Abstract
Euler buckling is the elastic instability of a column subjected to longitudinal compression forces at its ends. The buckling instability occurs when the compressing load reaches a critical value and an infinitesimal fluctuation leads to a large amplitude deflection. Since Euler's original study, this process has been extensively studied in homogeneous, isotropic, linear-elastic solids. Here, we examine the nature of the buckling in inhomogeneous soft composite materials. In particular, we consider a soft host with liquid inclusions both large and small relative to the elastocapillarity length, which lead to softening and stiffening of a homogeneous composite respectively. However, by imposing a gradient of the inclusion volume fraction or by varying the inclusion size we can deliberately manipulate the spatial structure of the composite properties of a column and thereby control the nature of Euler buckling.
Highlights
An elastic beam under a sufficiently large compressible axial load collapses or buckles when an infinitesimal deflection destroys the equilibrium
We formulate the equilibrium configurations of inhomogeneous compressed rods in terms of planar elastica, we derive the corresponding approximation of small deflections, we introduce the key concepts of static stability of elastic rods adapted to the particular case at hand, we review the generalized Eshelby and Peierls theories for composite elastic materials with capillary effects, and we describe the nondimensionalization of the problem
We have studied the buckling of inhomogeneous soft composite columns or rods with axially varying elasticity
Summary
An elastic beam under a sufficiently large compressible axial load collapses or buckles when an infinitesimal deflection destroys the equilibrium. Kirchhoff [15,16] and Clebsch [17,18] described the basic theoretical analysis of elastic rods by replacing the stress acting inside a volume element with a resultant force and the moment vectors attached to a body defining curve. By determining how the spatial variation of R and φ modify Euler buckling we provide a framework of either tailoring a material response or explaining observations in naturally occurring soft composites Canonical examples of the latter include slender composite structures, such as insect extremities [26,27], plant stems [28,29], bones [30], bacterial biofilaments [31], and plant tendrils [32].
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