Uncertainty quantification for viscoelastic composite materials using time-separated stochastic mechanics基于时间分离随机力学的黏弹性复合材料不确定性量化
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Giesler H, Junker P, 2024. Uncertainty quantification for viscoelastic composite materials using time-separated stochastic mechanics. Probabilistic Engineering Mechanics, 76: 103618.DOI: 10.1016/j.probengmech.2024.103618
摘要 | Abstract
随着复合材料使用的日益增长，对其相关行为的精细模拟技术需求也在增加。一个重要方面是考虑由于均质复合材料中组成材料参数波动所引起的响应不确定性。这种固有的随机性会导致微观尺度上的随机应力和宏观尺度上的不确定性响应。迄今为止，基体材料的黏弹性响应严重阻碍了复合材料行为高效预测方法的应用。本工作采用时间分离随机力学 (time-separated stochastic mechanics, TSM) 方法来解决这一问题。我们展示了如何通过少量确定性有限元模拟来逼近代表体积元的微观尺度应力和均质化宏观尺度应力的不确定性。研究关注的量包括应力期望值、标准差以及在微观和宏观尺度上的概率分布函数。结果显示，时间分离随机力学能够以极少的计算成本很好地逼近参考结果，相比于蒙特卡罗模拟，计算成本大大降低。关键词: 时间分离随机力学, 不确定性材料参数, 复合材料, 计算均质化With the growing use of composite materials, the need for high-fidelity simulation techniques of the related behavior increases. One important aspect to take into account is the uncertainty of the response due to fluctuations of the material parameters of the constituent materials of the homogenized composite. This inherent randomness leads to stochastic stresses on the microscale and uncertain macroscale response. Until now, the viscoelastic response of the matrix material seriously hindered the application of efficient methods to predict the composite material behavior. In this work, a novel method based on the time-separated stochastic mechanics (TSM) is developed to address this problem. We present how the uncertainty of the microscale stresses of a representative volume element and the homogenized macroscale stresses can be approximated with a low number of deterministic finite element simulations. Quantities of interest are the expectation, standard deviation, and the probability distribution function of the stresses on micro- and macroscale. The results showcase that the TSM is able to approximate the reference results very well at a minimal fraction of the computational cost needed for Monte Carlo simulations.Keywords: Time-separated stochastic mechanics; Uncertain material parameters; Composite materials; Computational homogenization![]()
Fig. 1. Exemplary representative volume element of a composite
Fig. 2. Probability density function for some Lamé parameters
Fig. 3. Finite element mesh of the composite
Fig. 4. Evolution of the error measures for the stresses on the microscale over time
Fig. 5. Comparison of the homogenized stresses
图 6: 不同时刻蒙特卡罗方法与时间分离随机力学估计的宏观应力范数概率密度函数Fig. 6. Probability density function of the norm of the macroscopic stresses estimated by the Monte Carlo method (MC) and the TSM at different time instants
图 7: 蒙特卡罗与时间分离随机力学估计的概率分布函数总变差距离误差的演化Fig. 7. Evolution of the d_TV error between the estimated probability distribution functions by MC and TSM
作者信息 | Authors
Hendrik Geisler, 通讯作者 (Corresp.) 德国莱布尼茨汉诺威大学 (Leibniz University Hannover) 连续介质力学研究所Email: geisler@ikm.uni-hannover.de
德国莱布尼茨汉诺威大学 (Leibniz University Hannover) 连续介质力学研究所
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
