Challenging Questions:
- Crystal Plasticity near Boundaries
One of the major fundamental questions in mechanics of elastoplastic crystalline materials is the role and origin of grain-boundaries. In particular, modeling grain boundaries has remained a major non-trivial hurdle in developing a multiscale theory of crystal plasticity. However, the construction of such theories requires the fundamental understanding of how a deformed crystal behaves near boundaries, as they can emerge inside a crystal (through grain boundaries) or engineered (crystal-substrate, matrix-inclusion in composites or free surface boundaries). Over the last decade, it has been clarified that crystal plasticity near (micrometer-close) such boundaries is stochastic and abrupt. The origin and modeling of such behaviors are currently topics of investigation.
- Friction and jamming in granular and amorphous solids
Jamming describes mechanically stable systems, composed of particulate matter, that arise out of fast quenches (for example, pushing a pile of sand in a box). The mechanical properties of such systems, such as the elastic modulus or vibrational character, can be thought to be in principle associated to the properties of other amorphous solids, such as glass or rubber. However, the appropriate understanding of jamming in granular solids requires the appropriate incorporation of the microscopic physics.
I am interested in chara
cterizing of the effects of friction on jamming, given that friction is the most abundant feature of such systems. We have built a statistical mechanics picture for frictionally jammed solids and we have introduced a geometric model for friction which we successfully applied to jamming. We further aim to analyze the spatial and vibrational character of jammed solids with friction and identify the possible universal pattern formation during plastic deformation.
- Dynamical spatial organization phenomena in complex disordered systems.
Disorder in complex systems may be included either in the model parameters or the initial conditions of the dynamical equations of motion. Disordered complex systems often display remarkable onsets of spatial organization, emergen
t after relatively small externally applied probes (such as external stress, magnetic field or pressure). A characteristic example is slip localization in glasses, where a featureless microstructure gives rise to razor-thin (nanometer scale) slip bands under modest external shear stress. Another example is the organization of featureless-looking dislocation ensembles into fractal structures under small external stresses during fatigue tests in crystalline samples (such as Al or Ni alloys). Further, spatial organization takes place when the quenching rate of a glass decreases below a critical rate and crystalline structure nucleates.
- Universal and interdisciplinary framework for aging/slow-relaxation phenomena in complex systems and the effects of disparate timescales on dynamical critical phenomena.
Aging phenomena are common in all materials at finite temperatures. Empirical knowledge in materials science tells us that the more complex the material microstructure is, the more dramatic the effects due to aging become, spanning a wide range of length and time-scales. Aging (or slow relaxation) mechanisms affect material response to a wide range of perturbations, mechanical or electromagnetic in origin. While experiments on the subject are abundant (e.g. due to high interest of the hardware industry on fatigue failure), no clear framework exists to describe the variety and impact of aging mechanisms on mechanical deformation phenomena. In particular, it is not clear when particular aging mechanisms (quantified in terms of local gradient terms in the equations of motion) lead to material failure and when not. In addition, slow aging effects alter significantly the statistics of stochastic events during mechanical deformation of single crystals, and the change cannot be predicted unless a general model with coexisting timescales is considered. A general framework for the analysis of possible slow relaxation effects in complex interacting systems, would be as important to the applied mathematics and physics communities as it would to the airplane and other hardware industries.