Yield stress in amorphous solids: A mode-coupling theory analysis

Abstract

The yield stress is a defining feature of amorphous materials which is difficult to analyze theoretically, because it stems from the strongly non-linear response of an arrested solid to an applied deformation. Mode-coupling theory predicts the flow curves of materials undergoing a glass transition, and thus offers predictions for the yield stress of amorphous solids. We use this approach to analyse several classes of disordered solids, using simple models of hard sphere glasses, soft glasses, and metallic glasses for which the mode-coupling predictions can be directly compared to the outcome of numerical measurements. The theory correctly describes the emergence of a yield stress of entropic nature in hard sphere glasses, and its rapid growth as density approaches random close packing at qualitative level. By contrast, the emergence of solid behavior in soft and metallic glasses, which originates from direct particle interactions is not well described by the theory. We show that similar shortcomings arise in the description of the vibrational dynamics of the glass phase at rest. We discuss the range of applicability of mode-coupling theory to understand the yield stress and non-linear rheology of amorphous materials.

15 pages, 8 figures

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• The shear modulus of glasses: results from the full replica symmetry breaking solution
• Out-of-equilibrium dynamical mean-field equations for the perceptron model
• Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids
• Quantitative approximation schemes for glasses
• Large-scale structure of randomly jammed particles
• Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. I. The isotropic case
• Nonlinear rheology of dense colloidal systems with short-ranged attraction: A mode-coupling theory analysis
• Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain