Stanford Mechanics and Computation


Focus Areas

Computational mechanics

Computational mechanics is concerned with the development and application of computational methods based on the principles of mechanics and the field has had a profound impact on science and technology over the past three decades. It has effectively transformed much of classical Newtonian theory into practical and powerful tools for prediction and understanding of complex systems and for creating optimal designs. Active research topics within our Group include development of new finite element methods (e.g. discontinuous Galerkin method), computational acoustics and fluid­structure interaction, algorithms for dynamical and transient transport phenomena, adaptive solution schemes using configurational forces, modeling the behavior of complex materials and biological tissue. The group is actively engaged in methods and algorithm development for high­performance computing including massively parallel computing. A recent emphasis is concerned with the coupling of techniques for analysis at the quantum, atomistic and continuum levels to achieve multi­scale modeling.

Multiphysics Modeling


Multiphysics modeling arises from the need to model complex mechanical, physical and/or biological systems with functionalities dependent on interactions among chemical, mechanical and/or electronic phenomena. These systems are often characterized by wide ranges in time and length scales which requires the development of technologies to describe and model, using numerical and mathematical techniques, the coupling between those scales with the goal of designing and/or optimizing new engineering devices. Myriad different applications exist ranging from novel molecular scale devices based on nanotubes and proteins, to sensors and motors that operate under principles unique to the nanoscale. Computer simulation is playing an increasingly important role in nano­science research to identify the fundamental atomistic mechanisms that control the unique properties of nano­scale systems.

Computational Bioengineering

Computational bioengineering is a quickly advancing field of research and is providing opportunities for major discoveries of both fundamental and technological importance in the coming years. The interface between biology and computational engineering will be one of the most fruitful research areas as the ongoing transformation of biology to a quantitative discipline promises an exciting phase of the biological revolution in which engineers, and especially those employing computation, will play a central role. As physical models improve and greater computational power becomes available, simulation of complex biological processes, such as the biochemical signaling behavior of healthy and diseased cells, will become increasingly tractable. A particular challenge along these lines lies in the multiscale modeling of biomechanical phenomena bridging the gap between the discrete cell level and the continuous tissue level. The potential scientific and technological impact of computational bioengineering can hardly be overstated. The group is playing an active part in this research effort at Stanford with current collaborative projects with the School of Medicine in areas such as the modeling of the mechanics of the ear and hearing, the eye and vision, growth and remodeling, simulation of proteins and mechanically gated ion channels, tissue engineering and stem cell differentiation.

Microscale Mechanical Measurements

'Micro­scale devices for system monitoring and modeling are also used for measuring nanoscale mechanical behavior. In the Mechanics and Computation Group we have a special interest in micro and nanoscale mechanical behavior, including material properties and the biomedical applications of nanofabricated devices. Research includes developing diagnostic tools, measurement and analysis systems, and reliable manufacture methods. Active projects include piezoresistive force sensing and optimal processing, cell stimulation and force measurements, understanding the biological sense of touch, and silicon probes for microscopy and sensing.