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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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