Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions.

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

Perturbation-induced granular fluidization as a model for remote earthquake triggering.

Studying the effect of mechanical perturbations on granular systems is crucial for understanding soil stability, avalanches, and earthquakes. We investigate a granular system as a laboratory proxy for fault gouge. When subjected to a slow shear, granular materials typically exhibit a stress overshoot before reaching a steady state. We find that short seismic pulses can reset a granular system flowing in steady state so that the stress overshoot is regenerated. This feature is shown to determine the stability of the granular system under different applied stresses in the wake of a perturbation pulse and the resulting dynamics when it fails. Using an analytical aging-rejuvenation model for describing the overshoot response, we show that our laboratory-derived theoretical framework can quantitatively explain data from two fault slip events triggered by seismic waves.

Predicting frictional aging from bulk relaxation measurements.

The coefficient of static friction between solids normally increases with the time they have remained in static contact before the measurement. This phenomenon, known as frictional aging, is at the origin of the difference between static and dynamic friction coefficients but has remained difficult to understand. It is usually attributed to a slow expansion of the area of atomic contact as the interface changes under pressure. This is however challenging to quantify as surfaces have roughness at all length scales. In addition, friction is not always proportional to the contact area. Here we show that the normalized stress relaxation of the surface asperities during frictional contact with a hard substrate is the same as that of the bulk material, regardless of the asperities' size or degree of compression. This result enables us to predict the frictional aging of rough interfaces based on the bulk material properties of two typical polymers: polypropylene and polytetrafluoroethylene.

Quantitative Understanding of the Onset of Dense Granular Flows.

The question of when and how dense granular materials start to flow under stress, despite many industrial and geophysical applications, remains largely unresolved. We develop and test a simple equation for the onset of quasistatic flows of granular materials which is based on the frictional aging of the granular packing. The result is a nonmonotonic stress-strain relation which-akin to classical friction-is independent of the shear rate. This relation suffices to understand the quasistatic deformations of aging granular media, and its solid-to-liquid transition. Our results also elucidate the (flow) history dependence of the mechanical properties, and the sensitivity to the initial preparation of granular media.

Non-monotonic Dynamics in the Onset of Frictional Slip.

The transition from static to dynamic friction is often described as a fracture instability. However, studies on slow sliding processes aimed at understanding frictional instabilities and earthquakes report slow friction transients that are usually explained by empirical rate-and-state formulations. We perform very slow ( ∼ nm/s) macroscopic-scale sliding experiments and show that the onset of frictional slip is governed by continuous non-monotonic dynamics originating from a competition between contact aging and shear-induced rejuvenation. This allows to describe both our non-monotonic dynamics and the simpler rate-and-state transients with a single evolution equation.