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.

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

“…We refer among others to Dally (1979), Ravi-Chandar and Knauss (1984a,b), Knauss and Ravi-Chandar (1985), Ramulu and Kobayashi (1985), Fineberg et al (1991), Satoh (1996), Fineberg (1996, 1999), Fineberg and Marder (1999), and references therein, for a discussion of some experimental observations. Numerical simulations of the problem have been reported in Falk et al (2001), Klein et al (2001), Belytschko et al (2003), Zhou and Molinari (2004), Zhou et al (2005), Huespe et al (2006), Song et al (2006), Duarte et al (2007), Karedla and Reddy (2007), Remmers et al (2008), Zhang et al (2007), Zi et al (2007), to mention just a few references employing a variety of different numerical approaches.…”

Materials become insensitive to flaws at nanoscale: Lessons from nature

“…To model failure mechanisms in nanomaterials, we have developed a virtual internal bond (VIB) (22,23) method, which incorporates an atomic cohesive force law into the constitutive model of materials. Fig.…”

Concrete Fracture Prediction Using Virtual Internal Bond Model with Modified Morse Functional Potential

“…The essential fracture characteristic of the VIB model is that the fracture energy depends on the element size [13], which can be explained by the path independent Jintegral [14]. Because of the path independence, a contour is selected along the upper and lower bound of a localization zone QIL) where stress softening occurs for a mode I fracture [13].…”

“…Because of the path independence, a contour is selected along the upper and lower bound of a localization zone QIL) where stress softening occurs for a mode I fracture [13]. The selected contour results in the symmetric stress and displacement field, and then we obtain J for mode 1, J = h, [p,,dX,=G, (10) where P22 is the 1st Piola-Kirchhoff stress along the X2 direction.…”