主讲人：Carolin Birk, University of Duisburg-Essen（德国杜伊斯堡-埃森大学）
报告主题：Recent developments in brittle fracture modelling using the scaled boundary finite element method
邀请人：章子华 教授
主持人：房小梁 副教授
报告时间：2024年11月27日（周三）上午 10:00—11:00
报告地点：做爱视频 思禹建工楼A408
报告摘要：
Fracture phenomena are ubiquitous in several engineering applications. The numerical modelling of fracture and damage is challenging for various reasons. In brittle fracture processes, stress singularities occur at the crack tip, which must be represented accurately in a simulation. Discrete crack propagation modelling requires re-meshing procedures that can be tedious, particularly in 3D. Smeared approaches such as the phase-field method (PFM) lend themselves to modelling of complex fracture phenomena such as crack branching and merging, since they do neither require crack propagation criteria nor procedures to deal with geometry evolution. On the other hand, the PFM is based on a regularization of crack geometry using a small length scale parameter. Resolution of the latter, however necessitates the use of very fine meshes near the crack and thus leads to very high numerical effort in three-dimensional situations.
The scaled boundary finite element method (SBFEM) can be used to address the above challenges. It facilitates the formulation of generalized polygon elements that provide great flexibility with respect to meshing. In this talk, recent developments in brittle fracture modelling using SBFEM will be summarized. In the context of discrete fracture modelling, polygon meshes are used in order to limit re-meshing to the region in the vicinity of the crack tip. Here, open polygons are employed near the crack tip, such that stress-singularities are represented semi-analytically. The procedure will be explained for the case of thermally-induced fracture including recent developments for dynamic thermoelastic fracture modelling. In the context of smeared crack propagation modelling, hierarchical meshes are used, which facilitate rapid size transition in fracture zones. An adaptive phase-field modelling approach based on SBFEM will be summarized and applied to three-dimensional problems. Here, novel aspects include the use of an iterative solver that exploits the similarity of cells in a balanced octree mesh. In summary, the core procedures for modelling discrete and smeared crack propagation using SBFEM will be demonstrated and illustrated using various examples.