A Continuum-Microscopic Model

14 Creating accurate, macroscopic scale models of microscopically heterogeneous media is computation15 ally challenging. The difficulty is increased for materials with time-varying microstructures. Common 16 modeling approaches for heterogeneous media include purely continuum-based models and homogeniza17 tion methods. However, these methods tend to blur the inhomogeneities of the material that can influence 18 local mechanical properties. Continuum-microscopic (CM) models are a class of methods that incorpo19 rate microscopic information into faster macroscopic models of the medium. CM methods have been used 20 for heterogeneous media with static microstructures. This article presents an extension of a basic CM 21 algorithm to model heterogeneous media with time-varying microstructures. Fibrous media are chosen as 22 a class of materials upon which to test the algorithm. Information from the material’s microstructure is 23 saved over time in the form of probability distribution functions (PDFs). These PDFs are then extrapo24 lated forward in time to predict what the microstructure will look like in the future. Keeping track of the 25 microstructure over time allows for accurate computation of the local mechanical parameters used in the 26 continuum-level equations. The model was tested on a generic fibrous material with randomly oriented 27 and crosslinked fibers. Results show that the mechanical parameters computed with this algorithm are 28 similar to those computed with a fully-microscopic model. Errors for continuum level variables in the 29 5-10% range are deemed an acceptable trade-off for the large savings in computational expense offered 30 by this algorithm. 31