Towards Simulations of Pervasive Fracture Across Structural Scales

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2020

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Abstract

Fracture is a fundamental mechanism of material and structural failure and remains one of the most long-standing research topics within computational solid mechanics. Propagating cracks exhibit a rich behavior governed by the delicate interplay between macroscopic elasticity and microscopic failure mechanisms in the neighborhood of the crack tip. This dissertation takes a closer look at enabling the computational modeling of pervasive fracture and material failure across disparate spatial scales. While the search for a generally applicable approach is a continuous effort, variational fracture models have established themselves as the dominant numerical analysis method for the simulation of these processes. The main appeal of variational approaches to fracture mechanics is that they diminish the need for an a priori knowledge of the crack path or ad hoc assumptions in the form of crack path selection laws and completely eliminate the need for interface tracking.

The research presented in this dissertation aims at remedying some of the most vexing issues surrounding the variational modeling of fracture. A variational description of dynamic fracture tailored for cohesive fracture mechanics is postulated. The model applies beyond the well-known Griffith regime where both the maximum stress and the critical strain become infinite as the regularization length scale vanishes. Another distinct issue lies in the identification of a sharp crack surface when a strict "smeared crack" point-of-view is embraced. This issue is revisited through the lens of optimization, where the notion of the auxiliary damage field plays an important role. Additionally, this dissertation discusses the development of a scalable and performant implementation of a scale-bridging extended/generalized finite element method to resolve the disparate physical and geometric length scales and provide some relief to the sheer computational expense of variational fracture problems. Several numerical experiments are conducted to substantiate the proposed theories and methodologies.

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Geelen, Rudy (2020). Towards Simulations of Pervasive Fracture Across Structural Scales. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/20859.

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