Metal-coordination mediated physical hydrogels exhibit high strength/toughness and intriguing mechanical behaviors with the pronounced rate-dependent viscoelasticity and loading-path dependent strain softening. Also, the stress of the reloaded gels increases with more waiting time, indicating a self-healing effect. This paper aims to develop a constitutive model to capture these complex mechanical behaviors of the metal-coordination mediated physical hydrogels. The theoretical framework incorporates two main physical mechanisms: the microscopic kinetic dissociation/association of cross-links and inelastic conformational changes of gel networks. The model predictions agree well with the experimental data of gel responses under different scenarios, which simultaneously capture the time-dependent stress response, relaxation, hysteresis, self-healing behavior, as well as ultimate failure. The present work can provide theoretical guidance and methodological support for the design and practical applications of tough hydrogels mediated by metal-coordinated bonds as load-bearing materials.

金属配位介导的物理水凝胶表现出高强度/韧性，并具有引人注目的速率依赖性粘弹性和加载路径依赖性应变软化的有趣机械性能。同样，重新加载的凝胶的应力随着等待时间的增加而增加，表明具有自我修复作用。本文旨在建立一个本构模型来捕获金属配位介导的物理水凝胶的这些复杂的机械行为。理论框架包括两个主要的物理机制：交联的微观动力学解离/缔合和凝胶网络的非弹性构象变化。模型预测与不同情况下凝胶反应的实验数据非常吻合，这些数据同时捕获了随时间变化的应力反应，松弛，滞后，自我修复行为以及最终失败。本研究可为以金属配位键为载体的硬水凝胶的设计和实际应用提供理论指导和方法论支持。