From chains to networks: An adaptive, coarse-grained method for simulating elastomers at the rubbery plateau.

摘要

Computational modeling for elastomers still faces unique challenges due to the fact that phenomena of interest require a large range of length scales in order to capture material properties. Behaviors like crazing and the strength of double network hydrogels require length scales smaller than chain length to appropriately model. However, a typical elastomer has on the order of 10 19 crosslinks in one mL of volume, which means that a simulation that is entirely resolved to the scale of chain lengths is computationally prohibitive. To study these behaviors computationally requires a new method that can bridge a wide range of length scales while still preserving the underlying physics of the problem.;This work presents a new, multi-scale, adaptive method for the simulation of deformation in elastomer networks. Recent research has indicated that elastomer networks do not deform perfectly affinely although large regions of the network can be approximated as doing so. We assume that topographically local parts of the network deform affinely, and have developed a very fast interpolation method that allows us to find the energy, forces, and stiffness in these affine parts of the network. By iteratively refining our network and testing our affinity assumption, we end up with networks in which many crosslinks can be described with relatively few degrees of freedom, and the positions of some crosslinks are determined explicitly. The advantage of this method is that large networks can be computationally simulated while still preserving fine scales in regions of interest.