[P1-56] FTMP-based Modeling and Simulations of Glassy Polymers.
Multiscale modeling of glassy solids, such as polymers and metallic glasses, will require mathematically rational as well as effective treatments of the glassy states (free volume) responsible for carrying the viscoplastic flow. For amorphous polymers, it is rephrased as “modeling network degrees of freedom (NW-DOFs)” in connection with the orientating polymer chains. The “glassy states” can then be expressed in this context as those with curled and/or entangled chains with no net orientation, whereas the “strength” is attributed to their fully-extended counterparts with the alignments in the load-bearing direction, referred to as orientation hardening. To express the NW-DOFs, we introduce Finslerian geometry for an extended description of FTMP, together with the polymer-slip system-based kinematics proposed by Shizawa, et al. as the framework that allows direct treatments of the orientation change of the consisting polymer chains in a similar manner to the conventional crystal plasticity. The current extension enables one to deal explicitly with the associated microscopic degrees of freedom of underlying kinds, e.g., cross-linking and unzipping. Targeted material here is PMMA for modeling the early-stage viscoplastic and the attendant softening responses as typical mechanical properties of engineering polymers. By allocating the vecotrial field in the extended Finslerian formalism to the representative direction of the polymer chains, together with the associated fabric tensor field, the study attempts to express the NW-DOFs. Assuming that the NW-DOFs are given as a function of the incompatibility, on the basis of the “flow-evolutionary” perspectives in FTMP, the evolving “free volume” can be effectively expressed, with which both the targeted properties are successfully reproduced. The free volume change, on the other hand, is shown to qualitatively agree with that reported in the literature.