isotropic reference stiffness tensor
- \( \varvec{\lambda}^{0} \),\( \varvec{\mu}^{0} \) :
-
Lamé parameters of reference stiffness tensor
- \( \Upgamma_{ijkl}^{0} \) :
-
Green’s operator
- \( \upxi \) :
-
Coordinates in Fourier space
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Jiang, T., Xu, W. & Shao, J. Multiscale Study of the Nonlinear Behavior of Heterogeneous Clayey Rocks Based on the FFT Method. Rock Mech Rock Eng 48, 417–426 (2015). https://doi.org/10.1007/s00603-014-0581-1
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DOI: https://doi.org/10.1007/s00603-014-0581-1