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Register a new userShear bands as manifestation of a criticality in yielding amorphous solids
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Amorphous solids increase their stress as a function of an applied strain until a mechanical yield point whereupon the stress cannot increase anymore, afterwards exhibiting a steady state with a constant mean stress. In stress controlled experiments the system simply breaks when pushed beyond this mean stress. The ubiquity of this phenomenon over a huge variety of amorphous solids calls for a generic theory that is free of microscopic details. Here we offer such a theory: the mechanical yield is a thermodynamic phase transition, where yield occurs as a spinodal phenomenon. At the spinodal point there exists a divergent correlation length which is associated with the system-spanning instabilities (known also as shear bands) which are typical to the mechanical yield. The theory, the order parameter used and the correlation functions which exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solids that undergo mechanical yield.
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Considering a recently proposed model for the yielding of amorphous solids under cyclic shear deformation, we show that it can be analyzed by mapping it, in the simplest case, to a random walk in a confining potential with an absorbing boundary. The dynamics is governed by the first passage time into the absorbing state, which captures the essential features of the original model, thereby providing insight into the observed robustness of earlier results. Including the possibility of activated escape from absorbing states leads to a unique determination of a threshold energy and yield strain, and further, suggests an appealing approach to understanding fatigue failure.
Amorphous solids display a ductile to brittle transition as the kinetic stability of the quiescent glass is increased, which leads to a material failure controlled by the sudden emergence of a macroscopic shear band in quasi-static protocols. We numerically study how finite deformation rates influence ductile and brittle yielding behaviors using model glasses in two and three spatial dimensions. We find that a finite shear rate systematically enhances the stress overshoot of poorly-annealed systems, without necessarily producing shear bands. For well-annealed systems, the non-equilibrium discontinuous yielding transition is smeared out by finite shear rates and it is accompanied by the emergence of multiple shear bands that have been also reported in metallic glass experiments. We show that the typical size of the bands and the distance between them increases algebraically with the inverse shear rate. We provide a dynamic scaling argument for the corresponding lengthscale, based on the competition between the deformation rate and the propagation time of the shear bands.
The mechanical failure of amorphous media is a ubiquitous phenomenon from material engineering to geology. It has been noticed for a long time that the phenomenon is scale-free, indicating some type of criticality. In spite of attempts to invoke Self-Organized Criticality, the physical origin of this criticality, and also its universal nature, being quite insensitive to the nature of microscopic interactions, remained elusive. Recently we proposed that the precise nature of this critical behavior is manifested by a spinodal point of a thermodynamic phase transition. Moreover, at the spinodal point there exists a divergent correlation length which is associated with the system-spanning instabilities (known also as shear bands) which are typical to the mechanical yield. Demonstrating this requires the introduction of an order parameter that is suitable for distinguishing between disordered amorphous systems, and an associated correlation function, suitable for picking up the growing correlation length. The theory, the order parameter, and the correlation functions used are universal in nature and can be applied to any amorphous solid that undergoes mechanical yield. Critical exponents for the correlation length divergence and the system size dependence are estimated. The phenomenon is seen at its sharpest in athermal systems, as is explained below; in this paper we extend the discussion also to thermal systems, showing that at sufficiently high temperatures the spinodal phenomenon is destroyed by thermal fluctuations.
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the response of such athermal solids are governed by local conditions of mechanical equilibrium, i.e., force and torque balance of its constituents. Here we show that these constraints have the mathematical structure of a generalized electromagnetism, where the electrostatic limit successfully captures the anisotropic elasticity of amorphous solids. The emergence of elasticity from local mechanical constraints offers a new paradigm for systems with no broken symmetry, analogous to emergent gauge theories of quantum spin liquids. Specifically, our $U(1)$ rank-2 symmetric tensor gauge theory of elasticity translates to the electromagnetism of fractonic phases of matter with the stress mapped to electric displacement and forces to vector charges. We corroborate our theoretical results with numerical simulations of soft frictionless disks in both two and three dimensions, and experiments on frictional disks in two dimensions. We also present experimental evidence indicating that force chains in granular media are sub-dimensional excitations of amorphous elasticity similar to fractons.
Understanding the mechanical response and failure of solids is of obvious importance in their use as structural materials. The nature of plastic deformation leading to yielding of amorphous solids has been vigorously pursued in recent years. Investigations employing both unidirectional and cyclic deformation protocols reveal a strong dependence of yielding behaviour on the degree of annealing. Below a threshold degree of annealing, the nature of yielding changes qualitatively, to progressively more discontinuous yielding. Theoretical investigations of yielding in amorphous solids have almost exclusively focused on yielding under unidirectional deformation, but cyclic deformation reveals several interesting features that remain largely un-investigated. Focusing on athermal cyclic deformation, I investigate a family of models based on an energy landscape description. These models reproduce key interesting features observed in simulations, and provide an interpretation for the intriguing presence of a threshold energy.
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