Search Results (6)

We numerically studied localized elastic distortions in curved, effectively two-dimensional nematic shells. We used a mesoscopic Landau-de Gennes-type approach, in which the orientational order is theoretically considered by introducing the appropriate tensor nematic order parameter, while the three-dimensional shell shape is described by the curvature tensor. We limited our theoretical consideration to axially symmetric shapes of nematic shells. It was shown that in the surface regions of stomatocyte-class nematic shell shapes with large enough magnitudes of extrinsic (deviatoric) curvature, the direction of the in-plane orientational ordering can be mutually perpendicular above and below the narrow neck region. We demonstrate that such line-like nematic distortion configurations may run along the parallels (i.e., along the circular lines of constant latitude) located in the narrow neck regions of stomatocyte-like nematic shells. It was shown that nematic distortions are enabled by the order reconstruction mechanism. We propose that the regions of nematic shells that are strongly elastically deformed, i.e., topological defects and line-like distortions, may attract appropriately surface-decorated nanoparticles (NPs), which could potentially be useful for the controlled assembly of NPs. Full article

This paper employs the discrete element method (DEM) to study the mechanical properties of artificial crushed stone. Different grain shapes and gradations are considered, and three types of 3D artificial stone models are generated based on the statistical conclusions in the relevant literature and the observed data. Concurrently, the 3D models of the artificial stones are divided into three groups by their shape parameters (elongation index and flatness index). Furthermore, three types of gradation with different Cu (coefficient of uniformity) and Cc (coefficient of curvature) are also considered. Then, several 3D triaxial compression tests are conducted with the numerical methods to determine the relationship between the grain shapes and their mechanical characteristics. The test results showed that there was a positive correlation between a particles’ angularities and the maximum deviatoric stress in the triaxial compression tests when there were obvious distinctions between the particles. In addition, gradations had a conspicuous impact on the stiffness of the sample. The stress–strain curve possessed a larger slope when the coefficient of curvature was bigger. In terms of shear strength, the results in this paper align well with the traditional shear strength envelope which are convincing for the dependability of the methods used in this paper. The radial deformation capacity and volume strain of the specimen during the triaxial compression tests are also examined. It is believed that there were great differences in deformability between different samples. At the mesoscopic level, the change in coordination number is identified as the fundamental reason for the change in volume strain trend. Full article

The general strain gradient theory of Mindlin is re-visited on the basis of a new set of higher-order metrics, which includes dilatation gradient, deviatoric stretch gradient, symmetric rotation gradient and curvature. A strain gradient bending theory for plane-strain beams is proposed based on the present strain gradient theory. The stress resultants are re-defined and the corresponding equilibrium equations and boundary conditions are derived for beams. The semi-inverse solution for a pure bending beam is obtained and the influence of the Poisson’s effect and strain gradient components on bending rigidity is investigated. As a contrast, the solution of the Bernoulli–Euler beam is also presented. The results demonstrate that when Poisson’s effect is ignored, the result of the plane-strain beam is consistent with that of the Bernoulli–Euler beam in the couple stress theory. While for the strain gradient theory, the bending rigidity of a plane-strain beam ignoring the Poisson’s effect is smaller than that of the Bernoulli–Euler beam due to the influence of the dilatation gradient and the deviatoric stretch gradient along the thickness direction of the beam. In addition, the influence of a strain gradient along the length direction on a bending rigidity is negligible. Full article

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding. Full article

This paper presents theory and simulation of viscous dissipation in evolving interfaces and membranes under kinematic conditions, known as astigmatic flow, ubiquitous during growth processes in nature. The essential aim is to characterize and explain the underlying connections between curvedness and shape evolution and the rate of entropy production due to viscous bending and torsion rates. The membrane dissipation model used here is known as the Boussinesq-Scriven fluid model. Since the standard approaches in morphological evolution are based on the average, Gaussian and deviatoric curvatures, which comingle shape with curvedness, this paper introduces a novel decoupled approach whereby shape is independent of curvedness. In this curvedness-shape landscape, the entropy production surface under constant homogeneous normal velocity decays with growth but oscillates with shape changes. Saddles and spheres are minima while cylindrical patches are maxima. The astigmatic flow trajectories on the entropy production surface, show that only cylinders and spheres grow under the constant shape. Small deviations from cylindrical shapes evolve towards spheres or saddles depending on the initial condition, where dissipation rates decrease. Taken together the results and analysis provide novel and significant relations between shape evolution and viscous dissipation in deforming viscous membrane and surfaces. Full article

To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications. Full article