Microstructure-based, multiscale modeling for the mechanical behavior of hydrated fiber networks

Abstract

A multiscale formulation is derived for the mechanics of a dilute fiber network microstructure, as occurs in in vitro reconstituted collagen gels, to accommodate the deterministic solution of a uniform-stress condition in the fiber network. The macroscale two-phase equations are derived based on the integral volume-averaging approach of the spatial averaging theorem, modified for the averaging volume to deform materially in the solid phase and thereby ensuring consistent network mass conservation. For low-Reynolds-number fiber-fluid interaction with no hydrodynamic interaction between fibers, the macroscale Darcy law arises naturally as a function of average fiber orientation and volume fraction, with no additional empirical specification. The macroscale equations are solved using finite element analysis with the averaging volumes centered at Gauss points of integration. The macroscale solid stress and fluid velocity are obtained by microscale deterministic solution of network and Stokesian mechanics within the averaging volume at each Gauss point, whereas the macroscale displacements and fluid pressure are solved as interpolated finite element field variables. The theory when applied to describe confined compression of collagen gels reproduced the strain-rate dependent behavior observed in poroelastic materials. The deformation of the averaging region and the reorientation of the collagen network in response to strain are also discussed. © 2008 Society for Industrial and applied Mathematics.