Related papers: Buckling transition and boundary layer in non-Eucl…
Suspensions of colloidal microplates in contoured 2D elastic fluids sheets are dominated by the bending mechanics and shear rigidity of the plates and the contrasting in-plane shear flow of the 2D fluid. Using the phase separated…
We study two closely related, nonlinear models of a viscoplastic solid. These models capture essential features of plasticity over a wide range of strain rates and applied stresses. They exhibit inelastic strain relaxation and steady flow…
A discrete tensegrity framework can be thought of as a graph in Euclidean n-space where each edge is of one of three types: an edge with a fixed length (bar) or an edge with an upper (cable) or lower (strut) bound on its length. Roth and…
We model the formation and evolution of wrinkles in a floating elastic sheet under uniaxial compression. This is a canonical setup in the study of wrinkling, and whilst its static equilibrium configuration is well characterised, its…
This work investigates the morphological stability of a soft body composed of two heavy elastic layers, attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the…
In our analysis, we show that Efrati et al.'s publication is inconsistent with the mathematics of plate theory. However it is more consistent with the mathematics of shell theory, but with an incorrect strain tensor. Thus, the authors'…
The theory of Nested Figures of Equilibrium, expanded in Papers I and II, is investigated in the limit where the number of layers of the rotating body is infinite, enabling to reach full heterogeneity. In the asymptotic process, the…
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…
We investigate a specific finite element model to study the thermoelastic behavior of an elastic body within the context of nonlinear strain-limiting constitutive relation. As a special subclass of implicit relations, the thermoelastic…
We consider the inverse problem of determining the possible presence of an inclusion in a thin plate by boundary measurements. The plate is made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. The…
Compressive mechanical stress exceeding a critical value leads to the formation of periodic surface buckling patterns in film-substrate systems. A comprehensive understanding of this buckling phenomenon is desired in applications where the…
This paper presents a finite element model for the analysis of crack-tip fields in a transversely isotropic strain-limiting elastic body. A nonlinear constitutive relationship between stress and linearized strain characterizes the material…
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…
The elastocapillary instability of a flexible plate plunged in a liquid bath is analysed theoretically. We show that the plate can bend due to two separate destabilizing mechanisms, when the liquid is partially wetting the solid. For…
In this paper, we derive a dynamic surface elasticity model for the two-dimensional midsurface of a thin, three-dimensional, homogeneous, isotropic, nonlinear gradient elastic plate of thickness $h$. The resulting model is parameterized by…
In this note, we address several issues, including some raised in recent works and commentary, related to bending measures and energies for plates and shells, and certain of their invariance properties. We discuss overlaps and distinctions…
We analyze the asymptotic behavior of a junction problem between a plate and a perpendicular rod made of a nonlinear elastic material. The two parts of this multi-structure have small thicknesses of the same order $\delta$. We use the…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
Designing smart devices with tunable shapes has important applications in industrial manufacture. In this paper, we investigate the nonlinear deformation and the morphological transitions between buckling, necking, and snap-through…
We prove that, in the limit of vanishing thickness, equilibrium configurations of inhomogeneous, three-dimensional non-linearly elastic rods converge to equilibrium configurations of the variational limit theory. More precisely, we show…