A Structure Based Constitutive Model for Bat Wing Skins, A Soft Biological Tissue

2010 ◽  
Author(s):  
Seyul Son ◽  
Yanli Wang ◽  
N. C. Goulbourne
Keyword(s):  
Constitutive Model ◽  
Biological Tissue ◽  
Collagen Fibers ◽  
Fiber Bundles ◽  
Ground Substance ◽  
Mathematical Treatment ◽  
Soft Biological Tissue ◽  
Elastin Fiber ◽  
Wing Skin ◽  
Bat Wing

Bat wing skin is a soft biological tissue that is used to enable flight (amongst other physiological roles) in bats such as the Glossophaga Soricina. To describe and predict wing behavior during flight, a high fidelity constitutive model validated by rigorous experimentation is required. Understanding the role that the tissue microstructure plays in achievable flight patterns and maneuverability will bring closer understanding of adaptations between species that yield specific flight behaviors and will also provide a template for developing synthetic skins for biomimicry in unmanned micro air vehicles. A structural continuum model that incorporates principal structural features of the wing skin can potentially provide a link between structure and functionality. Mesoscopic elastin fiber bundles on the order of hundreds of microns are the key constituents in the structure of bat wing. They are embedded in a base matrix composed by elastic ground substance and randomly oriented collagen fibers. The wing sweeps through very large deformations during flight and the fiber bundles undergo finite strains and large rotations presumed affine in the current treatment. To date, all the biological materials studied and modeled are comprised of stiff collagen fibers. The wing skin, on the other hand, is modeled as hyperelastic with distributed elastin fiber bundles with orientations belonging to two disparate families. Two families of fiber bundles have shown prominent difference in mechanical properties. More importantly, the bundle diameters vary dramatically with respect to bundle orientation even within each family. A mathematical treatment is formulated in this paper to capture the overall effect of distribution of diameters and distribution of orientations of fiber bundles based on the framework of Gasser et al [1]. This formulation is suitable in a general case when two fiber properties both vary spatially and they can be described using distribution functions such as Von Mises distribution.

A Structurally Motivated Constitutive Model for Bat Wing Skin

2014 ◽  
Author(s):  
Alyssa J. Skulborstad ◽  
N. C. Goulbourne
Keyword(s):  
Constitutive Model ◽  
Deformation Gradient ◽  
Compressive Loading ◽  
Strain Energy Function ◽  
Tissue Response ◽  
Material Behavior ◽  
Elastin Fiber ◽  
The Matrix ◽  
Wing Skin ◽  
Bat Wing

Unique among animal flyers, bats have highly flexible and stretchable thin wing membranes. The connection between the structural constituents of bat wing skin, its material behavior, and flight abilities is not yet known. In this work we propose a structurally motivated constitutive model for the wing skin. Within a continuum mechanics framework, the proposed strain energy function for the wing skin is the sum of contributions due to the matrix and two mesoscopic fiber families, one oriented primarily spanwise consisting of elastin fiber bundles and the other family oriented chordwise consisting of muscle fibers. While the fibers are flat and straight when the wing is somewhat open, the matrix exhibits corrugations due to compressive loading from the pre-stretched spanwise fibers. This mismatch in the natural configurations of components is accounted for in the model by a decomposition of the deformation gradient of the spanwise fibers. The material parameters are fit with a procedure motivated by the underlying deformation mechanisms of the tissue corresponding to the regions of the j-shaped constitutive curves. The proposed model is fit to the first set of biaxial experimental stress-strain data for bat wing skin and captures the general features of the tissue response well.

Collagen and elastin fibers in human pulmonary alveolar walls

1988 ◽  
Vol 64 (4) ◽  
pp. 1659-1675 ◽  
Author(s):  
S. S. Sobin ◽  
Y. C. Fung ◽  
H. M. Tremer
Keyword(s):  
Transpulmonary Pressure ◽  
Collagen Fibers ◽  
Capillary Blood ◽  
Fiber Bundles ◽  
Cube Root ◽  
Inflation Pressure ◽  
Frequency Distributions ◽  
Normal Distributions ◽  
Statistical Frequency ◽  
The Mean

The morphology and morphometric data of collagen and elastin fibers in the pulmonary alveolar walls are presented. Specimens were obtained from postmortem lungs quick-frozen at specified transpulmonary pressures. Collagen was stained by silver, and elastin was stained by orcein. Photomicrographs were composed by computer. Young lungs typically show small collagen fibers that radiate from the "posts," whereas larger fiber bundles traverse the septum irrespective of capillary blood vessels. In older lungs, rings of collagen around the posts appear enlarged. Elastin bundles do not show obvious variation in pattern with age and inflation pressure. Statistical frequency distributions of the fiber width and curvature are both skewed, but the square root of the width and the cube root of the curvature have approximate normal distributions. Typically, for young lungs at transpulmonary pressure of 4 cmH2O, the mean of (width)1/2 (in micron1/2) for collagen fibers is 0.952 +/- 0.242 (SD), that of (curvature)1/3 (in micron-1/3) is 0.349 +/- 0.094. The corresponding values for elastin are 0.986 +/- 0.255 and 0.395 +/- 0.094.

scholarly journals Ferroelectricity and piezoelectricity in soft biological tissue: Porcine aortic walls revisited

2017 ◽  
Vol 111 (13) ◽  
pp. 133701 ◽  
Author(s):  
Thomas Lenz ◽  
Regina Hummel ◽  
Ilias Katsouras ◽  
Wilhelm A. Groen ◽  
Marlies Nijemeisland ◽  
...  
Keyword(s):  
Biological Tissue ◽  
Soft Biological Tissue

A Physically-Based Anisotropic Discrete Fiber Model for Fibrous Soft Tissues

2010 ◽  
Author(s):  
C. Flynn ◽  
M. B. Rubin ◽  
P. M. F. Nielsen
Keyword(s):  
Soft Tissues ◽  
Mechanical Response ◽  
Continuous Distribution ◽  
Collagen Fibers ◽  
Fiber Bundles ◽  
Parameter Study ◽  
Rabbit Skin ◽  
Pig Skin ◽  
Proposed Model ◽  
Physically Based

Physically-based fibrous soft tissue models often consider the tissue to be a collection of fibers with a continuous distribution function to represent their orientations. This study proposes a simple model for the response of fibrous connective tissues in terms of a discrete number of fiber bundles. The proposed model consists of six weighted fiber bundles orientated such that they pass through opposing vertices of an icosahedron. A novel aspect of the proposed model is the use of a simple analytical function to represent the undulation distribution of the collagen fibers. The mechanical response of the elastin fiber is represented by a neo-Hookean hyperelastic equation. A parameter study was performed to analyze the effect of each parameter on the overall response of the model. The proposed model accurately simulated the uniaxial stretching of pig skin with an 8% error-of-fit for stretch ratios up to 1.8. The model also accurately simulated the biaxial stretching of rabbit skin with a 10% error-of-fit for stretch ratios up to 1.9. The stiffness of the collagen fibers determined by the model was about 100 MPa for the rabbit skin and 900 MPa for the pig skin, which are comparable with values reported in the literature. The stiffness of the elastin fibers in the model was about 2 kPa.

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