一种用于（非）线性软化建模的微形态本构框架

中文摘要 AI 辅助

土和岩石中的非线性剪切软化通常使用经验模量衰减规律来描述。在本工作中，我们在Eringen-Mindlin微形态框架内研究非线性软化，通过将其附加本构参数解释为耦合、内部松弛和微惯性。微形态连续体被视为一种动态增强的有效介质，其中宏观变形与内部微结构变形场相互作用。这种相互作用自然产生频率相关的有效弹性质，并在宏观波传播与未解析的微结构动力学之间提供物理联系。我们表明，非线性剪切软化可以通过宏观变形与内部变形之间耦合的逐渐减弱来描述。随着这种耦合在剪切应变增加时减弱，有效剪切模量降低。在低频极限下，所得本构关系呈双曲形式，与经典的Hardin-Drnevich定律密切相关。该模型针对砂土剪切模量衰减的实验室测量进行了验证，并以少量物理可解释参数重现了观察到的非线性行为。所提出的框架提供了一种新的非线性软化和频率相关行为的描述，无需显式了解底层微结构几何。经典的经验模量衰减曲线作为宏观与内部变形之间相互作用的宏观结果而出现。

英文摘要

Nonlinear shear softening in soils and rocks is commonly described using empirical modulus-reduction laws. In this work, we investigate nonlinear softening within the Eringen--Mindlin micromorphic framework by interpreting its additional constitutive parameters in terms of coupling, internal relaxation, and micro-inertia. The micromorphic continuum is viewed as a dynamically enriched effective medium in which the macroscopic deformation interacts with an internal microstructural deformation field. This interaction naturally produces frequency-dependent effective elastic properties and provides a physical connection between macroscopic wave propagation and unresolved microstructural dynamics. We show that nonlinear shear softening can be described by a progressive reduction of the coupling between macroscopic and internal deformation. As this coupling weakens with increasing shear strain, the effective shear modulus decreases. In the low-frequency limit, the resulting constitutive relation takes a hyperbolic form closely related to the classical Hardin--Drnevich law. The model is validated against laboratory measurements of shear-modulus reduction in sand and reproduces the observed nonlinear behavior with only a small number of physically interpretable parameters. The proposed framework provides a new description of nonlinear softening and frequency-dependent behavior without requiring explicit knowledge of the underlying microstructural geometry. Classical empirical modulus-reduction curves emerge as a macroscopic consequence of the interaction between macroscopic and internal deformation.

发表机构

• Institut de Physique du Globe de Paris, CNRS, Université de Paris（巴黎地球物理研究所，法国国家科学研究中心，巴黎大学）

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