The main focus of my research is the mechanical properties of serially-repeating structures. Whether in single instances (vertebral columns, fin rays) or in meshes or sheets (batoid wings). The complex properties in these systems that stem from interactions of individual elements with their neighbors can create mechanical environments that are seemingly 'more than the sum of the parts'.
In addition, I am interested in hydrodynamics and locomotory mechanics, as well as robotics and other methods for re-creating the motion of animals.
Here is a list of my publications (click on links for PDF's):
Surfperch gait transition energetics
Batoid wing morphology
Narcine tooth reorientation
See below for more detailed descriptions of some of the projects that I am/have been involved in.
Project
Description
Wing skeleton morphology
The skeleton of the pectoral fins of batoids (rays, skates and guitarfish) is composed of cartilages (radials) that are arranged in serially repeating fin rays that radiate from the pectoral girdle. Morphological differences in the size, shape, arrangement, calcification pattern, and connections between these rays tracks both phylogeny and locomotor style. This paper detailed the differences that are found between different families of batoids, and offered some hypotheses about their effects on the physics of how they swim. For instance, the radials of many undulatory swimmers (e.g. round rays) grow differentially after they bifurcate near the edge of the wing. These differential growth rates cause the joints between the radials to be juxtaposed in such a way that radials are forced to bend against each other when the fin is bent. This acts as a passive stiffening mechanism on the edge of the wing, where most of the motion in undulatory swimmers is concentrated.
Another form of variation found in batoid wings is in the patterns of calcification that are found on the outside of the radials. Pictured at left are some cleared and stained radials from the wing of a skate. The red indicates calcified material. The arrangement of this calcification is nearly optimal (in terms of second moment of area) for the maximal resistance to bending. There are many patterns of calcification ranging from a dorsal and ventral series as shown here to the complete encasement that is commonly found in more oscillatory swimmers.
Modeling force vectors of the batoid wing skeleton
In order to tease apart the physical contributions of various morphologies, I have set out to model the force interactions of joints and cross-bracing in batoids wings. Using Matlab 7.1, I have written code to map, differentiate, and calculate the hypothetical force interactions between radial joints. Interestingly, the joints that occur between radials are arrangeed such that they form lines that describe different patterns on the pectoral fin of different swimming types. The wings of undulatory swimmers (right) are characterized by concentric semi-circles that mimic the wing edge. Oscillatory swimmers, however, have joint patterns that may form such extreme patterns as joint lines that are almost perpendicular to the wing's leading edge. Hypothetically, the patterns of joints form low-stress patterns that cause the wing to bend in specific patterns, even with the relatively linear arrangement of the wing musculature.
The code written is designed so that for each manually-input joint, spatial relationships to neighboring joints are calculated, and the vectors created by joint interactions are calculated based on assumed medio-lateral force applications. These vectors are then added over the wing or sub-sections of the wing to map the hypothetical intrisic force channelization of the wing skeleton.
Cantilever bending forces of batoid wing radials
As the third chapter of my thesis, I will gather data on the stiffness of radials from several species. These measurements will serve as initial starting points for more detailed modelling experiments as well as empirical insight into the effect of different calcification patterns on overall stiffness of the individual radials. In addition, the force necessary to bend the joints will be measured.
Preliminary measurements indicate that there may be up to a 9-fold decrease in bending stiffness between radials and joints. This would indicate that nearly all bending in the wing occurs at the joints, if they are not otherwise reinforced.
Biomimetic elasmobranch backbones
Work done in conjunction with Tom Koob and John H. Long as part of a larger experiment dealing with the evolution of backbone morphology and selection on morphological traits.
Fresh backbones from three species of elasmobranch were dynamically tested to determine elastic and viscoelastic properties. Species were found to react very differently to increasing lateral displacement of the vertebral columns.
In addition, prototype biomimetic vertebral columns were built using a rapid prototyper and cross-linked collagen matrix. Dynamic testing of these physical models revealed intriguing viscoelastic properties in serially-repeating beam structures.
