Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2014 / Article
Special Issue

Computational Methods for Fracture

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Editorial | Open Access

Volume 2014 |Article ID 593041 | 2 pages | https://doi.org/10.1155/2014/593041

Computational Methods for Fracture

Received15 May 2014
Accepted15 May 2014
Published20 Jul 2014

The numerical study of fracture has far-reaching applications throughout engineering and science. Its importance is becoming even more significant that engineers and materials scientists are thriving to devise new lighter and stronger materials from the bottom up.

Simulating fracture requires devising suitable models, discretizing the resulting partial differential equations, and solving them numerically. Each of those three steps poses its own difficulties which have been tackled in various ways, both academically and for practical applications.

This special issue deals with a range of such models: discretization and solution methods applied to a number of problems ranging from rock mechanics to surgical simulation requiring tackling various loading spectra, ranging from fast dynamics to quasistatic loading, and leading to a number of different failure modes, from brittle to ductile fracture.

The topics of this issue can be decomposed into five groups:

Models have been developed with special emphasis on rock mechanics and multi-field problems in fracture [1, 2] with applications, for example to coupled thermohydromechanical model of jointed hard rock for compressed air energy storage, and to rock failure [3].

Discretization methods have been heavily investigated, to address the difficulties faced by the standard finite element method [4], in particular, associated with remeshing as the cracks evolve. The issue discusses recent developments in meshless methods, including a posteriori error estimation and adaptive methods.

Dynamic fracture is in itself a wide field of study. Papers in this issue focus on explicit dynamics and tackle, in particular, the issue of energy dissipation during crack growth and the simulation of fracture in thin shells due to dynamic and implosive or explosive loading.

Model reduction methods have recently been developed for fracture simulations. Algebraic model reduction such as the proper orthogonal decomposition (POD) is not inherently well-suited to such problems [58]. This issue discusses one possibility relying on the combination of POD with meshfree methods.

Parameter identification in fracture mechanics is a topic of special interest in practical applications and a necessary step to provide convincing and predictive modeling and simulation tools. Two methods are discussed in this issue, both for crack parameter identification and multifield problems in fracture.

Through these five topics, we believe the issue gives a fair reflection of the current state of the art, with a heavy focus on modeling and simulation methods, although covering the whole spectrum of applications and methodologies would require a much more substantial volume.

Timon Rabczuk
Stéphane P. A. Bordas
Goangseup Zi

References

  1. X. Zhuang, C. Augarde, and S. Bordas, “Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling,” International Journal for Numerical Methods in Engineering, vol. 86, no. 2, pp. 249–268, 2011. View at: Publisher Site | Google Scholar | Zentralblatt MATH
  2. X. Zhuang, C. E. Augarde, and K. M. Mathisen, “Fracture modeling using meshless methods and levels sets in 3D: framework and modeling,” International Journal for Numerical Methods in Engineering, vol. 92, no. 11, pp. 969–998, 2012. View at: Publisher Site | Google Scholar | MathSciNet
  3. H. Zhu, X. Zhuang, Y. Cai, and G. Ma, “High rock slope stability analysis using the enriched meshless Shepard and least squares method,” International Journal of Computational Methods, vol. 8, no. 2, pp. 209–228, 2011. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  4. Y. Cai, X. Zhuang, and C. Augarde, “A new partition of unity finite element free from the linear dependence problem and possessing the delta property,” Computer Methods in Applied Mechanics and Engineering, vol. 199, no. 17–20, pp. 1036–1043, 2010. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  5. P. Kerfriden, P. Gosselet, S. Adhikari, and S. P. A. Bordas, “Bridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems,” Computer Methods in Applied Mechanics and Engineering, vol. 200, no. 5–8, pp. 850–866, 2011. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  6. P. Kerfriden, J. C. Passieux, and S. P. A. Bordas, “Local/global model order reduction strategy for the simulation of quasi-brittle fracture,” International Journal for Numerical Methods in Engineering, vol. 89, no. 2, pp. 154–179, 2012. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  7. P. Kerfriden, O. Goury, T. Rabczuk, and S. P. A. Bordas, “A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics,” Computer Methods in Applied Mechanics and Engineering, vol. 256, pp. 169–188, 2013. View at: Publisher Site | Google Scholar | MathSciNet
  8. P. Kerfriden, K. M. Schmidt, T. Rabczuk, and S. P. A. Bordas, “Statistical extraction of process zones and representative subspaces in fracture of random composites,” International Journal for Multiscale Computational Engineering, vol. 11, no. 3, pp. 253–287, 2013. View at: Publisher Site | Google Scholar

Copyright © 2014 Timon Rabczuk et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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