Analysis of crack parameters under mixed mode loading by modified exponential matrix method. (August 2019)

• Record Type: Journal Article
• Authors: Nianga, J.M.; Mejni, F.; Kanit, T.; Imad, A.; Li, J.
• Is Part Of: Theoretical and applied fracture mechanics. Volume 102(2019)
• Page Start: 30
• Page End: 45
• Publication Date: 2019-08
• Subjects: Exponential matrix method MEM -- Stress intensity factor SIF -- T-stress -- Mixed mode -- Symplectic method; Fracture mechanics -- Periodicals; 620.1126
• DOI: 10.1016/j.tafmec.2019.04.007
• Languages: English
• ISSNs: 0167-8442

Abstract

Highlights: Introduction of a new analytical method to evaluate mixed mode SIFs and T-stress. Hamiltonian approach to the problem of a cracked linear elastic material. Systematic and particularly easy determination of eigensystems. Implementation of the solution in the form of a linear combination of eigenvectors. Comparison of the obtained results with those of literature. Abstract: This paper deals with a new analytical method, the exponential matrix method EMM, for calculating the T-stress and the stress intensity factors SIFs under mixed mode loading. The linear, elastic, two-dimensional and stationary equations of the crack problem are transformed into a Hamiltonian system. This is solved by the proposed method involving eigensolutions which satisfy the adjoint symplectic orthogonality by means of performing an angular stress variation with respect to the radial stress. A good description of the expected solution of the studied problem is then obtained as a linear combination of these eigensolutions. To illustrate the validity of the present method, some numerical examples are used and the results obtained are compared with those of literature.