|
|
Research The group is currently interested in some basic questions in non-equilibrium and statistical physics as revealed in various problems in materials science and solid mechanics. We are especially interested in problems that involve many interacting time and length scales, where conceptual and mathematical bridges between microscopic physics and continuum field theories are essential. In many of these problems the major challenge is to understand how collective microscopic processes give rise to emergent macroscopic behaviors that can be described by relatively simple partial differential equations; these should be fully consistent with fundamental principles of physics and thermodynamics and incorporate a few constitutive relations to link between the different scales. Dynamic fracture
The ability of solids to withstand mechanical forces is one of their fundamental properties. When a solid is loaded externally, there reaches a point where its global energy can be reduced by breaking into pieces, i.e by creating new free surfaces instead of continuing to store mechanical energy. The major vehicle for these failure processes are cracks, which are non-equilibrium propagating dissipative structures. Cracks are "natural laboratories" for probing material behavior under extreme conditions as their tips concentrate stresses and strains that approach a mathematical singularity. Moreover, crack propagation involves many interacting time and length scales ranging from the linear elastic forcing on large scales to the strong non-linearities and dissipation on the small scales near the crack's tip. Cracks often exhibit rather complex dynamics, including some poorly understood instabilities, and the laws that govern their motion have remained an object of constant study for nearly a century. My research aims at understanding the origin of crack tip instabilities and the structure of the near tip region. The research combines theoretical tools (classical field theory, asymptotic expansions, perturbation theory, complex analysis, field singularities) and close interaction with experimental work.
Selected publications:
Statistical physics of cracks (roughness)
One of the major goals of the physics of complex systems is to characterize the patterns observed in nature and to explain how these emerge from simple mathematical models. The spatio-temporal dynamics of cracks generate a wealth of patterns that call for theoretical investigation. One of the remarkable properties of many fracture surfaces is that they exhibit self-affine symmetry. This property implies that the fluctuations of the surface about its mean height are statistically invariant under an anisotropic scale transformation characterized by a roughness exponent. We have developed several stochastic, quasi-static crack growth models that account for the interplay between the mechanics of cracks with complex geometries and material disorder. These models generated rough fracture surfaces with self-affine scaling properties.
Selected publications:
Nonequilibrium thermodynamics of driven glassy systems
Glassy systems are usually regarded as the paradigmatic examples of non-equilibrium systems because they exhibit an anomalously slow relaxation behavior and a broken time-translation invariance (ergodicity breaking). These systems are driven even further from equilibrium when deformed by externally applied forces. Under such conditions, standard equilibrium thermodynamics is inapplicable. Therefore, a basic theoretical question is whether there exists a generalized thermodynamic formalism for such systems. In a recent work we have developed an internal-variable, effective-temperature non-equilibrium thermodynamics for glass-forming materials driven away from thermodynamic equilibrium by external forces. The basic idea is that the slow configurational degrees of freedom of such materials are weakly coupled to the fast kinetic-vibrational degrees of freedom and therefore these two subsystems can be described by different temperatures during deformation. The configurational subsystem contains coarse-grained internal variables that are state variables that account for the effect of the evolving glassy structure on various mechanical properties. We highlighted the need for understanding how both energy and entropy are shared by the different components of the system and use the first and second laws of thermodynamics to constrain the equations of motion for the internal variables and the effective temperature.
Selected publications:
Irreversible plastic deformation
The ability of solids to deform irreversibly, i.e. plastically, is of enormous importance to human kind. Yet, we have a rather limited fundamental understanding of the physics of plastic deformation in amorphous and heavily dislocated solids. The ultimate theoretical challenge in these fields is to develop dynamic equations of motion - the analog of the Navier Stokes equations - for amorphous and heavily dislocated solids. Building on advances in understanding amorphous materials, through detailed experiments and computer simulations, we have recently extended the original Shear-Transformation-Zones (STZ) theory to conform with the internal-variable, effective-temperature non-equilibrium thermodynamics discussed above. Furthermore, we have recently explored the implications of this thermodynamic framework to strain hardening theory of heavily dislocated polycrystalline solids.
Selected publications:
|
