Computational Homogenization of Random Network Microstructures in Soft Matter Materials
Christian Linder (Stanford University)
SES Medal Symposium in honor of D.J. Steigmann
Tue 10:45 - 12:15
MacMillan 115
In this presentation, a new mean field approach to describe the microscopic deformation and the homogenization of materials with inherent network microstructures such as elastomers, hydrogels, soft biological tissues, non-woven fabrics, or cellular foams is proposed. Employing the concept of maximal advance paths, a kinematic link between its macroscopic affine path and its microscopic averaged deformation is found and solved numerically through a constraint minimization principle. Here, the network functionality plays a key role since the more fibers are connected at a junction point, the higher is the probability to find among them a fiber oriented closely to the advance direction resulting in an affine network deformation. A non-affine network deformation is observed for a functionality of four, for which the constraint takes a particularly interpretable form, as soon as a non-linear fiber response is assumed. The proposed approach is illustrated for several particular types of networks characterized by a different fiber response. In particular, the case of flexible polymer chains and stiff bio-filaments are considered. In addition, discrete network simulations are used to validate the assumptions employed for the statistical description of the soft matter material's homogenized response. In those discrete networks, the network functionality is strictly enforced, making standard tessellation concepts not applicable for this task. Also the periodicity of discrete unit cells is taken into account and due to the presence of zero energy modes the solution is not unique and requires certain regularization. Those discrete simulations suggest possibilities of future improvements of the maximal advance path constraint homogenization procedure.