Computing the effective response of heterogeneous materials with thermomechanically coupled constituents by an implicit fast Fourier transform‐based approach

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.

A review of nonlinear FFT-based computational homogenization methods

“…The effective properties of thermoelastic composites may also be computed by FFT-based methods [112,220]. A full thermomechanical coupling strategy was recently proposed [221].…”

An FE-DMN method for the multiscale analysis of thermomechanical composites

“…To this end, we compare the DMN's predicted effective stress σ , the associated effective dissipation D as well as the change of the absolute temperature θ = θ − θ0 to a high-fidelity full-field solution on the microscopic scale. To compute the reference solution, we use the implicit staggered solution scheme of Wicht et al [23], an inexact Newton-CG [77] solver and the discretization by trigonometric polynomials as introduced by Moulinec-Suquet [17,18]. First, to obtain accurate inelastic results, a suitable resolution and size of the RVE needs to be determined first.…”

“…As an alternative to FE models on the microscale, FFT-based computational micromechanics [17][18][19] may be used to solve the thermomechanical cell problem more efficiently giving rise to the so-called FE-FFT method [20][21][22]. Recently, Wicht et al [23] proposed an efficient, fully implicit FFTbased solution scheme for thermomechanical composites.…”

An FE-DMN method for the multiscale analysis of thermomechanical composites

“…To this end, we compare the DMN's predicted effective stress σ, the associated effective dissipation D as well as the change of the absolute temperature θ = θ − θ0 to a high-fidelity full-field solution on the microscopic scale. To compute the reference solution, we use the implicit staggered solution scheme of Wicht et al [23], an inexact Newton-CG [77] solver and the discretization by trigonometric polynomials as introduced by Moulinec-Suquet [17,18]. First, to obtain accurate inelastic results, a suitable resolution of the RVE needs to be determined.…”

“…As an alternative to FE models on the microscale, FFT-based computational micromechanics [17][18][19] may be used to solve the thermomechanical cell problem more efficiently giving rise to the so-called FE-FFT method [20][21][22]. Recently, Wicht et al [23] proposed an efficient, fully implicit FFT-based solution scheme for thermomechanical composites.…”