Computing the effective response of heterogeneous materials with thermomechanically coupled constituents by an implicit fast Fourier transform‐based approach. (23rd November 2020)

• Record Type: Journal Article
• Authors: Wicht, Daniel; Schneider, Matti; Böhlke, Thomas
• Is Part Of: International journal for numerical methods in engineering. Volume 122:Number 5(2021)
• Page Start: 1307
• Page End: 1332
• Publication Date: 2020-11-23
• Subjects: composites -- FFT‐based micromechanics -- homogenization -- thermomechanical coupling -- viscoelasticity; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6579
• Languages: English
• ISSNs: 0029-5981

Abstract

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.