MICROSTRUCTURE AND MATERIAL CHARACTERIZATION OF BAT WING TISSUE FOR - PDF document

18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS MICROSTRUCTURE AND MATERIAL CHARACTERIZATION OF BAT WING TISSUE FOR ACTIVE SKIN COMPOSITES N. Goulbourne 1 , * Y. Wang 1 , S. Son 2 , A. Skulborstad 1 1 Aerospace Engineering, University of Michigan, Ann Arbor, USA 2 Mechanical Engineering, Virginia Tech, Blacksburg, USA *(ngbourne@umich.edu) Keywords : bat wing, skin tissue, anisotropic, fiber microstructure 1 Introduction anisotropy of the material [1]. Motivated by Bat skins have an inherent microstructure yielding histology information of the wing membrane of the specific macroproperties that enable unique flight bat, a statistical treatment is formulated in this paper style and aerodynamic footprint. It is based on this to capture the effect of the distribution of fiber cross- key observation that we have undertaken the first sectional area and the distribution of the number of systematic study of bat skins to investigate its fibers, which has not been done before. material properties commensurate with specific 2.2 Constitutive Model behaviors and functionality. Given the We present a generalized statistical treatment to multifunctional quality of bat skins: water-proofing, gas exchange, thermo-regulation, load-bearing model tissues containing more than one dispersive fiber property for the first time [2]. The work is airfoils, an array of airflow receptors, touch sensors, motivated by observations in bat wing tissue of two food-trapping, to name a few, it is ultimately a challenge to isolate those specific membrane orthogonally aligned families of fiber bundles, with prominent differences in fiber diameters and fiber properties that are integral to flight maneuvers. spacing [3]. The diameter of the fiber bundle varies Investigating the mechanics of bat skins specifically dramaticaly with fiber orientation even within each in relation to first their macroproperties and ideally family. As a result, the previously proposed fiber their microstructure is one of the novel density function, which only accounts for the discriminators of this research that could provide a major advancement towards designing synthetic number of fibers in different direction, is not sufficient to represent the overall anisotropy of the skins for artificial bat flight. In this presentation, we material. Here, a statistical treatment (Von Mises highlight our initial findings as to the microstructure and material behavior of bat wing skins. distribution) is applied to integrate two distributed properties – 1) the number of fibers and 2) the fiber cross-sectional area in different directions – into one effective fiber density function. 2 Material Characterization and Model 2.1 Material Properties For two families of fibers, the anisotropic strain energy function W is of the following form: Understanding the role that tissue structure plays in rendering specific mechanical properties and = W ( F , a , a ) W ( I , I , I , I , I , I , I , I , I ), (1) macroscopic functionality will provide a template 01 01 1 2 3 4 5 6 7 8 9 for developing synthetic materials in bio-mimicry. where F is the deformation gradient, the fiber Structurally based constitutive models can offer orientations are a 01 and a 02 , and I i are the stretch insight into the functions and mechanics of each invariants. The nine invariants are tissue component. For most soft biological tissues, 1 including arterial walls and skin tissue, the main = = − = 2 2 I tr C , I [(tr C ) tr C ], I det C , 1 2 3 load-carrying constituent is presumed to be the 2 distributed collagen fibers, which are embedded in = ⊗ = ⊗ 2 I C : ( a a ), I C : ( a a ), I an isotropic base matrix, composed of ground 4 0 1 0 1 5 01 01 6 substance. It is believed that the organization of the collagen fibers (micron length scale) gives rise to the

= ⋅ ⋅ = ⋅ 2 type but the stiffness of each bundle is proportional a a a Ca a a I ( ) , I ( ) . 8 01 02 01 02 9 01 02 to its cross-sectional area. Thus, the modified fiber density function is defined later in Equation (2) 37 such that will represent the fraction of For biological materials reinforced by two families the total bundle stiffness in the direction between φ of fibers, the strain energy function may be split into φ + φ two parts. One part is associated with isotropic and d . deformations, denoted by W iso , and the other part associated with anisotropic deformations, denoted The average bundle cross-sectional area at different by W aniso . Since the collagen fibers, which are orientations is considered as a function of its presumed to be the main load-carrying constituent at orientation. Similar to the original fiber density a higher strain, are not activated in the lower range function, we introduce a normalized average cross- of the strain, W iso is only associated with the base sectional area distribution function modeled as a π - matrix and W aniso with collagen fibers. Therefore, periodic Von Mises distribution for each family of fiber bundles. We derive the new invariant for one = + W W ( F ) W ( F , a 01 a , ). (3) family of fibers in this section. iso aniso 02 It is usually sufficient to use a Neo-Hookean model Notice that I 9 in Equation 7 is a constant. Also, for the isotropic part of the strain energy function because most biological tissues may be considered associated with the ground substance in most cases incompressible, I 3 and J are also constants with the (Holzapfel & Ogden 2010). For the anisotropic part, value of 1. To further simplify the formulation, as in similar to the motivation under Fung’s model, Holzapfel et al. 2000, we exclude the isotropic exponential functions are chosen in a invariants – I 1 and I 2 , the invariants associated with phenomenological sense to capture the stiffening C 2 – I 5 and I 7 , and also I 8 from the anisotropic part of effect mentioned above. Therefore, we obtain, the strain energy function. Thus, (4) (5) It is worth pointing out that I 4 and I 6 have specific (6) physical meanings, each representing the square of the stretch ratios in the direction of a 01 and a 02 , where c and k i (i=1, 2) are material parameters, respectively. while (i=1, 2) are dimensionless parameters which In previous studies, fibers of the same type (collagen will affect the shape of the stress-strain curve. or elastin) are treated as having the same stiffness. We derive a new structure tensor and a new Therefore, the number of fibers in a certain direction invariant is sufficient to describe the stiffness of the material (7) in that direction. As a result, the constructed fiber density function proposed by Lanir, Gasser and (8) Holzapfel only counts the number of fibers in where the modified dispersion parameter and different orientations. However, in some tissues, it has been observed that the fiber or fiber bundle I modified invariant are µ 4 diameters vary significantly with fiber orientation within each family [3,4]. This introduces a second (44) distributed parameter that should be incorporated in the formulation. To model these characteristics, the fiber density function obtained by Holzapfel et al is The fiber distribution is initially aligned about modified [6]. In this framework, all the fiber bundles in the same family are treated as the same the original dominant fiber angle 0°. The area