Using computer simulations to prevent material failure

Professor Christian Linder of Stanford University has been awarded the Friedrich Wilhelm Bessel Research Prize for developing computational methods that simulate how materials behave under stress. In the coming months, he will be collaborating with biomechanics expert Professor Oliver Röhrle of the University of Stuttgart.

“I’m happy to be back at the University of Stuttgart, where I can reconnect with former colleagues,” says Christian Linder. More than 20 years ago, he moved from Graz to Stuttgart to pursue a Master’s degree after completing his engineering studies. That year and a half laid the foundation for a relationship that continues to this day.

After earning his doctorate in the United States, he returned to his alma mater in 2008, where he served as a junior professor for several years. He first met Oliver Röhrle at the Simulation Technology Cluster of Excellence and quickly came to appreciate him as a colleague. “It’s wonderful that our friendship has now developed into a scientific collaboration,” says Linder, who has been Professor of Mechanics at Stanford University since 2013.

Together with Röhrle, he will investigate the titanium alloys now used in most implants and found in the bodies of an increasing number of people.

The two scientists have developed a computer model that can simulate the behavior of titanium implants. How do they change shape under long-term stress? How do they fatigue? And how can manufacturing processes such as 3D printing be optimized so that the implants are both lightweight and as stable as possible? After all, an artificial hip is designed to function in the body for many years despite the constant stress it is subjected to.

“To answer questions like these, we use finite element models,” explains Linder. In this process, a solid is divided into a very large number of smaller elements (e.g., millions of tiny tetrahedra or cubes). Using a computer, it is possible to approximate the behavior of each element, including how it responds to forces and transfers them to neighboring elements. This makes it possible to simulate materials with complex geometries and even composite materials.

Linder is considered one of the world’s leading experts in the development of such simulations and in adapting them to different research questions. “We contribute our biomechanical expertise—for example on the forces acting on an artificial hip joint inside the body,” explains Röhrle, who heads the Institute for Modeling and Simulation of Biomechanical Systems in Stuttgart.

In the coming months, the two scientists plan to address additional research questions and hope this will provide new insights into a phenomenon that might one day even be used to generate energy: flexoelectricity. This phenomenon describes the development of spontaneous electrical polarization in some materials in response to a mechanical strain gradient (i.e., a strain that varies from one point in the material to another).

“We want to gain a better understanding of the phenomenon of flexoelectricity, particularly in flexoelectric semiconductors,” says Linder. At some point, it may be possible to use this effect in sensors that provide early warning of deformations caused by material fatigue or to power “wearables” such as computer chips that continuously monitor blood sugar levels.

Röhrle nominated Linder for the Friedrich-Wilhelm-Bessel Prize and is therefore all the more delighted that his colleague has received the award. Over the next twelve months, Linder plans to make several extended research visits to Stuttgart and other German universities. “One of the goals of the award is to strengthen ties among researchers across national borders,” says Röhrle. “I’m very much looking forward to working with Christian Linder, whom I greatly respect both professionally and personally.”