Several phenomenological models have been proposed in the last decades to understand and describe the phenomenology of elastic hysteresis observed in dynamic experiments, i.e. the combination of nonlinear phenomena, usually referred to as “fast” and “slow” dynamics, including harmonic generation, resonance frequency shift, time variation of elastic properties when large conditioning strain is applied. These models correctly reproduce various experimental observations for repeated loading–unloading cycles in quasi-static conditions, but they lack a convincing interpretation in terms of possible physical mechanisms. The aim of this work is to provide a model for the description of the dynamic behavior of a material with an internal microcrack, which attempts to link measurable macroscopic observables to physical crack features at the microscale (e.g. crack concentration, roughness, adhesion, elasticity and plasticity). The existence of adhesive/continuous phases, of crack activation thresholds, of harmonic generation and of the presence of metastable equilibrium states are emerging features of the model and are proposed herein as a possible source of slow dynamics effects. The proposed model can serve as a basis for the extension to a more macroscopic view, i.e. a material containing a network of microcracks.

在过去的几十年中，已经提出了几种现象学模型来理解和描述在动态实验中观察到的弹性滞后现象，即非线性现象的组合，通常被称为“快速”和“慢速”动力学，包括谐波产生，共振频率位移，当施加较大的调节应变时弹性性能的时间变化。这些模型正确地再现了在准静态条件下反复进行装卸循环的各种实验观察结果，但是它们在可能的物理机制方面缺乏令人信服的解释。这项工作的目的是提供一个模型，用于描述具有内部微裂纹的材料的动态行为，该模型试图将可测量的宏观可观测值与微观尺度上的物理裂纹特征联系起来（例如 裂纹浓度，粗糙度，附着力，弹性和塑性）。胶粘剂/连续相的存在，裂纹活化阈值，谐波的产生以及亚稳态平衡状态的存在是该模型的新兴特征，并在本文中被提出作为缓慢动力学效应的可能来源。所提出的模型可以作为扩展到更宏观的视图的基础，即包含微裂纹网络的材料。