This paper aims at presenting a thermodynamically consistent elastoplastic fractional time-dependent damage model for describing short- and long-term behaviors of rock-like materials. The model utilizes generalized potential theory with a yield criterion, a non-associated flow rule and an isotropic plastic hardening function for describing the evolution of plasticity. A time-dependent Lemaitre-type damage is introduced through fractional derivative considering the short- and long-term evolution of microstructure, which leads to progressive degradation of elastic modulus and failure strength of material. In this context, both instantaneous and delayed deformations shall be well described within the unique constitutive model. For practical application, an efficient and convergent semi-implicit return mapping (SRM) algorithm involving a plasticity-damage decoupling corrector is developed. The proposed model is finally adopted to predict the mechanical and deformation behavior of several types of rocks under different loading conditions in conventional or quasi-static (different loading strain rate) triaxial compression tests, creep tests and relaxation tests. Comparisons between model predictions and experimental data demonstrate that the proposed model has the capability to reproduce main features of short and long-term behaviors of rock-like materials.

中文翻译：

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类岩石材料的热力学一致弹塑性分数时间相关损伤模型

本文旨在提出一种热力学一致的弹塑性分数时间相关损伤模型，用于描述类岩石材料的短期和长期行为。该模型利用具有屈服准则、非关联流动规则和各向同性塑性硬化函数的广义势理论来描述塑性的演变。考虑微观结构的短期和长期演变，通过分数导数引入时间相关的Lemaitre型损伤，导致材料的弹性模量和破坏强度逐渐退化。在这种情况下，瞬时变形和延迟变形都应在独特的本构模型中得到很好的描述。对于实际应用，开发了一种高效且收敛的半隐式返回映射 (SRM) 算法，该算法涉及可塑性损伤解耦校正器。所提出的模型最终被用于预测几种岩石在常规或准静态（不同加载应变率）三轴压缩试验、蠕变试验和松弛试验中在不同加载条件下的力学和变形行为。模型预测与实验数据的比较表明，所提出的模型能够再现类岩材料短期和长期行为的主要特征。所提出的模型最终被用于预测几种岩石在常规或准静态（不同加载应变率）三轴压缩试验、蠕变试验和松弛试验中在不同加载条件下的力学和变形行为。模型预测与实验数据的比较表明，所提出的模型能够再现类岩材料短期和长期行为的主要特征。所提出的模型最终被用于预测几种岩石在常规或准静态（不同加载应变率）三轴压缩试验、蠕变试验和松弛试验中在不同加载条件下的力学和变形行为。模型预测与实验数据的比较表明，所提出的模型能够再现类岩材料短期和长期行为的主要特征。