论文标题

幂律材料的分数粘弹性模型

Fractional viscoelastic models for power-law materials

论文作者

Bonfanti, Alessandra, Kaplan, Jonathan Louis, Charras, Guillaume, Kabla, Alexandre J

论文摘要

软材料通常表现出独特的幂律粘弹性响应,该响应是由于其复杂的内部结构中存在的时间尺度的广泛分布而产生的。准确描述软材料的流变行为的有前途的工具是分数演算。但是,由于分数运营商的异常符号和非平凡的特性,其在科学界的使用仍然受到限制。这篇评论旨在为广泛的受众提供对分数粘弹性模型的清晰可访问的描述,并展示这些模型提供统一的方法来表征幂律材料的能力。使用一致的框架来分析流变学数据将有助于对软和生物材料的经验行为进行分类,并更好地理解其反应。

Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft materials is fractional calculus. However, its use in the scientific community remains limited due to the unusual notation and non-trivial properties of fractional operators. This review aims to provide a clear and accessible description of fractional viscoelastic models for a broad audience, and to demonstrate the ability of these models to deliver a unified approach for the characterisation of power-law materials. The use of a consistent framework for the analysis of rheological data would help classify the empirical behaviours of soft and biological materials, and better understand their response.

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