Related papers: A topological counting rule for shells
Given a manifold with boundary, one can consider the space of subsurfaces of this manifold meeting the boundary in a prescribed fashion. It is known that these spaces of subsurfaces satisfy homological stability if the manifold has at least…
For a large class of tilings, including the Penrose tiling in two dimension as well as the icosahedral ones in 3 dimension, the continuous hull of such a tiling inherits a minimal lamination structure with flat leaves and a transversal…
In the paper, we consider the rigidity problem of the infinite hexagonal triangulation of the plane under the piecewise linear conformal changes introduced by Luo in [5]. Our result shows that if a geometric hexagonal triangulation of the…
Topology captures the essence of what remains unchanged under a transformation. In this study, a topological invariant called super conformality was found to preserve a critical angle between the constitutive plane and its second order…
For homogeneous, isotropic, nonlinearly elastic materials, the form of the homogeneous deformation consistent with the application of a Cauchy shear stress is derived here for both compressible and incompressible materials. It is shown that…
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…
In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…
Isostasy explains why observed gravity anomalies are generally much weaker than what is expected from topography alone, and why planetary crusts can support high topography without breaking up. Classical isostasy, however, neglects internal…
The characterization and mechanical stability of charged thin shells with spherical symmetry are analyzed in the context of Einstein-Born-Infeld theory. The study of stability is performed by considering linearized perturbations preserving…
We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a…
Experimentally measuring the elastic properties of thin biological surfaces is non-trivial, particularly when they are curved. One technique that may be used is the indentation of a thin sheet of material by a rigid indenter, whilst…
This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit…
Liquid shells (e.g. double emulsions, vesicles etc.) are susceptible to interfacial instability and rupturing when driven out of mechanical equilibrium. This poses a significant challenge for the design of liquid shell based micro-machines,…
Entangled networks are ubiquitous in tissues, polymers, and fabrics. However, their mechanics remain insufficiently understood due to the complexity of the topological constraints at the network level. Here, we develop a mathematical…
A 3D fluid-structure interaction solver based on an improved weakly-compressible moving particle simulation (WC-MPS) method and a geometrically nonlinear shell structural model is developed and applied to hydro-elastic free-surface flows.…
In the context of finite elasticity, we propose plate models describing the spontaneous bending of nematic elastomer thin films due to variations along the thickness of the nematic order parameters. Reduced energy functionals are deduced…
Based on a coordinate transformation approach, Pendry {\it et al.} have reported electromagnetically anisotropic and inhomogeneous shells that, in theory, completely shield an interior structure of arbitrary size from electromagnetic fields…
Snap-fits are versatile mechanical designs in industrial products, which enable the repeated assembling and disassembling of two solid parts. This important property is attributed to a fine balance between geometry, friction, and bending…
We carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of Gamma-convergence. In contrast to what one naturally would expect, our result shows that the limiting…
We systematically explore the self-assembly of semi-flexible polymers in deformable spherical confinement across a wide regime of chain stiffness, contour lengths and packing fractions by means of coarse-grained molecular dynamics…