A finite element perspective on nonlinear FFT-based micromechanical simulations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F17%3A00312836" target="_blank" >RIV/68407700:21110/17:00312836 - isvavai.cz</a>
Result on the web
<a href="http://arxiv.org/abs/1601.05970" target="_blank" >http://arxiv.org/abs/1601.05970</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/nme.5481" target="_blank" >10.1002/nme.5481</a>
Alternative languages
Result language
angličtina
Original language name
A finite element perspective on nonlinear FFT-based micromechanical simulations
Original language description
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the finite element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency results from handling the kernel of this equation by the fast Fourier transform (FFT). However, the kernel is derived from an auxiliary homogeneous linear problem, which renders the extension of FFT-based schemes to nonlinear problems conceptually difficult. This paper aims to establish a link between FE-based and FFT-based methods in order to develop a solver applicable to general history-dependent and time-dependent material models. For this purpose, we follow the standard steps of the FE method, starting from the weak form, proceeding to the Galerkin discretization and the numerical quadrature, up to the solution of nonlinear equilibrium equations by an iterative Newton-Krylov solver. No auxiliary linear problem is thus needed. By analyzing a two-phase laminate with nonlinear elastic, elastoplastic, and viscoplastic phases and by elastoplastic simulations of a dual-phase steel microstructure, we demonstrate that the solver exhibits robust convergence. These results are achieved by re-using the nonlinear FE technology, with the potential of further extensions beyond small-strain inelasticity considered in this paper.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
20505 - Composites (including laminates, reinforced plastics, cermets, combined natural and synthetic fibre fabrics; filled composites)
Result continuities
Project
<a href="/en/project/GA13-22230S" target="_blank" >GA13-22230S: A hybrid multiscale predictive modelling tool for heterogeneous solids</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal for Numerical Methods in Engineering
ISSN
0029-5981
e-ISSN
1097-0207
Volume of the periodical
111
Issue of the periodical within the volume
10
Country of publishing house
US - UNITED STATES
Number of pages
24
Pages from-to
903-926
UT code for WoS article
000407854500001
EID of the result in the Scopus database
2-s2.0-85014905783