A finite element perspective on nonlinear FFT-based micromechanical simulations

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

A finite element perspective on nonlinear FFT-based micromechanical simulations

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

A finite element perspective on nonlinear FFT-based micromechanical simulations

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20505 - Composites (including laminates, reinforced plastics, cermets, combined natural and synthetic fibre fabrics; filled composites)

Projekt

<a href="/cs/project/GA13-22230S" target="_blank" >GA13-22230S: Hybridní víceúrovňové nástroje modelování heterogenních pevných látek</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal for Numerical Methods in Engineering

ISSN

0029-5981

e-ISSN

1097-0207

Svazek periodika

111

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

24

Strana od-do

903-926

Kód UT WoS článku

000407854500001

EID výsledku v databázi Scopus

2-s2.0-85014905783