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Computing the effective response of heterogeneous materials with thermomechanically coupled constituents by an implicit fast Fourier transform‐based approach
Author(s) -
Wicht Daniel,
Schneider Matti,
Böhlke Thomas
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6579
Subject(s) - micromechanics , microscale chemistry , homogenization (climate) , fast fourier transform , materials science , fourier transform , isothermal process , computation , viscoelasticity , adiabatic process , context (archaeology) , computer science , algorithm , mechanics , mathematics , composite material , mathematical analysis , physics , thermodynamics , composite number , biodiversity , ecology , paleontology , mathematics education , biology
Abstract Thermomechanical couplings are present in many materials and should therefore be considered in multiscale approaches. Specific cases of thermomechanical behavior are the isothermal and the adiabatic regime, in which the behavior of real materials differs. Based on the consistent asymptotic homogenization framework for thermomechanically coupled generalized standard materials, the present work is devoted to computing the effective thermomechanical behavior of composite materials in the context of fast Fourier transform (FFT)‐based micromechanics. Exploiting the homogeneity of the temperature on the microscale, we develop a fast implicit staggered solution scheme for the coupled problem, which is compatible to existing strain‐based micromechanics solvers. Due to its implicit formulation, the algorithm permits large time steps for computations involving strong thermomechanical coupling. We investigate the performance of modern FFT‐based algorithms combined with the proposed thermomechanical solution strategy. In this context, the Barzilai–Borwein method is identified as particularly efficient, inducing only a small overhead compared with the traditional isothermal setting. We demonstrate the effectiveness of the presented approach for short‐fiber reinforced composites with viscoelastic matrix behavior.