This work introduces a theoretical framework for continuum damage and healing mechanics by extending stress decomposition to account for tensile, compressive, and shear stresses. In addition to the spectral stress decomposition into tensile and compressive components, we extend the existing stress decomposition method to address shear stresses. The extraction of shear stresses employs two hypotheses, considering both same-signed and opposite-signed principal stresses. This stress decomposition approach yields three damage variables [Formula: see text] and three healing variables [Formula: see text]. The damage formulation is discussed in terms of equivalent strain and conjugate force, while the healing formulation is based on the initial damage state and healing time. We explore the influence of material parameters and healing time on damage and healing evolution. Furthermore, we analyze the relationship between nominal stress-to-effective stress ratio, damage variables, and healing time. Lastly, we present a thermodynamically consistent formulation for damage-healing processes, acknowledging that this work establishes a theoretical formulation. The proposed method is validated by analyzing the performance of an L-shaped concrete specimen using three damage variables and one healing variable. These results illustrate the model's ability to effectively capture the damage and healing phenomena. The practical implementation of the proposed formulation will be pursued numerically using innovative healing techniques and a pseudo-damage healing approach, which will be detailed in future work.

中文翻译：

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准脆性材料中的多应力损伤和愈合机制：理论概述

这项工作通过扩展应力分解来解释拉伸、压缩和剪切应力，介绍了连续损伤和愈合力学的理论框架。除了将谱应力分解为拉伸和压缩分量之外，我们还扩展了现有的应力分解方法来解决剪切应力。剪切应力的提取采用两种假设，同时考虑同号和异号主应力。这种应力分解方法产生三个损伤变量[公式：参见文本]和三个愈合变量[公式：参见文本]。损伤公式根据等效应变和共轭力进行讨论，而愈合公式则基于初始损伤状态和愈合时间。我们探索材料参数和愈合时间对损伤和愈合演变的影响。此外，我们分析了名义应力与有效应力比、损伤变量和愈合时间之间的关系。最后，我们提出了损伤修复过程的热力学一致公式，承认这项工作建立了一个理论公式。通过使用三个损伤变量和一个愈合变量分析 L 形混凝土试件的性能，对所提出的方法进行了验证。这些结果说明了该模型有效捕捉损伤和修复现象的能力。将使用创新的治疗技术和伪损伤治疗方法在数字上追求所提出的公式的实际实施，这将在未来的工作中详细说明。