A novel super symplectic analytical singular element for crack propagation along a bimaterial interface

Abstract

In the last few years, the corresponding author and colleagues proposed a type of symplectic analytical singular elements (SASEs) for various crack problems, such as cracks in plate and shell, bimaterial crack, dynamic crack, crack in viscoelastic media, etc. However, the SASE is still confined to stationary cracks. In this contribution, we propose a new super symplectic analytical singular element (SSASE) for crack propagation along a bimaterial interface. The shape of the SSASE is extended from the normally used circle to general convex polygon, and it can work well on a fixed mesh with triangles or quadrilaterals, thus more proper for modelling crack propagation. The proposed element uses the symplectic eigen solution to define its internal fields, thus most of the advantages of the SASE family are reserved. The proposed element is verified and validated through a few numerical examples. The present contribution has established a new platform for the modelling of the progressive failure process along a bimaterial interface and has also extended the application of the analytical symplectic dual approach to the numerical approach for crack propagations.