Affiliation:
1. Institute of Engineering Mathematics University of Duisburg‐Essen Essen Germany
2. Fraunhofer Institute for Industrial Mathematics ITWM Kaiserslautern Germany
Abstract
AbstractImposing nonperiodic boundary conditions for unit cell analyses may be necessary for a number of reasons in applications, for example, for validation purposes and specific computational setups. The work at hand discusses a strategy for utilizing the powerful technology behind fast Fourier transform (FFT)‐based computational micromechanics—initially developed with periodic boundary conditions in mind—for essential boundary conditions in mechanics, as well, for the case of the discretization on a rotated staggered grid. Introduced by F. Willot into the community, the rotated staggered grid is presumably the most popular discretization, and was shown to be equivalent to underintegrated trilinear hexahedral elements. We leverage insights from previous work on the Moulinec–Suquet discretization, exploiting a finite‐strain preconditioner for small‐strain problems and utilize specific discrete sine and cosine transforms. We demonstrate the computational performance of the novel scheme by dedicated numerical experiments and compare displacement‐based methods to implementations on the deformation gradient.
Funder
Deutsche Forschungsgemeinschaft
Reference103 articles.
1. A fast numerical method for computing the linear and nonlinear mechanical properties of composites;Moulinec H;Comptes Rend Acad Sci Sér II,1994
2. A numerical method for computing the overall response of nonlinear composites with complex microstructure;Moulinec H;Comput Methods Appl Mech Eng,1998
3. Elastic constants of polycrystals;Zeller R;Phys Status Solidi,1973
4. Bounds for effective elastic moduli of disordered materials;Kröner E;J Mech Phys Solid,1977
5. Micromechanics of defects in solids
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献