Modeling Deformation and Flow of Disordered Materials
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Jean-Louis Barrat and Juan J. de Pablo Abstract Disordered, glassy materials are arguably one of the least understood states of condensed matter. Yet, they are ubiquitous in everyday life (polymers, “soft” glasses such as toothpaste, various emulsions, pastes, and foams) and in demanding applications (metallic glasses). Much of what is known about this important class of materials has been the result of truly concerted experimental and molecular modeling efforts. It is now generally accepted that amorphous materials exhibit dynamic and mechanical heterogeneities, but efforts to incorporate these into truly multiscale modeling approaches have been limited. This article describes the current state of affairs, along with many of the challenges that must be met to arrive at a fundamental understanding of amorphous materials and their response to external stresses.
Introduction Amorphous materials are ubiquitous in everyday life. “Glasses” surround us in many different forms, from the silicates in windowpanes to the amorphous polymers that constitute most plastics. More recently, bulk metallic glasses have emerged as particularly promising materials in terms of their mechanical properties. Such amorphous systems can be described as forming a state of matter that exhibits solid-like and liquid-like characteristics. Their mechanical properties make them appear solid, but their structure is disordered, or amorphous, similar to that of liquids. A seemingly different category of amorphous systems is formed by “soft” glasses, that is, complex fluids that present solid-like behavior under low stress and that flow under an applied load. Toothpaste and various sorts of emulsions, pastes, and foams are prototypical examples of such systems. The uses of “hard” and “soft” glasses are of course very different, with mechanical properties that may vary by many orders of magnitude. Soft systems, on the one hand, are usually described in terms of their rheological properties as thixotropic,
yield-stress fluids, with the corresponding practical applications (concrete, paints, drilling mud, cosmetic creams or foams, etc.). Hard amorphous systems, on the other hand, are usually seen as structural materials, with properties and uses comparable to those of crystalline solids. Still, from a conceptual and modeling standpoint, both types of systems offer similar challenges. They are disordered at the scale of their elementary constituents, which, in the case of soft glasses, might be mesoscopic entities such as colloidal particles, bubbles, or grains. They resist flow, but can “yield” under sufficient loading and, to some extent, the same vocabulary (yield stress, flow curve, plasticity, strain softening, etc.) can be used to describe their flow behavior. They are generally metastable, and their evolution (aging or creep) involves a wide spectrum of time scales. No obvious length scales can be identified in the microstructure. The last two points exemplify the intrinsic challenge posed by these materials for multiscale modeling methods. The
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