A5032838031- Composite Material Mechanics
- Advanced Mathematical Modeling in Engineering
- Composite Structure Analysis and Optimization
- Numerical methods in engineering
- Elasticity and Material Modeling
- Advanced Numerical Methods in Computational Mathematics
- Rock Mechanics and Modeling
- Nonlocal and gradient elasticity in micro/nano structures
- Advanced Numerical Analysis Techniques
University of Kaiserslautern
2014-2019
Summary The FFT‐based homogenization method of Moulinec–Suquet has recently emerged as a powerful tool for computing the macroscopic response complex microstructures elastic and inelastic problems. In this work, we generalize to problems discretized by trilinear hexahedral elements on Cartesian grids physically nonlinear elasticity We present an implementation basic scheme that reduces memory requirements factor four conjugate gradient storage necessary nine compared with naive...
Abstract The FFT‐based homogenization method proposed by Moulinec and Suquet [1] in 1994 to solve the Lippmann‐Schwinger equation has recently become more popular due its computational speed accuracy. It is based on regular voxel grids can work segmented CT images directly. Given an interface description sub‐voxel scale we show that using voxels with appropriately chosen stiffness significantly enhances accuracy of computed effective properties decreases voxelation effects solution. (© 2014...
We approximate the quasi-static equation of linear elasticity in translation invariant spaces on torus. This unifies different FFT-based discretisation methods into a common framework and extends them to anisotropic lattices. analyse connection between discrete solution demonstrate numerical benefits. Finite element arise as special case periodised Box spline translates.
Abstract A matrix‐free homogenization method making use of the fast Fourier transform (FFT) to work on structured grids was introduced by Moulinec and Suquet in 1994. Due its simplicity computational advantages, this so‐called Basic Scheme has provided basis for many works past two decades. An extension presented Tran, Monchiet Bonnet allows quasi‐static equations linear elasticity include effects from higher‐order derivatives expanding strain displacement as asymptotic series. To compute...
In this paper, we first introduce the reader to Basic Scheme of Moulinec and Suquet in setting quasi-static linear elasticity, which takes advantage fast Fourier transform on homogenized microstructures accelerate otherwise time-consuming computations. By means an asymptotic expansion, a hierarchy problems is derived, whose solutions are looked at detail. It highlighted how these generalized homogenization depend each other. We extend fit new problem class give some numerical results for two orders.