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Register a new userA refined dynamic finite-strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle
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Based on previous work for the static problem, in this paper we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out the bending effect as well as to reduce the number of shell constitutive relations, a further refinement is performed, which leads to a refined dynamic finite-strain shell theory with only two shell constitutive relations (deducible from the given three-dimensional (3D) strain energy function) and some new insights are also deduced. By using the weak formulation of the shell equations and the variation of the 3D Lagrange functional, boundary conditions and the two-dimensional (2D) shell virtual work principle are derived. As a benchmark problem, we consider the extension and inflation of an arterial segment. The good agreement between the asymptotic solution based on the shell equations and that from the 3D exact one gives verification of the former. The refined shell theory is also applied to study the plane-strain vibrations of a pressurized artery, and the effects of the axial pre-stretch, pressure and fibre angle on the vibration frequencies are investigated in detail.
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Single layer core/shell structures consisting of graphene as core and hexagonal boron nitride as shell are studied using first-principles plane wave method within density functional theory. Electronic energy level structure is analysed as a function of the size of both core and shell. It is found that the confinement of electrons in two dimensional graphene quantum dot is reduced by the presence of boron nitride shell. The energy gap is determined by the graphene states. Comparison of round, hexagonal, rectangular and triangular core/shell structures reveals that their electronic and magnetic states are strongly affected by their geometrical shapes. The energy level structure, energy gap and magnetic states can be modified by external charging. The core part acts as a two-dimensional quantum dot for both electrons and holes. The capacity of extra electron intake of these quantum dots is shown to be limited by the Coulomb blockade in two-dimension.
Context: We study the impact of two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from a one-dimensional stellar evolution code are used to produce a model of a large stellar convection zone representative of a young low-mass star. Methods: We perform hydrodynamic implicit large-eddy simulations of compressible convection using the MUltidimensional Stellar Implicit Code (MUSIC). Because MUSIC has been designed to use realistic stellar models produced from one-dimensional stellar evolution calculations, MUSIC simulations are capable of seamlessly modeling a whole star. Simulations in two-dimensional spherical shells that have different radial extents are performed over hundreds of convective turnover times, permitting the collection of well-converged statistics. Results: We evaluate basic statistics of the convective turnover time, the convective velocity, and the overshooting layer. These quantities are selected for their relevance to one-dimensional stellar evolution calculations, so that our results are focused toward the 321D link. The inclusion in the spherical shell of the boundary between the radiative and convection zones decreases the amplitude of convective velocities in the convection zone. The inclusion of near-surface layers in the spherical shell can increase the amplitude of convective velocities, although the radial structure of the velocity profile established by deep convection is unchanged. The impact from including the near-surface layers depends on the speed and structure of small-scale convection in the near-surface layers. Larger convective velocities in the convection zone result in a commensurate increase in the overshooting layer width and decrease in the convective turnover time. These results provide support for non-local aspects of convection.
In this paper we combine the Parareal parallel-in-time method together with spatial parallelization and investigate this space-time parallel scheme by means of solving the three-dimensional incompressible Navier-Stokes equations. Parallelization of time stepping provides a new direction of parallelization and allows to employ additional cores to further speed up simulations after spatial parallelization has saturated. We report on numerical experiments performed on a Cray XE6, simulating a driven cavity flow with and without obstacles. Distributed memory parallelization is used in both space and time, featuring up to 2,048 cores in total. It is confirmed that the space-time-parallel method can provide speedup beyond the saturation of the spatial parallelization.
In order to accelerate implementation of hyperelastic materials for finite element analysis, we developed an automatic numerical algorithm that only requires the strain energy function. This saves the effort on analytical derivation and coding of stress and tangent modulus, which is time-consuming and prone to human errors. Using the one-sided Newton difference quotients, the proposed algorithm first perturbs deformation gradients and calculate the difference on strain energy to approximate stress. Then, we perturb again to get difference in stress to approximate tangent modulus. Accuracy of the approximations were evaluated across the perturbation parameter space, where we find the optimal amount of perturbation being $10^{-6}$ to obtain stress and $10^{-4}$ to obtain tangent modulus. Single element verification in ABAQUS with Neo-Hookean material resulted in a small stress error of only $7times10^{-5}$ on average across uniaxial compression and tension, biaxial tension and simple shear situations. A full 3D model with Holzapfel anisotropic material for artery inflation generated a small relative error of $4times10^{-6}$ for inflated radius at $25 kPa$ pressure. Results of the verification tests suggest that the proposed numerical method has good accuracy and convergence performance, therefore a good material implementation algorithm in small scale models and a useful debugging tool for large scale models.
Three-dimensional (3D) imaging techniques appeal to a broad range of scientific and industrial applications. Typically, projection slice theorem enables multiple two-dimensional (2D) projections of an object to be combined in the Fourier domain to yield a 3D image. However, traditional techniques require a significant number of projections. The significant number of views required in conventional tomography not only complicates such imaging modalities, but also limits their ability to image samples that are sensitive to radiation dose or are otherwise unstable in time. In this work, we demonstrate through numerical simulations and an eigenvalue analysis that a recently developed technique called ankylography enables 3D image reconstruction using much fewer views than conventional tomography. Such a technique with the ability to obtain the 3D structure information from a few views is expected to find applications in both optical and x-ray imaging fields.
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