The MDM fracture mechanics codes are used to establish design criteria for newly developed composite materials, particularly heat-resistant brittle composites used in the manufacturing of turbine blades. Four distinct models have been implemented for the following cases:

• Axisymmetric cracking and boundary conditions (Pagano, 1991)
• Transverse and shear loading and associated cracking patterns in composite cylinders (Pagano and Tandon, 1994)
• Axisymmetric problems incorporating the effects of friction (Tandon and Pagano, 1996)
• Transverse cracking and delamination problems (Schoeppner and Pagano, 1998)

All four codes are serial Fortran implementations of Reissner's variational theorem (Reissner, 1950), and all of them share the same basic data structures and programming logic. The core methodology produces a continuous polynomial solution that may be used to generate one or more discrete solutions. First solutions cost 10-20 times as much as subsequent analyses.

We found all of these codes to be particularly sensitive to round-off error. This problem had been overcome through the use of a special extended-precision (128-bit) floating point (FP) system featured by Hewlett-Packard/Convex platforms. Unlike other FP systems, H-P supports an unusually wide range of exponent values. This not only implies a restriction on portability, but the extended precision FP operations are only supported in software and therefore, single-processor performance is also poor.

The solution to both the performance and portability problems amounts to the integration of a discrete ODE solver. Because the developers of the original algorithm knew the general form of the solution equations, they went about constructing a continuous approximation to this form. The sensitivity problem is a side-effect of this approach. The key observation was that the relevant equations could also be solved in a discrete fashion, thus eliminating the source of the current overflow and underflow problems.

Our ideas were presented to the AFRL materials research team at the end of July, 1999. They concurred that the proposed methodology is valid and agreed to a collaborative working arrangement in which:

• PET will identify an appropriate ODE solver in the public domain and implement an example code based on one of the existing MDM preprocessors
• AFRL will perform the necessary modifications to the MDM codes based on the PET example
• Validation and benchmarking of the finished product will be a joint effort involving both AFRL and ASC PET

Funding for the project was approved by PET in February, 2000. Contract modifications are currently in progress. Scheduled date of project initiation is April 1, 2000.

OBJECTIVES

An area of particular interest to the CSM Computational Technical Area (CTA) is the identification and analysis of heavily used research codes that have resisted movement to high performance multiprocessor computers. One such code, the Axisymmetric Damage Model maintained by a materials group at AFRL/Wright, was identified a little over a year ago.

Execution of the MDM code suite has been restricted to H-P platforms due to a fundamental portability problem. A solution to this problem was recently discovered by the NCSA CSM Group. The primary objective of this project is therefore to assist the AFRL development group in implementing the indicated changes.

The project represents a focused effort that will resolve portability problems while simultaneously yielding a significant performance improvement. It is a collaborative project involving the developers of the MDM codes and the PET CSM and PTES groups represented at ASC.

DELIVERABLES

Deliverable components of this project include:

• Identify a suitable public domain package for solving boundary value problems represented by systems of ordinary differential equations
• Design an example test program and validate results generated by the selected package
• Assist in validating and benchmarking the resultant code modifications made by AFRL to the suite of MDM codes (total of four codes supporting distinct boundary conditions)

All research code developed during the evaluation and collaboration phases of this project will remain the property of AFRL and will be returned to the AFRL point-of-contact (POC) for the project.

CUSTOMERS

Customers include Drs. Nicholas Pagano, Gregory Shoeppner (AFRL/ML), and G. P. Tandon (University of Dayton Research Institute) as well as other groups that depend on the information their research provides. Dr. Ruth Pachter, Senior Scientist at ASC, has also been a staunch supporter of this work.

The portable nature of the new code will allow it to proliferate and thus the ultimate number of users affected by this transition is much greater than the list of specific customers presented above.

Problem analysis and the collaborative solution techniques we apply might also be used to promote the quality of PET user support provided by the NCSA CSM Group and the ASC MSRC PTES team.

BENEFIT TO THE WARFIGHTER

We expect to achieve a significant performance improvement by implementing the new solution procedure described above. Currently, the typical execution time is a few hours on an H-P Exemplar. We aim to reduce the average execution time to a few minutes.

This will have a profound effect on the way in which fracture analysis is performed by the AFRL Materials group. Sequences of analyses might be turned towards optimization of new material designs. The portability of the new design will also allow the MDM codes to run correctly on virtually any platform.

PROJECT DEPENDENCIES AND SCOPE

The success of this project does not depend on the award of any other proposal.

RISK ELEMENT

The risk element associated with this project is negligible.

RELATED MATERIALS

• PET CSM Activities, review includes a significant section on the Axisymmetric Damage Model with related images presented at the DoD High Performance Computing Modernization Program's 1998 Users Group Conference, Houston TX, June 1998.
• A Case Study in Porting Strategy: The Axisymmetric Damage Model, Proceedings of the DoD High Performance Computing Modernization Program 1998 Users Group Conference, Houston TX, June 1998.

REFERENCES

Pagano, N. J., Axisymmetric Micromechanical Stress Fields in Composites, Proceedings of the 1991 IUTAM Symposium on Local Mechanics Concepts for Composite Material Systems, Springer Verlag, Berlin, pages 1-26 (1991)

Pagano, N. J., and Tandon, G. P., 2D Damage Modes in Unidirectional Composites under Transverse Tension and/or Shear, v. 1, Mech. of Comp. Mater. and Struc., pages 119-155 (1994)

Reissner, E., On a Variational Theorem in Elasticity, J. Math. Phys., v. 29, pages 90-95 (1950)

Schoeppner, G. A., and N. J. Pagano, Stress Fields and Energy Release Rates in Cross-Ply Laminates, Int. J. Solids, Structures, v. 35, p. 1025-1055 (1998)