Physics-based Modeling of Brittle Fracture: Cohesive Formulations and the Application of Meshfree Methods

Abstract

Simulation of generalized fracture and fragmentation remains an ongoing challenge in computational fracture mechanics. There are difficulties associated not only with the formulation of physically-based models of material failure, but also with the numerical methods required to treat geometries that change in time. The issue of fracture criteria is addressed in this work through a cohesive view of material, meaning that a finite material strength and work to fracture are included in the material description. In this study, we present both surface and bulk cohesive formulations for modeling brittle fracture, detailing the derivation of the formulations, fitting relations, and providing a critical assessment of their capabilities in numerical simulations of fracture. Due to their inherent adaptivity and robustness under severe deformation, meshfree methods are especially well-suited to modeling fracture behavior. We describe the application of meshfree methods to both bulk and surface approaches to cohesive modeling. We present numerical examples highlighting the capabilities and shortcomings of the methods in order to identify which approaches are best-suited to modeling different types of fracture phenomena.

Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method

“…Considerable amount of analytical, experimental, and numerical work has been reported in the literature on intersonic crack growth Huang and Gao 2001;Klein et al 2001;Rosakis 2002;Guo et al 2003;Hao et al 2004;Xia et al 2004Xia et al , 2005. The term "intersonic speed" is referred to as the crack-tip velocity between shear and dilatational wave speeds of the material, while the term 'sub-Rayleigh speed' is referred to as the crack-tip velocity less than the Rayleigh wave speed of the material.…”

J resistance behavior in functionally graded materials using cohesive zone and modified boundary layer models

“…They assume that the metal phase (Ti) controls the crack growth, and thus the extinction of cohesive elements is based on the critical displacement of the metal phase δ c met (see Section 3 for more detail). Insertion of intrinsic cohesive elements introduces an artificial compliance to the structure (e.g., Baylor, 1998;Klein et al, 2000;Zhang, 2003). The magnitude of the artificial compliance is primarily related to the initial slope of the traction-displacement curve.…”

A bifurcation-based decohesion model for simulating the transition from localization to decohesion with the MPM

“…Several kinds of decohesion models have been proposed in the open literature, as discussed by the representative papers [16,20,26]. To achieve computational efficiency, however, the location and orientation of decohesion are either mesh-dependent or based on the maximum tensile stress (strain) without performing a discontinuous bifurcation analysis.…”

“…As indicated by Belytschko et al [3], and recently demonstrated by Klein et al [16] for model-based simulation with cohesive formulations, the meshless (meshfree) methods are uniquely suitable for those problems, for which the conventional meshbased methods are handicapped, such as localized large deformations, propagation of cracks and separation of continuum. In fact, the key difference among different spatial discretization methods is the way how the gradient and divergence terms are calculated.…”