Related papers: Design of pre-stressed plate-strips to cover non-d…
The paper deals with the fabrication of nano-shells from pre-stressed nano-plates release. Due to geometrical and technological restrictions we have to cover a given surface with three-dimensional thin ribbons. We discuss the key role of…
Multistable structures are objects with more than one stable conformation, exemplified by the simple switch. Continuum versions are often elastic composite plates or shells, such as the common measuring tape or the slap bracelet, both of…
Bistable shells can reversibly change between two stable configurations with very little energetic input. Understanding what governs the shape and snap-through criteria of these structures is crucial for designing devices that utilize…
A flat plate can bend into a curved surface if it experiences an inhomogeneous growth field. In this article a method is described that numerically determines the optimal growth field giving rise to an arbitrary target shape, optimizing for…
We examine the stability of a soft dielectric plate deformed by the coupled effects of a mechanical pre-stress applied on its lateral faces and an electric field applied through its thickness under charge control. The electric field is…
The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian…
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive…
We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…
Residual stresses may appear in elastic bodies due to the formation of misfits in the micro-structure, driven by plastic deformations, thermal or growth processes. They are especially widespread in living matter, resulting from the dynamic…
In this paper, we study the problem of shape-programming of incompressible hyperelastic shells through differential growth. The aim of the current work is to determine the growth tensor (or growth functions) that can produce the deformation…
Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the…
The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication…
In this paper, a theoretical scheme is proposed for shape-programming of thin hyperelastic plates through differential growth. First, starting from the 3D governing system of a hyperelastic (neo-Hookean) plate, a consistent finite-strain…
A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding…
A theory is presented showing that cloaking of objects from antiplane elastic waves can be achieved by elastic pre-stress of a neo-Hookean nonlinear elastic material. This approach would appear to eliminate the requirement of metamaterials…
Shells are ubiquitous thin structures that can undergo large nonlinear elastic deformations while exhibiting combined modes of bending and stretching, and have profound modern applications. In this paper, we have proposed a new Isogeometric…
Orthotropic shell structures are ubiquitous in biology and engineering, from bacterial cell walls to reinforced domes. We present a rescaling transformation that maps an orthotropic shallow shell to an isotropic one with a different local…
Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic…
While isotropic in-plane swelling problems for thin elastic sheets have been studied extensively in recent years, many shape-programmable materials, including nematic solids and 3D-printed structures, are anisotropic, as are most industrial…
Stress-induced shaping, which deforms thin substrates utilizing stressed surface coatings, has enabled and enhanced a host of applications in past decades. Owing to the touchless fabrication process compatible with modern planar technology,…