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.

We demonstrate, by theoretical analysis and molecular dynamics simulation, a mechanism for fabricating nanotubes by self-bending of nanofilms under intrinsic surface stress imbalance due to surface reconstruction. A freestanding Si nanofilm may spontaneously bend itself into a nanotube without external stress load, and a bilayer SiGe nanofilm may bend into a nanotube with Ge as the inner layer, opposite of the normal bending configuration defined by misfit strain.

In the attached paper, we have used Variational Analysis techniques (in particular, the theory of epi-convergence) to prove the continuity of maximum-entropy basis functions. In general, for non-smooth functionals, moving objectives and/or constraints, the tools of Newton-Leibniz calculus (gradient, point-convergence) prove to be insufficient; notions of set-valued mappings, set-convergence, etc., are required. Epi-convergence bears close affinity to Gamma- or Mosco-convergence (widely used in the mathematical treatment of martensitic phase transformations). The introductory material on convex analysis and epi-convergence had to be omitted in the revised version; hence the material is by no means self-contained. Here are a few more pointers that would prove to be helpful. Our main point of reference is Variational Analysis by RTR and RJBW; the Princeton Classic Convex Analysis by RTR provides the important tools in convex analysis. For convex optimization, the text Convex Optimization by SB and LV (available online) is excellent. The lecture slides provide a very nice (and gentle) introduction to some of the important concepts in convex analysis. The epigraphical landscape is very rich, and many of the applications would resonate with mechanicians.

On a different topic (non-planar crack growth), we have coupled the x-fem to a new fast marching algorithm. Here are couple of animations on growth of an inclined penny crack in tension (unstructured tetrahedral mesh with just over 12K nodes): larger `time' increment and smaller `time' increment. This is joint-work with Chopp, Bechet and Moes (NSF-OISE project). I will update this page as and when more relevant links are available.

From this Modern Mechanix scan of a 4 page article from the 1924 issue of Popular mechanics, we learn about Lincoln, the inventor!

Biasing reaction pathways with mechanical force, Charles R. Hickenboth, Jeffrey S. Moore, Scott R. White, Nancy R. Sottos, Jerome Baudry & Scott R. Wilson, Nature 446, 423-427 (22 March 2007).

The New York Times Magazine this weekend featured a Harvard undergraduate student from China, and her work to shake up education in China. The article is long, but if you grew up in China, it should be a quick read, and fun. If you grew up in US or Europe, perhaps this is a helpful read, just to learn how other people live.