Low-density fibrous composites and structural foams are composed of three components: fiber, binder, and air. Their mechanical properties are strongly linked to constituent strength and stiffness behavior, but can also depend strongly on fiber or cell size, length, distribution, and orientation.

In this study, we are investigating the role of each of these parameters and their relationship with strength, stiffness, permeability, tortuosity as a function of fiber or cell and binder shape, size, location, distribution, strength, and stiffness. Our theoretical representation is based network models, in which each of the fibers or cell constituent is modeled as an individual element. Most studies completed in the past have focused only on the linear, small deformation behavior. Our efforts are incorporating the large displacement but small strain behavior of these elements.

In the figures on the left, we show a typical microstructure (top) and then the mesh representation (bottom) of a low-density composite network. These representations are used to generate the complete three-dimensional stiffness tensor for the composite. We are also interested in the effective permeability and tortuosity of these fibrous networks, and are exploring network and discrete-element models of the composites to determine the nature of these quantities.

In the two figures below, a typical structural foam is shown as is its recasting as an effective assembly of one-dimensional structural components that replace the cellular structure with a network representation. We have computed the effective stiffness properties of these foams, and are currently comparing these against experiment.

This work is currently being funded by the Colorado Advanced Materials Institute and Johns-Manville Corporation, and is being accomplished in close collaboration with Dr. Karsten Thompson of LSU. Current researchers include Dr. Fernando Ramirez, Mr. C. J. Riley, Mr. Arcot Srinivasan, and Professor Paul Heyliger (CSU).

The images above are a representation of a three-dimensional low-density composite with a random fiber orientation distribution. The actual microstructure is on the top. In the lower figure, the small dark circles represent either nodal locations of binder or the intersection of the fiber and the control volume. This network gives the equivalent continuum constitutive behavior as shown below, with the stress-strain behavior shown for the six stress components. As one might expect, there is a clear distinction between the on-axis stress and those transverse to the applied stress.

The image below and right represents a three-dimensional structural foam. Using a sequential process of digitization, we replace an effective continuum with a representation of one-dimensional elements that have the effective lumped area as do the closed walls of the foam. We can then use this simplified representation to again compute the effective bulk mechanical properties of this unusual solid. The foam images are courtesy of Dr. Karsten Thompson of LSU. Below left: a view near CSU's mountain campus, Summer, 2018; clearing out deadfall just Like the Sidonians (12b), Wind Tunnel, Devil's Head; for years, we had the place to ourselves: White as Snow (12a), Sheep Mountain, Poudre Canyon; the hidden and obscure Walk Through Fire (12c), Chuck Norris Wall, DH; calf-hooking the caffe latte crux of the remote and unforgettable Knotted Cord (12b), Torn Curtain, DH; deep in the heart of dream world: the Schrammies of the Elbsandstein, Germany; shaded in the morning, beautiful all day long: Of Course I Still Love You (12a/b), Falcon, DH. Climbing photos by the incomparable Greg Hand.