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Introduction
Scalability of the DG Method
References

Advances in Cohesive Zone Modeling of Dynamic Fracture

Profile image of Raul RadovitzkyRaul Radovitzky
https://doi.org/10.1007/978-1-4419-0446-1
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57 pages

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Abstract

In this chapter, we review the state of the-art in computational methods for modeling dynamic fracture of brittle solids based on the popular cohesive element approach. The discussion includes a detailed review of the underlying theory, its implementation via interface elements in its two different flavors: the intrinsic and extrinsic approach, as well as the application of the method to different concrete problems in dynamic fracture. Limitations and numerical issues are discussed in detail. As a means to address some of these issues, we describe an alternative approach based on a discontinuous Galerkin (DG) reformulation of the continuum problem that exploits the virtues of the existing cohesive element methods. The scalability and accuracy of the DG method for fracture mechanics is demonstrated through wave propagation and spall tests in ceramics. Lastly, some unresolved open problems and numerical issues pertaining to cohesive zone modeling of fracture are briefly discussed.

Key takeaways
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  1. Cohesive Zone Modeling (CZM) effectively represents dynamic fracture processes through phenomenological traction-separation laws.
  2. The Discontinuous Galerkin (DG) method improves scalability and accuracy for fracture simulations compared to traditional cohesive methods.
  3. Numerical issues like mesh dependency and artificial compliance significantly impact the accuracy of fracture modeling.
  4. The chapter reviews state-of-the-art computational methods, assessing their theoretical foundations, applications, and limitations.
  5. CZM's limitations include constraints on crack propagation paths, necessitating innovative solutions like adaptive meshing and advanced formulations.

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International Journal for …, 2007

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Raul Radovitzky

Computer Methods in Applied Mechanics and Engineering, 2011

A scalable algorithm for modeling dynamic fracture and fragmentation of solids in three dimensions is presented. The method is based on a combination of a discontinuous Galerkin (DG) formulation of the continuum problem and Cohesive Zone Models (CZM) of fracture. Prior to fracture, the flux and stabilization terms arising from the DG formulation at interelement boundaries are enforced via interface elements, much like in the conventional intrinsic cohesive element approach, albeit in a way that guarantees consistency and stability. Upon the onset of fracture, the traction-separation law (TSL) governing the fracture process becomes operative without the need to insert a new cohesive element. Upon crack closure, the reinstatement of the DG terms guarantee the proper description of compressive waves across closed crack surfaces. The main advantage of the method is that it avoids the need to propagate topological changes in the mesh as cracks and fragments develop, which enables the

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The use of cohesive theories of fracture in 3D numerical simulations
Anna Pandolfi

The finite element simulation of high-velocity dynamical processes involving fracture and fragmentation is one of the most demanding problems in computational mechanics. Difficulties arise especially when the nature of the problem requires a full three dimensional model. To simulate fracture, cohesive laws have been widely used in combination with finite elements, either as boundary conditions, or by enriching the set of shape functions of solid elements to include a displacement jump. An alternative successful approach introduces cohesive surfaces along boundary surfaces of continuum elements, through an automatic procedure combined with an explicit dynamic code. The presence of a characteristic time scale confers to cohesive models combined with dynamics an intrinsic rate-dependence without the need of modeling explicitly viscosity behaviors. Applications to experimental tests on brittle materials (dynamic Brazilian tests on cylinders in ceramics), aluminum (dynamic expansion of rings), graphite-epoxy composite (mixed mode dynamic loading), and the simulation of quasistatic fracture in biological fiber reinforced tissues (breaking of plaque on atherosclerotic artery) demonstrate the versatility of the method, and attest its ability to reproduce the most significant features of fracture processes.

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Formulation and Implementation of Cohesive Fracture Models in the Symmetric Galerkin Boundary Element Method. Study of Mode I Crack Growth
Alberto Salvadori

Se desarrolla e implementa, en un código computacional, una formulación simétrica de ecuaciones integrales de contorno para la solución de problemas con presencia de grietas, cuya propagación está controlada por un modelo cohesivo de fractura. Se considera un material homogéneo isótropo y elástico-lineal. El código desarrollado se aplica al ensayo wedge split, comparando los resultados numéricos obtenidos con los datos experimentales disponibles en la bibliografía. Es importante mencionar que el uso del método de los elementos de contorno es bastante atractivo para esta clase de problemas debido a que todas las no linealidades se encuentran localizadas en el contorno de un dominio elástico-lineal.

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Recent Advances in Cohesive Zone Modelling of Fracture
Madridge Journals

International Journal of Aeronautics and Aerospace Engineering, 2019

Cohesive zone modelling is commonly used in treating complicated damage, failure and fracture phenomena in different materials and mechanical components; however, a number of the disadvantages, difficulties or even inherent problems exist. This paper reviews some recent critical progress in cohesive zone models (CZMs) at different scales. Four new potential-based and non-potential-based CZMs proposed by McGarry et al. cleared the inherent problems with the well-known Xu-Needleman CZM. A multiscale CZM by Zeng and Li introduced a local quasi-continuum medium that obeys the Cauchy–Born rule to model the bulk material and then a coarse grained depletion potential to formulate the cohesive force and displacement relations inside the cohesive zone, based on an idea in colloidal physics. First-principle calculation of mixed-mode responses of a metal-ceramic interface by Guo et al. showed a promising way to construct an accurate interface cohesive law. A nonlocal cohesive zone model for finite thickness interfaces developed by Paggi and Wriggers are able to accounts for the complex failure phenomena affecting the material microstructure of the interface region, through a continuum damage mechanics concept. These studies provide novel constitutive laws of CZMs and open up new possibilities in improving the cohesive modeling of fracture and failure.

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Dynamic Cavitation Inception by Wave Propagation Across Solid–Fluid Interface With Varying Solid Surface Wettability
Tomohisa Kojima

Journal of Pressure Vessel Technology

Fluid–structure interaction (FSI) problems are important because they may induce serious damage to structures. In some FSI problems, the interaction mechanism is strongly dependent on the wave propagation across the solid–fluid interface. In this study, we attempted a quantitative evaluation of the effect of the solid surface wettability on the wave propagation across the solid–fluid interface with FSI in the case of longitudinal wave propagation vertically toward the interface. During the experiments, while the water was continuously compressed by the solid buffer motion, cavitation bubbles appeared being originated from the buffer–water interface as a result of the transmitted tensile wave propagating across the interface in a cycle. It was confirmed that interfacial boundary condition as wettability could change the wave transmission behavior owing to changes in the cavitation occurrence. It was also confirmed that the worse the wettability, the more severe the cavitation intensi...

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