Timothy Fowler
Acoustic Emission
Marcelo Canga (PhD student)
The use of conventional iterative techniques such as conjugate gradient methods has not been effective in the analysis of large deformation problems. In order to achieve convergence the standard practice requires the analyst to reduce the bulk modules by a factor of one hundred or so. In applications such as flex joints this cannot be tolerated. We are developing a pre-conditioner that will be inexpensive and effective so that the real material properties of an elastomer can be used.
This project is highly relevant to the primary goals of the OTRC- development of knowledge and training of engineers in the exploitation of deep water petroleum production. This program contributes to the development of realistic models to predict damage to structures subject to numbers of load cycles, and guides to effective design of joints and connections. The use of flex joints will certainly be critical in reducing the repeated bending moment applied to the risers/tendons - the design of effective composite structural systems.Initially we studied the application of standard finite element techniques to the problem of modeling cracked elastomeric components. When solutions to the equilibrium equations could be found, rates of the release of strain energy calculated in the finite element models agreed well with limited available test data as well as with analytical solutions that are known for the simplest problems. The configuration of the crack was assumed known and only the rate of growth predicted. In the second year we attempted to develop a computational strategy for predicting not only the rate of crack growth but also its direction. It was determined that better solution techniques would be required to treat the problem. Also, improved modeling of the contact problem would be necessary. In the third year we have concentrated on the development of a multi-level iterative solution scheme. In three-dimensional problems this may relieve the artificial constraints that appear to be a major source of our difficulties. We are developing an element-by-element algorithm for the construction of a pre-conditioner for use with conjugate gradient solution methods. Using this pre-conditioner we can achieve rates of convergence of the method that are independent of the bulk modulus. We have demonstrated the effectiveness of the method. The important aspect of the work in progress is the development of a computationally efficient algorithm.
There is an ongoing joint industry funded program on Fatigue Life of Laminated Elastomeric Bearings that is being carried out by Materials Engineering Research Laboratories of Hertford England. Dr. Becker works with the JIP. At The University of Texas Austin the CAM (Computational and Applied Mathematics) group, comprising engineering, mathematics and computer science faculty and students, have developed a variety of software tools that will be useful in implementing our proposed methods.
The results of this project will provide a sound starting point for the development of a production program. With the availability of the finite element solver that we will develop , along with some important development in material modeling, it will be practical to put together a code that will predict the initiation and growth of fatigue cracks in flex joints. The design of these components will be improved and rational monitoring of the components in the field will be possible.
October 1992 to September 1996
Graduate student theses:
Michael Lunneau's 1993 MS Thesis, "Crack Modeling in Elastomers"
Tammy Long's 1993 MS Thesis (and OTRC report), "A Finite Element Study of Crack Initiation and Growth in Hyperelastic Materials"
Marcelo Canga PhD dissertation (est. Dec 1996)OTRC Report:
" A Finite Element Study of Crack Initiation and Growth" Tammy L. Long and E. B. Becker, Dec 1993
Invited Talks (not listed) and Journal Articles:
" Finite Element Calculation of Energy Release Rate of 2-D Rubbery Material Problems with Non- Conservative Crack Surface Tractions" J. H. Chang and E.B. Becker, International Journal for Numerical Methods in Engineering Vol 33, pp 907-927, 1993.
" A Finite Element Procedure for Axisymmetric Elastomeric Solids Under General Loading" R. E. Marusek and E. B. Becker, International Journal for Numerical Methods in Engineering Vol 36, pp 2031-2048, 1993.