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Computing the effective response of heterogeneous materials with thermomechanically coupled constituents by an implicit fast Fourier transform‐based approach
International Journal for Numerical Methods in Engineering ( IF 2.9 ) Pub Date : 2020-11-04 , DOI: 10.1002/nme.6579
Daniel Wicht 1 , Matti Schneider 1 , Thomas Böhlke 1
Affiliation  

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.

中文翻译:

通过基于隐式快速傅立叶变换的方法计算具有热机械耦合成分的异质材料的有效响应

热机械耦合存在于许多材料中,因此应在多尺度方法中加以考虑。热力学行为的特定情况是等温和绝热状态,其中实际材料的行为有所不同。基于热机械耦合的通用标准材料的一致渐近均匀化框架,本工作致力于在基于快速傅里叶变换(FFT)的微力学环境下计算复合材料的有效热机械行为。在微观尺度上利用温度的均匀性,我们为耦合问题开发了一种快速的隐式交错求解方案,该方案与现有的基于应变的微力学求解器兼容。由于其隐式表述,该算法允许大量的时间步长进行涉及强热机械耦合的计算。我们将结合提出的热机械解决方案策略研究基于FFT的现代算法的性能。在这种情况下,Barzilai–Borwein方法被认为是特别有效的方法,与传统的等温设置相比仅产生很小的开销。我们证明了所提出的方法对于具有粘弹性基体行为的短纤维增强复合材料的有效性。
更新日期:2020-11-25
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