Breakdown of elasticity in amorphous solids

Abstract

What characterizes a solid is the way that it responds to external stresses. Ordered solids, such as crystals, exhibit an elastic regime followed by a plastic regime, both understood microscopically in terms of lattice distortion and dislocations. For amorphous solids the situation is instead less clear, and the microscopic understanding of the response to deformation and stress is a very active research topic. Several studies have revealed that even in the elastic regime the response is very jerky at low temperature, resembling very much the response of disordered magnetic materials 1-6 . Here we show that in a very large class of amorphous solids this behaviour emerges upon decreasing temperature, as a phase transition, where standard elastic behaviour breaks down. At the transition all nonlinear elastic moduli diverge and standard elasticity theory no longer holds. Below the transition, the response to deformation becomes history-and time-dependent.Our work connects two different lines of research on amorphous solids such as structural, colloidal and granular glasses. The first focuses on their behaviour at low temperature. With the aim of understanding the response of glasses to deformations, there have been extensive numerical studies of stress versus strain curves obtained by quenching model systems at zero temperature. One of the main outcomes is that the increase of the stress is punctuated by sudden drops related to avalanche-like rearrangements both before and after the yielding point [1][2][3][4][5][6] . This behaviour makes the measurements, and even the definition of elastic moduli fairly involved. In a series of works, Procaccia et al. have given evidence that in some models of glasses, such as Lennard-Jones mixtures (and variants), nonlinear elastic moduli exhibit diverging fluctuations, and linear elastic moduli differ depending on the way they are defined from the stress-strain curve 7,8 . Another independent research stream has focused on gaining an understanding of the jamming and glass transitions of hard spheres both from real-space and mean-field theory perspectives 9,10 . The exact solution obtained in the limit of infinite dimensions revealed that by increasing the pressure a hard sphere glass exhibits a transition within the solid phase, where multiple arrangements emerge as different competing solid phases 11,12 . This is called the Gardner transition, in analogy with previous results in disordered spin models 13,14 . Recent simulations have confirmed that in three dimensions these different arrangements indeed become increasingly long-lived, possibly leading to ergodicity breaking 15 . These mean-field analyses complement and strengthen all the remarkable results found in the past two decades on jammed hard spheres glasses. The major outcome of these real-space studies was the discovery that amorphous jammed solids are marginally stable-that is, characterized by soft modes and critical behaviour, and in consequence by properties which are very different from those of usual crystalline ...

Experimental Evidence of the Gardner Phase in a Granular Glass

“…Another fascinating observation, which must contain a signature of the Gardner phase, is the avalanche dynamics observed in the motion of an intruder pulled through the glass, at constant force or constant velocity [28,39]. Finally, the non-linear elasticity and dilatancy reported in [29,40,41], might have close connections to the breakdown of classical elasticity reported for amorphous solid in the Gardner phase [42][43][44][45].…”

Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions

“…A glass state can thus be described as an isolated set of configurations, with a typical mutual distance ∆, a typical distance from the reference configuration ∆r, and a finite relaxation time. Each glass state is then an amorphous solid characterized by a well-defined shear modulus and non-linear elastic susceptibilities (74). Neglecting the Debye contribution to the vibrational spectrum, such solid also displays a gapped vibrational density of states (75,76).…”

Structure in sheared supercooled liquids: Dynamical rearrangements of an effective system of icosahedra

“…These can be used to predict when and where deformations will take place in sheared systems [37][38][39][40]. Recently, shear has been used to access the so-called Gardner transition [41] between glass states with differing stabilities [42,43].…”