A Novel Approach for Modelling Crack Paths in Plate Structures for Dynamic Response Analysis

Cracks significantly affect the structural integrity and functionality of mechanical components. While most existing studies focus on identifying straight cracks using dynamic response (DR) data, the characterisation of crack paths, especially curved ones, remains limited. This gap is critical, as the path of crack propagation plays a vital role in determining the severity of structural damage, particularly in critical regions of plate structures. The large number of possible crack paths has made systematic research in this area difficult. Therefore, this study proposes a novel methodology for modelling both straight and curved crack paths in plate structures to analyse their DR using the Finite element method (FEM). Straight cracks are represented by coordinate pairs, while curved cracks are defined using second-order polynomial equations. A combination-based approach is employed to generate feasible curved paths within a bounded region, allowing variation in crack shapes, lengths, and geometries. The results demonstrate that the proposed methodology effectively reduces the total number of crack path configurations from 7140, an impractically large set for detailed analysis, to a manageable subset of 288. This reduction facilitates more efficient implementation in both numerical simulations and experimental investigations without compromising the representational diversity of crack path geometries. They also show that the crack path has a greater influence on the dynamic response than crack length, offering a more comprehensive framework for crack path identification and evaluation.