with Discontinuous Enrichment

for Applied Mechanics

John E. Dolbow

*December 1999*

The additional incorporation of near-tip functions allows for a natural application of the enriched approximation to fracture mechanics. The capability to accurately calculate stress intensity factors for a mesh which does not conform to the crack geometry is a distinct advantage of the method. In addition to two-dimensional linear elastic fracture, the extension of the method to the modeling of mixed-mode fracture in Mindlin-Reissner plates is examined. To this end, a domain form of the interaction integral is developed for the extraction of moment and shear force intensity factors. The application of discontinuous enrichment to model interfaces with nonlinear constitutive laws is also developed. In conjunction with a well developed iterative technique, several different constitutive laws are considered on the discontinuous interface, including frictional contact on the crack faces. The simulation of crack growth in this context is straightforward, as the enrichment functions alone model the crack geometry such that no remeshing is necessary. The simulated crack paths are shown to correlate well with experimental data, and consistent results are obtained with the method throughout.

The document is available in both pdf and postscript formats, as specified below.

- Preliminary
Pages [
*Title, Abstract, Acknowledgements, TOC, etc.*] [PDF, 13 pages] - Chapter 1
[
*Introduction*] [PDF, 9 pages] - Chapter 2
[
*Overview of Partition of Unity Methods*] [PDF, 20 pages] - Chapter 3
[
*Modeling Arbitrary Discontinuities*] [PDF, 42 pages] - Chapter 4
[
*An Enriched Formulation for Plate Fracture*] [PDF, 36 pages] - Chapter 5
[
*Nonlinear Constitutive Laws on Interfaces*] [PDF, 31 pages] - Chapter 6
[
*Crack Growth Simulations*] [PDF, 20 pages] - Chapter 7
[
*Conclusions and Future Work*] [PDF, 3 pages] - References
[
*References*] [PDF, 5 pages] - Appendices
[
*Appendix A and B*] [PDF, 10 pages]

Ph.D. Thesis (

- Preliminary
Pages [
*Title, Abstract, Acknowledgements, TOC, etc.*] [PS, 13 pages, 858K] - Chapter 1
[
*Introduction*] [PS, 9 pages, 849K] - Chapter 2
[
*Overview of Partition of Unity Methods*] [PS, 20 pages, 993K] - Chapter 3
[
*Modeling Arbitrary Discontinuities*] [PS, 42 pages, 2.0MB] - Chapter 4
[
*An Enriched Formulation for Plate Fracture*] [PS, 36 pages, 1.1MB] - Chapter 5
[
*Nonlinear Constitutive Laws on Interfaces*] [PS, 31 pages, 4.4MB] - Chapter 6
[
*Crack Growth Simulations*] [PS, 20 pages, 6MB] - Chapter 7
[
*Conclusions and Future Work*] [PS, 3 pages, 831K] - References
[
*References*] [PS, 5 pages, 840K] - Appendices
[
*Appendix A and B*] [PS, 10 pages, 898K]