Abstract
A modified FFT-based solver for the mechanical simulation of heterogeneous materials with Dirichlet boundary conditions
Highlights
Fast Fourier transform (FFT) based solvers for mechanics, initially proposed in [1], have attracted increasing interest in the context of simulation of heterogeneous materials
In the context of numerical homogenization of heterogeneous materials, the use of kinematic uniform boundary conditions (BC) (KUBC) provides an upper bound for the effective elastic behavior [4,5,6]
Taking advantage of efficient FFT-based solvers for solid mechanics to apply Dirichlet BC was addressed in [9]. This was implemented through the use of the so-called explicit jump immersed interface method (EJIIM) based on the application of standard central finite differences, with the simulated domain being embedded in a larger domain subjected to null displacement, and the introduction of “jumps” as additional unknowns
Summary
Fast Fourier transform (FFT) based solvers for mechanics, initially proposed in [1], have attracted increasing interest in the context of simulation of heterogeneous materials. Taking advantage of efficient FFT-based solvers for solid mechanics to apply Dirichlet BC was addressed in [9] This was implemented through the use of the so-called explicit jump immersed interface method (EJIIM) based on the application of standard central finite differences, with the simulated domain being embedded in a larger domain subjected to null displacement, and the introduction of “jumps” as additional unknowns. The discretization of equations corresponds to linear (hexahedral) FEs with reduced integration, the embedding part has elastic behavior (with eigenstrain), and the so-called eigendisplacement field is defined at the voxel corners located on the boundary This eigendisplacement field is unknown and adjusted to fulfill the condition on the displacement prescribed on the boundary (i.e., Dirichlet BC). The displacement u is defined at the corners together with the stress divergence div(σ)
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