Multiple Crack Growth and Coalescence in Meshfree Methods with Adistance Function-Based Enriched Kernel

Abstract

Distance fields are functions defining the minimum distance between any generic point inspace and the boundaries of an object. This paper shows some important properties of these fields andtheir derivatives. In fact, for polygonal lines, the derivatives of distance fields are discontinuous overthe finite length of the segment, but continuous all around the end-points. An immediate consequenceis their application as intrinsic enrichment of weight functions in meshless methods, for the treatmentof multiple arbitrary cracks. By introducing such explicitly known function for the distance fields,discontinuities can be easily incorporated in the kernel in a simple, multiplicative manner. The result-ing method allows a more straightforward implementation and simulation of the presence of multiplecracks in a meshless framework without using any of the existing algorithms such as visibility, trans-parency and diffraction. Furthermore, one of the main advantages of this approach is the automaticcoalescence of multiple interacting cracks, i.e. no particular enrichment functions are necessary at thejunction points.