1. To further explore the use of elastic Green’s functions in conjunction with boundary element analysis for modeling the mechanical behavior of advanced materials;

2. To identify areas for research collaboration and technology transfer between NIST and other organizations;

3. To plan a coordinated research and development program involving NIST, universities, and industries to develop efficient software tools for modeling the mechanical performance of advanced materials.

The 29 workshop attendees met for two and one-half days of presentations and discussion to meet the stated objectives of the workshop. The quality of presentations and subsequent discussions demonstrated that the workshop attracted the top researchers in the field of Green’s functions and boundary element analysis as well as a collection of individuals with a technical need for advanced analysis. Of the 29 participants, 11 were from universities, 8 from industries, and 10 from national laboratories. The presentations and discussions can therefore be considered as representative of the thinking in these separate sectors.

The discussion groups were formed based on subject matter and interest. The three groups were fracture, quantitative non-destructive evaluation, and computer aided engineering (CAE). Each group was charged with identifying the key technology issues, establishing the relevance of these issues to Green’s functions and boundary element analysis, and to identify specific projects. Ideally, each of the identified project teams would be composed of a representative from industry, university, and a national laboratory. The key issue that developed concerned relevance of the technology being discussed at the workshop to specific problems in industry. The methods of Green’s functions and boundary element analysis are useful tools provided the problems are amenable to the method. Several projects were identified at the conclusion of the workshop that precisely fit the proposed model.

The Green’s function methods discussed at the workshop are particularly powerful when applied to the fracture problem since the singular behavior of stress is incorporated directly into the model, no special techniques are needed for simulating the singularity. As such, the power of the Green’s function method is in the ability to extract analytic insights concerning the mechanics of material failure. The discussion group on fracture identified the key technical issues as grain boundary and size effects, interface "material" effects on interfacial fracture, diffuse cracking and damage in heterogeneous materials, near-interface cracking in thermal barrier coatings, and process-induced damage in manufacturing. The group considered which of these topical areas were amenable to analysis by Green’s function methods and identified two potential areas for developing specific projects. The first project area identified was fracture and damage in heterogeneous media. This involves consideration of multiple crack sites, damage accumulation, effect of rigid or ductile particles, effect of creep and stress-strain behavior, and the development of reliability models. The second area identified was fracture and fatigue of layered media. This would involve the effect of ductility or brittleness of the bonding layer(s), effect of high heat fluxes such as those experience by thermal barrier coatings, and the effect of interface geometry. In both the project areas the need for observation and experiments to guide and verify the theoretical developments was considered crucial.

The Green’s function methods have a long history in quantitative non-destructive evaluation due to the representation of point sources in infinite, semi-infinite, and finite domains. The quantitative non-destructive evaluation working group identified two key technology issues. First, characterization of multi-phase materials. This would include the forward problem as well as the inverse problem. The inverse problem is especially difficult sine the goal would be the detection of micro features in the heterogeneous material. This particular problem is relevant to modern materials since almost all advanced materials contain multiple phases and therefore interfaces. The multiple phases and microstructure directly effect the macro properties of the material. Therefore, the ability to sense and control microstructure is essential for advanced material applications. The specific problem identified under this problem statement was the development of time-domain boundary elements for materials characterization.

The second problem identified by the quantitative non-destructive evaluation working group was the modeling and optimization of measurement techniques. This relates to probe and sensor design, sensitivity analysis, and optimization. Additionally, issues such as probability of detection and characterization of subsurface features could be addressed. This topic is relevant when considering the design of experiments, validation of experimental techniques, and considering the congruence of models and experiments. Two specific projects were identified which would be helpful in solving this particular problem. First, a library of Green’s functions which would enable the experimentalist to have the full power of various Green’s functions available to predict the experimental response of a material under varying initial conditions. This would allow the experimentalist to play a number of "what if" games before beginning an experimental procedure. Second, the group identified the necessity of developing tools to link macroscopic properties to microstructural analysis through Green’s function based models and non-destructive measurements.

The third working group was focused on computer-aided engineering. This group identified process optimization and engineering of materials as the main technical areas. Several candidate projects were proposed where Green’s function methods might be useful. First, the further development of electrochemical machining technology requires increasingly sophisticated models to predict the final shape of the machined part. Similar projects in traditional machining, grinding, and profiling of rolled gears were also discussed. Second, the analysis of the growth of thin films was identified as a project well-suited to boundary element investigation as the conditions on the surface of the thin film have a dramatic role in the growth of the film. Both of these projects discussed by the CAE group could be approached through an integrated software product which would contain solid modeling capabilities, Green’s function-based analysis, adaptive meshing, optimal design routines, and a visualization capability.

Four projects were sponsored jointly by NIST and NSF as a direct outcome of the workshop on Green’s functions and boundary element analysis. In all these projects, NIST had the coordinating and enabling role. The list of these projects and the institutions and industries which were involved is given below:

1. Interface and near-interface cracking in automotive V-belts (Gates Rubber Company, NIST, Colorado School of Mines).
2. Cracking in thermal barrier coatings (United Technologies, NIST, Vanderbilt University, Colorado School of Mines).
3. A Green's function library (NIST, Iowa State University, Colorado School of Mines, Michigan Technological University).
4. Reliability of conductive adhesives (Motorola, 3M, NIST, Michigan Technological University, Colorado School of Mines).

Later, starting from Oct. 1996, SIMA (NIST) sponsored a major project on the development of a library of Green's functions on the Internet.