Multi-stress damage and healing mechanics in quasi-brittle materials: Theoretical overview

Abstract

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 $\left({\phi }^{\pm S}\right)$ and three healing variables $\left(h^{\pm S}\right)$ . 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.