Multiscale modeling of semiflexible random fibrous structures

Biological as well as manmade materials with fibrous microstructures are ubiquitous in everyday life. At a certain length scale of observation, these materials appear in the form of a random network of cross-linked (connected) filaments. The computational effort required for investigating the mechanics of these structures by modeling the deformation of each fiber is very large. Therefore, a proper representation of their overall mechanical properties requires developing multiscale schemes capable of describing the behavior of the discrete system with a continuum model without loss of essential microstructural details. This article discusses two approaches developed for solving boundary value problems on large fiber-network domains using scale coupling techniques. We present first considerations related to sequential multiscale modeling, in particular linked to the scale of transition from a discrete to a continuum model of the network. Further, we review a method designed to construct a continuum model for the network structure, which takes into account the intrinsic spatial correlations of network properties. In both techniques, the geometrical and structural properties of network constituents at micro-scales are considered in estimating the macro-scale behavior of the structure subjected to external loads.

► Fiber networks exhibit multiple internal length scales.
► These derive from geometric parameters and correlation lengths of mechanical fields.
► Representative volume elements must be larger than all these internal length scales.
► Smallest size of a representative volume element should be 15 times the fiber length.