research

Indentation is widely used to measure material mechanical properties such as hardness, elastic modulus, and fracture toughness (for brittle materials). Can one use indentation to extract material elastoplastic properties directly from the measured force-displacement curves? Or simply, is it possible to obtain material stress-strain curves from the corresponding indentation load-displacement curves? In an upcoming paper in JMPS titled "On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials," Xi Chen and colleagues at Columbia University and National Defense Academy, Japan show the existence of "mystical materials", which have distinct elastoplastic properties yet they yield almost identical indentation behaviors, even when the indenter angle is varied in a large range. These mystical materials are, therefore, indistinguishable by many existing indentation analyses unless extreme (and often impractical) indenter angles are used. The authors have established explicit procedures of deriving these mystical materials. In many cases, for a given indenter angle range, a material would have infinite numbers of mystical siblings, and the existence maps of the mystical materials are also obtained. Furthermore, they propose two alternative techniques to effectively distinguish these mystical materials. The study in this paper addresses the important question of the uniqueness of indentation test, as well as providing useful guidelines to properly use the indentation technique to measure material elastoplastic properties.

In nature, several species use flexible probes to actively explore their environment, and acquire important sensory information, such as surface topology and texture, water/air flow velocity, etc. For example, rats and other rodents have an array of facial vibrissae (or whiskers) with which they gather tactile information about the external world.  The complex mechanisms, by which mechanical deformations of the probe lead to neuronal activity in the animal’s nervous system are still far from being understood. This is due to the intricacy of the deformation mechanics of the flexible sensors, the processes responsible for transforming the deformation to electrical activity, and the subsequent representation of the sensory information by the nervous system. Understanding how these mechanosensory signals are transduced and extracted by the nervous system promises great insight into biological function, and has novel technological applications. To understand the mechanical aspect of sensory transduction, here we monitored the deformation of a rat’s vibrissa as it strikes rigid objects with different topologies (surface features) during locomotion, using high-speed videography. Motivated by our observations, we developed detailed numerical models to study the mechanics of such flexible probes. Our findings elucidate how active sensation with vibrissae might provide sensory information and in addition have direct implications in several technological areas. To put this in perspective, we propose strategies in which flexible probes can be used to characterize surface topology at high speeds, which is a desirable feature in several technological applications such as memory storage and retrieval. (The full article is attached)

Attached is a paper outlining ideas for averaging autonomous dynamics, based on a dynamical systems point of view.

People interested in computational multiscale modeling, especially of the sequential kind, as well as nonequilibrium statistical mechanics may find these ideas useful.