Related papers: Straightening: Existence, uniqueness and stability
Thin elastic two-dimensionnal systems under compressive stresses may relieve part of their stretching energy by developing out of plane undulations. We investigate experimentally and theoretically the indentation of an elastic disk…
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 paper is a theoretical and numerical study of the uniform growth of a repeating sinusoidal imperfection in the line of a strut on a nonlinear elastic Winkler type foundation. The imperfection is introduced by considering an initially…
The stability analysis of elastic rings subjected to various loading conditions is examined, focusing on stable and unstable configurations. The harmonic balance method is employed to investigate the stability range under different loading…
The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length {eta}, subject to pure bending, is considered. The two incremental equilibrium equations corresponding to a nonlinear pre-buckling state of…
We investigate the deformation of a longitudinally stretched rectangular sheet which is clamped at two opposite boundaries and free otherwise with experiments, numerical analysis and asymptotic analysis of the biharmonic elastic equation…
The classical flexure problem of non-linear incompressible elasticity is revisited assuming that the bending angle suffered by the block is specified instead of the usual applied moment. The general moment-bending angle relationship is then…
We prove existence and uniqueness for solutions to equilibrium problems for free-standing, traction-free, non homogeneous crystals in the presence of plastic slips. Moreover we prove that this class of problems is closed under G-convergence…
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…
A creased thin disk is generally bistable since the crease could be pushed through to form a stable cone-like inverted state with an elastic singularity corresponding to the vertex of the conical surface. In a recent study, we found that…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
We evaluate the loss of stability of axially compressed slender and thick-walled tubes subject to a residual stress distribution. The nonlinear theory of elasticity, when used to analyze the underlying deformation, shows that the residual…
In this work, we consider the existence of global solution and the exponential decay of a nonlinear porous elastic system with time delay. The nonlinear term as well as the delay acting in the equation of the volume fraction. In order to…
Surface roughness emerges naturally during mechanical removal of material, fracture, chemical deposition, plastic deformation, indentation, and other processes. Here, we use continuum simulations to show how roughness which is neither…
Thin elastic sheets bend easily, leading to mechanical instabilities such as wrinkling. Here, we investigate wrinkles at edges of bi-strips, which consist of two thin sheets, one that swells and one that does not, joined side-by-side. It is…
One of the oldest and most common structural engineering issues is the elastic buckling of circular rings under external pressure, which has a fundamental importance in a number of applications in general mechanics, engineering and…
Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric…
The elastic response of the crystalline sheet to the stretching deformation in the form of wrinkles has been extensively investigated. In this work, we extend this fundamental scientific question to the plastic regime by exploring the…
Wrinkles are often observed on the surfaces of compressed soft materials in nature. In the past few decades, the fascinating surface patterns have been studied extensively by using the linear bifurcation analysis under plane strain. The…
We analyze the buckling of a rigid thin membrane floating on a dense fluid substrate. The interplay of curvature and substrate energy is known to create wrinkling at a characteristic wavelength $\lambda$, which localizes into a fold at…