On Local Mechanical Properties of Thin Pressurized Shells with Combined Geometric and Material Anisotropies
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Date
2024-01-09
Authors
Sun, Wenqian
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
Thin elastic shells are ubiquitous in nature. Indentation measurements (i.e., poking) provide a useful way for probing mechanical properties of these shell structures.
While spherical and cylindrical shells made of isotropic materials are well studied, many shells in nature have geometric anisotropy (e.g., ellipsoidal pollen grains) and/or material anisotropy (e.g., cells that have special growth directions), and mechanics of these shells are relatively less understood.
I will present some new insights on indentation responses and buckling pressure of shells with geometric and material anisotropy using the shallow-shell theory.
First, I will describe the indentation stiffness of pressurized ellipsoidal and cylindrical elastic shells that are made of isotropic materials.
We are able to derive a closed form for the indentation stiffness of shells with arbitrary asphericity and internal pressure.
Our results provide theoretical support for previous scaling and numerical results on the stiffness of ellipsoids and allow us to isolate the distinct contributions of geometry and pressure-induced stresses on shell elasticity.
I will then add the effects of material orthotropy, which assigns different elastic properties along orthogonal directions.
For a commonly used model of orthotropy, we find a simple rescaling transformation that can effectively map a rectilinearly orthotropic shallow shell to an isotropic one with a different local geometry.
With the rescaling transformation, we obtain new analytical insights for indentation responses and buckling of orthotropic shells.
Our results provide a new perspective on how isotropic and orthotropic materials are related, isolate the effect of material orthotropy on shell elasticity, and can provide experimentalists with a means to analyze the internal pressure of biological structures that are made of orthotropic materials using atomic force microscopes.
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Keywords
Elasticity, Geometry, Shells