Onset of irreversibility and chaos in amorphous solids under periodic shear

Abstract

An important aspect of the physics of amorphous solids is the onset of irreversible behavior usually associated with yield. Here we study amorphous solids under periodic shear using quasi-static molecular dynamics simulations and observe a transition from reversible to irreversible deformation at a critical strain amplitude. We find that for small strain amplitudes the system exhibits a noisy but repetitive limit-cycle, similar to return point memory [1]. However, for large strain amplitudes the behavior becomes chaotic (shows sensitivity to initial conditions) and thus irreversible. We show that the chaotic behavior is a result of the shear band instabilities that arise for large strains and the convective displacement fields they create.Amorphous solids such as plastics, window glass and amorphous metals are an important and ubiquitous form of matter. Industrial processing of such materials commonly involves plastic deformation (for example plastic forming). While a microscopic mechanism of plastic deformation in these materials was identified [2-4] the collective behavior on the mesoscale is still being debated. Current theoretical understanding of amorphous solids includes mainly mean-field statistical mechanics theories that are based on the assumption that the behavior is stochastic. Therefore, the dynamics is described in terms of probability distributions which follow the evolution of localized particle rearrangements exhibiting a transition from jammed to flowing behavior [5][6][7][8]. Recent experiments and simulations on superconductor vortices, dilute colloidal dispersions and loosely packed granular materials show that these materials undergo a transition from reversible to irreversible diffusive behavior by varying the strength of an oscillatory external field [9][10][11][12][13][14][15][16][17]. In this work we study highly condensed amorphous solids (well above the jamming transition) under oscillatory shear and show that for small strain amplitudes these systems evolve into periodic limit cycles where particles change their positions during the cycle but keep following the same trajectories for consecutive cycles. These reversible rearrangements result in energy fluctuations, which for small strains are completely repetitive which resembles return point memory [1]. Above a critical strain amplitude, the system does not settle into a limit cycle and the motion is chaotic with a positive maximal Lyapunov exponent. This allows us to define a yield point, which can be difficult to determine from a stress strain curve (green curve Fig 1). We explain the onset of chaotic behavior as a result of a convective displacement fields which result from strain localization which generally appears during yield in amorphous solids [3,18,19]. Identifying and understanding the underlying mechanism of chaotic behavior opens the possibility of a quantitative understanding of structural changes that occur in these systems and their relation to the dynamics.We perform molecular dynamics simulations of a system of N po...

Period proliferation in periodic states in cyclically sheared jammed solids

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“…Yet, remarkably, these systems can fall into absorbing states-they can find their way back to previously visited energy minima even as they undergo multiple particle rearrangements. Thus these systems explore many such minima [14][15][16][17] over and over again. Finally, when γ t is increased to γ * t , the system undergoes an absorbing state transition to a phase in which the system never returns to previously visited minima.…”

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