A FFT-based method for computing the thermo-hydro-mechanical response of porous composites

Abstract:

Fast Fourier Transform (FFT) methods have been widely used for more than a decade as an alternative to more conventional numerical techniques (FEM, BEM). These methods allow estimating the elastic mechanical response of composite materials, by means of the discretization of the Lippmann-Schwinger equation, and the truncation of the Fourier series values. The basic scheme, a fixed-point algorithm of easy application, is limited when multiphase systems with both pores and infinitely rigid inclusions are used. Using the approach proposed by Sab et al. [1]1, we present the mathematical analysis of three different FFT-based numerical schemes for homogenization of porous composites in the framework of : (i) linear plasticity, evaluating the plastic evolution with von Mises, Drucker-Prager and Cam clay yield criteria, (ii) hydraulic and thermal fields, calculating the permeability tensor, Khom, from the Darcy/Darcy problem and the thermal conductivity tensor, λhom formulated for Fourier to Fourier upscaling, and (iii) thermoporomechanical (THM) coupling, where we use the constitutive relations of the porous solid [2] to calculate all the homogeneous operators of the THM matrix. The accuracy of each scheme is evaluated by comparisons with a finite element solver and analytical solutions for simple microstructures.

References:

[1] Sab, K., Bleyer, J., Brisard, S., & Dolbeau, M. (2024), An FFT-based adaptive polarization method for infinitely contrasted media with guaranteed convergence. Computer Methods in Applied Mechanics and Engineering, 427, 117012
[2] Coussy (2011), Mechanics and physics of porous solids. John Wiley & Sons

Short bio:

Maria earned her Master’s degree in Geotechnical Engineering from the Universidade de Brasília (Brazil, 2023). Since the same year, she has been pursuing a PhD at CERMES, within the Navier Laboratory, under the supervision of Prof. Jean-Michel Pereira and Prof. Patrick Dangla. Her research focuses on investigating thermo-hydro-mechanical couplings in frozen soils using FFT-based homogenization techniques.