Non-Euclidean plates are thin elastic bodies having no stress-free configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a three-dimensional reference metric, which may not necessarily be immersible in physical space. Here, based on a recently developed theory for such bodies, we characterize the transition from flat to buckled e...

Inspired by the imbricated scale-tissue flexible armor of elasmoid fish, we design hybrid stiff plate/soft matrix material architectures and reveal their ability to provide protection against penetration while preserving flexibility. Indentation and bending tests on bio-inspired 3D-printed prototype materials show that both protection and flexibility are highly tunable by geometrical parameters...

The shoulder of a packaging machine is a developable surface that guides the packing material without stretching or tearing. The shoulder is traditionally manufactured by bending a flexible plate along a given bending curve, also without stretching ortearing. In this paper, the shoulder geometry isdescribed mathematically b methods from classical differential geometry. For a given bending curve...

Inspired by recent results on self-avoiding inextensible curves, we propose and experimentally investigate a numerical method for simulating isometric plate bending without self-intersections. We consider nonlinear two-dimensional Kirchhoff model which is augmented via addition of tangent-point energy. The resulting continuous energy finite if only the corresponding deformation injective, i.e.,...

In this study, nonlinear bending of functionally graded (FG) circular sector plates with simply supported radial edges subjected to transverse mechanical loading has been investigated. Based on the first-order shear deformation plate theory with von Karman strain-displacement relations, the nonlinear equilibrium equations of sector plates are obtained. Introducing a stress function and a potent...