Microstructural model for the plasticity of amorphous solids

Abstract

Based on the concept of localized shear transformation zones (STZ), a thermodynamically consistent model for the viscoplastic deformation of amorphous solids is developed. The approach consists of a dynamic description of macroscopic viscoplasticity that is enriched by the evolution of number density and internal structure of the STZ for detailing the origin of viscoplastic flow. So doing, the activation of STZ upon deformation and their subsequent internal re-arrangements are treated as two distinct processes. The detail of the model permits to relate it to small-scale information obtained from experiments or atomistic computer simulations, e.g., in the form of STZactivation energies and an approximate STZ-volume. The model is illustrated on the example of polycarbonate.

Kinetic model for the mechanical response of suspensions of sponge-like particles

“…In this article, we have focused our attention on the irreversible particle dynamics, which finally amounts to specification of the mobility matrix m. Once the system of interest is specified in these terms, the mutual coupling between microscopic and macroscopic scales can be studied in terms of the particle dynamics in flow, eqn (25d), and the resulting stress tensor (27a). While (25d,27a) is the general form of our main result, for practical applications the realization in terms of the stress tensor (35) and the stochastic differential eqn ( 38) is more relevant.…”

“…For given flow field v, trajectories x(t) can be determined by numerical integration of (38). Based on these trajectories, the average mechanical response can be determined with the constitutive relation (35) for the macroscopic stress s F .…”

“…30,31 In this article, we use a derivative of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework by Grmela and € Ottinger, [32][33][34] as introduced earlier. 35 The GENERIC method for closed systems emphasizes to study the energy and entropy of the system as separate model ingredients, rather than only their composite Helmholtz free energy. The framework then makes very specific statements about how these two building blocks evolve in time, as a result of reversible and irreversible dynamics, respectively.…”

“…Once the thermodynamic properties are specified by an appropriate choice of the energy E[x] and the entropy S[x], conditions on the evolution of these functionals amount to conditions on the evolution of the variables x, by way of the chain rule. For closed systems, we have introduced the following conditions (1) as the ''weak formulation'' of GENERIC: 35 The reversible dynamics does not affect the total energy and entropy of the system,…”