Bioinspired Functionally Graded Shells and Plates: Exact Solutions

Abstract

Functional grading of biological tissues had been observed long before the concept of functionally graded materials was introduced in engineering. An example of a typical tissue is found a tendon-to-bone insertion site. At the microscopic level, grading of the orientation of collagen fibers combined with grading of the mineral content in the fibrocartilage produces a strong and energy absorbent attachment that is not reproduced upon healing after injury. Another biological example is sclera in the eye where variable orientation of collagen fibers may serve the function of minimizing the intraocular pressure and protecting against a development of glaucoma. A different stiffness of trabecular and cortical bones may also be attributed to structural reasons, a stiffer cortical bone being on the exposed surface, while a more compliant trabecular bone occupying the interior. Engineering problems considered in this paper and inspired by biological examples utilize grading of the material to optimize the stress distribution and absorb maximum amounts of energy. Exact solutions are demonstrated for cylinders graded in the radial direction and subject to axial loading and for radially graded spheres undergoing axisymmetric pressure. An approach to optimization of spherical caps with an opening at the apex is also discussed based on the grading concept reflecting the observations on sclera. Examples are shown for foam shells where the assumed variation of the stiffness tensor is consistent with experimentally proven micromechanics.

Department(s)

Mechanical and Aerospace Engineering

International Standard Book Number (ISBN)

978-160595124-9

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 DEStech Publications, All rights reserved.

Publication Date

01 Jan 2014

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