A major benefit of multiscale modeling is that it helps to shed light on constitutive assumptions in macroscopic approaches to mechanics [1]; the stress tensor and the rate of plastic deformation are of particular interest. Nonequilibrium statistical mechanics is a powerful technique in this field, and it has been applied to study the plastic deformation of solids [2,3]. In this presentation, the focus is on multiscale modeling of solids in the glassy state. Structural glasses are particularly interesting (and challenging) for two reasons: they can age in the course of time, and the microscopic carriers of plastic deformation have not been identified to date (in contrast to the well-known dislocations for crystalline materials). Molecular simulations will be used to study glassy materials, in particular polymers. The goal is to establish a fine level of description that is suitable for a subsequent coarse-graining step to the macroscopic continuum level.
When studying polymer glasses on a molecular level, the structural rearrangements related to physical ageing and plastic deformation are rare events, in comparison to the rapid and continuously ongoing molecular vibrations. For studying in an efficient manner these rare events while still keeping molecular detail, a procedure has been proposed that scans the space of molecular configurations specifically for local minima and transitions between them [4]. A key ingredient in this procedure is the calculation of the free energy under appropriate mechanical boundary conditions [5]. In this contribution, we present results of the rare-event sampling for atactic polystyrene - as a prototypical example - below its glass-transition temperature. In the absence of deformation, we obtain rate constants for the minimum-to-minimum transitions extended over 30 orders of magnitude, with well-defined peaks at the time scales corresponding to the subglass relaxations of polystyrene [6]. As deformation is imposed, we observe that the transition states go through an instability and eventually collapse abruptly onto one of the connected local minima; furthermore, we present results about the transition rates as a function of deformation [7]. It will be discussed how these observations will eventually relate to the rate of macroscopic plastic deformation.
Acknowledgment: Part of this work is support by the Dutch Polymer Institute (DPI), projects no. 745ft14 and 820.
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[7] G.G. Vogiatzis, L.C.A. van Breemen, M. Hütter, J. Phys. Chem. B (submitted, 2022).