Cartilage cell (chondrocyte) and multiphasic model simulation of mechanical interactions between a cell-matrix unit and extracellular matrix.

What do artificial cartilage, pharmaceutical dispensers, nanotechnology, atomic force microscopes, and laser welding have in common? All rely on the mathematics of materials for fundamental analysis and to achieve novel designs and advanced performance.

A Mathematics Department Research Training Group led by Ralph Smith, Pierre Gremaud, Mansoor Haider, Negash Medhin and Michael Shearer is developing activities for undergraduates, graduate students and postdocs with a $1.9 million five-year grant from the National Science Foundation. The effort focuses on five areas that are fundamental to emerging technologies: orthopedic biomaterials; multifunctional materials; polymers and composites, including carbon nanotubes; dynamics of thin material layers; and laser welding. The objective of the program is to train students and postdocs for academic and nonacademic careers that bridge applied mathematics, materials science, engineering, physics, and advanced technology.

The Orthopedic Biomaterials Group is focusing on the development of models, simulation packages, and experimental validation techniques to characterize the mechanical environment of cartilage cells. The goal is to understand the mechano-biological relationships in natural and engineered cartilage as a step toward the treatment of osteoarthritis.

The Polymers and Composites Group is using molecular dynamics simulations to investigate fundamental properties of long-chain molecules, including carbon nanotube composites. This will advance our fundamental knowledge about these materials, which are under consideration for applications ranging from large modular antennas to biomedical stents.

Similar objectives are being pursued by the Multifunctional Materials Group, which is investigating advanced systems that use piezoelectric, polymer, and shape-memory compounds. Applications include high-speed milling, atomic-force microscopy, and large space structures.

Modular antenna employing nanotube infused polymers and piezoelectric actuators.

Thin liquid films and granular flows are two of the phenomena being investigated by the Dynamics of Thin Material Layers Group. By combining analysis and numerical simulations, they are studying phenomena ranging from granular avalanches to surfactants in lungs.

The Laser Welding Group’s research ranges from fundamental analysis of the physics of laser welding and drilling to technological issues such as maximizing the depth of holes to be drilled.

In addition to giving students and postdocs research experience with emerging materials and applications, the program provides extensive interaction with disciplinary scientists and experiments. This interdisciplinary research experience complements integrated coursework, formal training modules, and internship and travel opportunities to prepare participants for both academic and nonacademic careers.

Details regarding the program can be found at the website http://www4.ncsu.edu/~mahaider/NCSU_RTG_Site/RTG_Homepage.html