2020/11/05 by Daniel Wicht, Matti Schneider, Thomas Böhlke · 20 citations
Computer Science · Engineering · Materials Science · Mathematics · #Adiabatic process #Advanced Mathematical Modeling in Engineering #Algorithm #Applied mathematics #Composite Material Mechanics #Composite material #Composite number #Computation #Computer science #Context (archaeology) #Fast Fourier transform #Fourier transform #Homogenization (climate) #Isothermal process #Materials science #Mathematical analysis #Mathematics #Mechanics #Micromechanics #Microscale chemistry #Nonlocal and gradient elasticity in micro/nano structures #Physics #Thermodynamics #Viscoelasticity
paper · doi:10.1002/nme.6579
published in International Journal for Numerical Methods in Engineering 122(5), 1307-1332 (Wiley)
openalex publication_date 2020/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.