In previous research, a high-mechanical- advantage actuator system inspired by the fibrillar networks in plant cell walls was developed. One of the basic elements in the actuator system is a composite tube consisting of a flexible matrix and multiple layers of oriented, high-performance fibers such as carbon. By tailoring the properties of the fibers and matrix of the flexible matrix composite (FMC) tube, one can create a material that is flexible in certain directions, yet compliant in others. For example, the ratio of Young's moduli in the directions parallel and transverse to the fibers can range from 102 to 104. Strands of such FMC material can be wound into a tube at selected angles relative to the winding axis (a process called filament winding) such that the tube can contract or elongate axially via internal pressurization. It was previously shown that large strain and large force can be achieved with individual, pressurized FMC tubes, and that parallel arrays of tubular elements can be integrated to form 2D adaptive structures (e.g., skins and plates with multiple tubes).

The F2MC Single Tube is modeled as a structure composed of two concentric cylinders filled with a compressible fluid: an inner liner layer and an outer FMC laminate.
Building upon and expanding from the previous research, the new work synthesizes an adaptive structure with variable mechanical properties utilizing fluidic FMC (F2MC) tube elements through valve control. By using high bulk modulus working fluids in conjunction with FMC tubes having selective fiber orientations, one can obtain significant changes in stiffness by simply opening or closing an inlet valve to the F2MC tubes. With an open valve, the system can be very flexible. Due to its high bulk modulus, the fluid is highly resistant to volume change when the valve is closed. Because of the fiber reinforcement, the fluid-filled FMC tubes will thus develop very high stiffness. The variable stiffness tube has the flexibility to be easily deformed when desired (low stiffness with open valve and circulating fluid) and to sustain significant loads when deformation is not desired (high stiffness with closed valve and no circulation). These capabilities of single F2MC tubes can also be carried over to multicellular structures composing many small-diameter F2MC tubes integrated into supporting matrix materials. The wide range of change in stiffness is valuable in many existing and potential applications, such as soft robotics, isolation mounts, and morphing aircraft.

In a previous effort, a simple model of the fluid-filled F2MC composite single tube was developed using a composite thin shell theory. The results from the model predicted that more than two orders of magnitude change in the stiffness of the F2MC tubes could be achieved between the open and closed valve configurations. However, there are several limitations to the model. First, the model does not consider the effect of a thin inner lining layer between the fluid and the FMC laminate. The inner lining layer may be needed to prevent leakage due to the high internal pressure generated by axial loading in the closed valve condition.

Second, thin shell theory does not take into account the radial compliance of the FMC wall. Finally, the previous model does not take into account the possibility of air entrainment in the working fluid. Such issues should be accounted for to accurately predict the stiffness of the tube — particularly in the closed valve configuration where all sources of compliance are important.

In the new work, a more comprehensive model was developed that can better capture the open/closed valve characteristics of the F2MC single tube system. The F2MC single tube is modeled as a structure composed of two concentric cylinders filled with a compressible fluid: an inner liner layer and an outer FMC laminate as shown in the figure. An elastomeric inner liner is subjected to a pressure p1 at the inner surface and a pressure of p2 at the outer surface.

The working fluid inside the F2MC tube performs a vital role. The constraining action of the fibers and the high bulk modulus of the working fluid provide the increased modulus of the closed valve condition over the open valve condition. One would expect a fluid of larger bulk modulus to lead to a larger modulus ratio. However, a change in fluid bulk modulus from B=0.1 to 10 GPa introduces only very little change in modulus ratio. This can be explained by examining the difference in bulk modulus between the working fluid and the inner liner material. For example, water has a bulk modulus of about 2 GPa, whereas the bulk modulus of the inner liner has a value of only 5.6 MPa ( K = E 3(1- 2n ) ) — more than two orders of magnitude less than that of water. Thus, under a closed valve condition, the compliant inner liner is compressed much more than the water, preventing the full utilization of the working fluid.

To further expand the concept of F2MC tube, a variable transverse stiffness honeycomb panel was proposed, where the traditional aluminum or laminated composite face sheets are replaced by layers of F2MC tubes embedded in a soft matrix material. A honeycomb core is effective in transferring the transverse load on the sandwich panel into axial loads on F2MC tubes, so that the variable F2MC stiffness in its axial direction is transformed into variable panel stiffness in its transverse direction.

The concept of tube segmentation is introduced to further increase the variable stiffness ratio; it can be realized by an embedded valve network. A sandwich beam with one single-segment F2MC tube on a honeycomb core provides a transverse stiffness ratio of no more than 4, so the concept of tube segmentation is introduced to further improve the beam performance.

The working fluid in each individual segment is independent with respect to others when the valve network is closed. Each segment can therefore be treated as an individual F2MC tube upon which the single-segment analytical model can be applied. A similar parametric study is carried out to investigate the effects of different F2MC designs on the beam stiffness ratio. The range of fiber angles for which the stiffness ratio is maximized is smaller compared to the singlesegment tube sandwich beam. The variable transverse stiffness accumulates from each segment so that the more segments in the tube, the higher the stiffness ratio. The effects of the inner liner thickness become more significant as compared to the beam with single-segment tube.

This work was done by K.W. Wang, Charles E. Bakis, and Christopher D. Rahn of Pennsylvania State University for the Air Force Office of Scientific Research.

AFRL-0116 Defense

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Fluidic Flexible Matrix Composites for Autonomous Structural Tailoring

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This article first appeared in the February, 2009 issue of Defense Tech Briefs Magazine.

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