Physics

Path integral formulation

Nonlinear system

Integral transform

Pure mathematics

Mathematics

Domain (mathematical analysis)

Multiple integral

Structural engineering

J integral

Engineering

Mathematical analysis

Integral equation

Strain energy release rate

Quantum mechanics

Applied mathematics

Field (mathematics)

Stress intensity factor

Fracture mechanics

Quantum

Integral domain

Engineering Fracture Mechanics

A critical overview of past research on the interaction integral (I-integral) method is presented. The I-integral is the two-state mutual energy release rate decided by a designable auxiliary field and the actual field. Due to the designability of the auxiliary field, the I-integral has been used extensively in extracting the individual stress intensity factors (SIFs) and the T-stress of a crack in single materials or at a bi-material interface. The practical implementation of the I-integral mainly experienced three periods. 1) In the last quarter of the twentieth century, the path-independent I-integral was developed for homogeneous materials subjected to static, dynamic and/or thermal loading. 2) In the 2000 s, the domain-form I-integrals were discussed to deal with inhomogeneous materials. 3) In the past decade, the domain-independent I-integral (DII-integral) was proposed for multi-interface materials. After that, we review the I-integrals for functional materials and the extensions of the I-integral to some new fracture problems. Subsequently, diverse practical applications are introduced. Various research works demonstrate that the I-integral is a most accurate and reliable approach to extracting the individual SIFs and T-stress for the materials obeying linear constitutive law or the materials with limited nonlinear effect. Finally, the advantages, limitations, and future issues of the I-integral method are discussed.

Interaction integral method for computation of crack parameters K–T – A review