Abstract The microstructural configuration of a material affects its macroscopic viscoelastic behavior, which suggests that materials can be engineered to achieve a desired viscoelastic behavior over a range of frequencies. To this end, we leverage topology optimization to find the optimized topology of a multi-phase viscoelastic composite to tailor its energy dissipation behavior as a function of frequency. To characterize the behavior of each material phase, we use a fractional viscoelastic constitutive model. This type of material model uses differential operators of non-integer order, which are appropriate to represent hereditary phenomena with long- and short-term memory. The topology optimization formulation aims to find the lightest microstructure that minimizes the sum of squared loss modulus residuals for a given set of target frequencies. This leads to the design of materials with either maximized loss modulus for a given target frequency or tailored loss modulus for a predefined set of frequencies. We present several numerical examples, both in 2D and 3D, which demonstrate that the microstructural configuration of multi-phase materials affects its macroscopic viscoelastic behavior. Thus, if properly designed, the material behavior can be tailored to dissipate energy for a desired frequency (maximized loss modulus) or for a range of frequencies (tailored energy dissipation behavior).

中文翻译：

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具有定制能量耗散的周期性多材料粘弹性微结构的分数拓扑优化

摘要 材料的微观结构配置影响其宏观粘弹性行为，这表明可以设计材料以在一定频率范围内实现所需的粘弹性行为。为此，我们利用拓扑优化来找到多相粘弹性复合材料的优化拓扑，以定制其作为频率函数的能量耗散行为。为了表征每个材料相的行为，我们使用分数粘弹性本构模型。此类材料模型使用非整数阶微分算子，适用于表示具有长短期记忆的遗传现象。拓扑优化公式旨在找到最轻的微结构，以最小化给定目标频率集的平方损耗模量残差之和。这导致材料的设计为给定的目标频率具有最大化的损耗模量或为预定义的一组频率定制的损耗模量。我们提供了几个 2D 和 3D 数值例子，它们证明了多相材料的微观结构配置影响其宏观粘弹性行为。因此，如果设计得当，可以定制材料行为以耗散所需频率（最大损耗模量）或一系列频率（定制的能量耗散行为）的能量。这表明多相材料的微观结构配置影响其宏观粘弹性行为。因此，如果设计得当，可以定制材料行为以耗散所需频率（最大损耗模量）或一系列频率（定制的能量耗散行为）的能量。这表明多相材料的微观结构配置影响其宏观粘弹性行为。因此，如果设计得当，可以定制材料行为以耗散所需频率（最大损耗模量）或一系列频率（定制的能量耗散行为）的能量。