A fast Fourier transform-based solver for elastic micropolar composites

Journal Article · 11 October 2023 · Computer Methods in Applied Mechanics and Engineering

DOI: https://doi.org/10.1016/j.cma.2023.116510 · OSTI ID:2311329

Francis, Noah M.  ^[1]; Pourahmadian, Fatemeh  ^[1]; Lebensohn, Ricardo A. ^[2]; Dingreville, Rémi  ^[3]

---

1. Univ. of Colorado, Boulder, CO (United States)
2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
3. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

• Research Organization: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF); National Science Foundation (NSF)
• Grant/Contract Number: NA0003525; 2201538
• OSTI ID: 2311329
• Report Number(s): SAND-2023-10837J
• Journal Information: Computer Methods in Applied Mechanics and Engineering, Vol. 418; ISSN 0045-7825
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English