The M-integral in fracture and damage mechanics: A review of developments and applications

This paper reviews the historical investigation and state-of-the-art developments of the M-integral and corresponding applications, from five key perspectives. Firstly, the origin of the M-integral and the cognitive process of its physical meanings have been recalled. Secondly, within the framework of fracture mechanics, attention is paid to the application of the M-integral in solving specific fracture problems, including the calculation of stress intensity factor, Zener's crack analysis and the fracture of piezoelectric materials. Thirdly, the use of the M-integral in describing damage evolution, damage or failure criteria and defect interactions of complex damage processes is summarized. Fourthly, the so-called two-state M-integral is discussed, with a focus on case studies including the fracture and damage induced by a composite wedge, nano-inclusions, etc. Last but not least, the experimental methods for measuring the M-integral are reviewed from different perspectives (e.g., contact and non-contact types). In conclusion, this article provides a comprehensive review of the developments and applications of the M-integral, and is particularly effective for failure analysis of multi-defected structures or advanced material systems.

Automated summary

This paper reviews the historical investigation and state-of-the-art developments of the M-integral and its corresponding applications. It provides a comprehensive analysis of the origin, physical meanings, application in fracture mechanics, damage evolution, two-state M-integral, and experimental methods for measuring the M-integral. The article is particularly effective for failure analysis of multi-defected structures or advanced material systems.