From Chains to Networks: An Adaptive, Coarse-Grained Method for Simulating Elastomers at the Mesoscale
Computational modeling for elastomers still faces unique challenges due to the wide range of length scales required in order to model the systems. Behaviors like crazing and the strength of double network hydrogels require length scales on the order of a chain length or smaller in order to capture the physical behavior. However, a typical elastomer has on the order of 1019 crosslinks in one mL of volume, which means that a simulation that is entirely resolved to the scale of chain lengths is computationally prohibitive. Methods bridging the atomic scale and elastomer chains currently exist, as do methods that bridge continuum chunks of the network and the macroscale. However, we still lack a method that allows us to smoothly move from the network to individual chains.
My current work is 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.
Figures show a 10,000 node elastomer network with a non-affine deformation in the top and center of the boundary. The picture at the upper left shows the exact solution for the deformation. The other three pictures show increasing levels of refinement and energy convergence using the new method.
Figure shows a 100,000 node elastomer network with a non-affine deformation in the top and center of the boundary. The blobs of color represent overlapping clusters. Each cluster allows for a solution with a decreased number of degrees of freedom.