Wrinkling composite sheets
We examine the buckling shape and critical compression of confined inhomogeneous composite sheets lying on a liquid foundation. The buckling modes are controlled by the bending stiffness of the sheet, the density of the substrate, and the size and the spatially dependent elastic coefficients of the...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Royal Society of Chemistry
2023
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| Summary: | We examine the buckling shape and critical compression of confined inhomogeneous composite
sheets lying on a liquid foundation. The buckling modes are controlled by the bending stiffness of
the sheet, the density of the substrate, and the size and the spatially dependent elastic coefficients
of the sheet. We solve the beam equation describing the mechanical equilibrium of a sheet when its
bending stiffness varies parallel to the direction of confinement. The case of a homogeneous bending
stiffness exhibits a degeneracy of wrinkled states for certain lengths of the confined sheet; we explain
this degeneracy using an asymptotic analysis valid for long sheets, and show that it corresponds to
the switching of the sheet between symmetric and antisymmetric buckling modes. This degeneracy
disappears for spatially dependent elastic coefficients. Medium length sheets buckle similarly to
their homogeneous counterparts, whereas the wrinkled states in large length sheets concentrate the
bending energy towards the soft regions of the sheet. |
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