Single-walled carbon nanotube modelling based on Cosserat surface theory

This paper studies the mechanical properties of single-walled carbon nanotubes (SWCNTs). In order to overcome the difficulty of spanning multi-scales from atomistic field to macroscopic space, the Cauchy-Born rule is applied to link the deformation of atom lattice vectors at the atomic level with the material deformation at a macro continuum level. SWCNTs are modelled as Cosserat surfaces, and the modified shell theory is adopted where a displacement field-independent rotation tensor is introduced, which describes the rotation of the inner structure of the surface, i.e. the micro-rotation. Empirical interatomic potentials are employed, so that the force and modulus fields can be computed by the derivations of potential forms from the displacement and rotation fields. A finite element approach is implemented. The Young’s modulus is predicted for SWCNTs in the paper

Diffeomorphic Metric Mapping and Probabilistic Atlas Generation of Hybrid Diffusion Imaging based on BFOR Signal Basis

We propose a large deformation diffeomorphic metric mapping algorithm to align multiple b-value diffusion weighted imaging (mDWI) data, specifically acquired via hybrid diffusion imaging (HYDI), denoted as LDDMM-HYDI. We then propose a Bayesian model for estimating the white matter atlas from HYDIs. We adopt the work given in Hosseinbor et al. (2012) and represent the q-space diffusion signal with the Bessel Fourier orientation reconstruction (BFOR) signal basis. The BFOR framework provides the representation of mDWI in the q-space and thus reduces memory requirement. In addition, since the BFOR signal basis is orthonormal, the L2 norm that quantifies the differences in the q-space signals of any two mDWI datasets can be easily computed as the sum of the squared differences in the BFOR expansion coefficients. In this work, we show that the reorientation of the $q$-space signal due to spatial transformation can be easily defined on the BFOR signal basis. We incorporate the BFOR signal basis into the LDDMM framework and derive the gradient descent algorithm for LDDMM-HYDI with explicit orientation optimization. Additionally, we extend the previous Bayesian atlas estimation framework for scalar-valued images to HYDIs and derive the expectation-maximization algorithm for solving the HYDI atlas estimation problem. Using real HYDI datasets, we show the Bayesian model generates the white matter atlas with anatomical details. Moreover, we show that it is important to consider the variation of mDWI reorientation due to a small change in diffeomorphic transformation in the LDDMM-HYDI optimization and to incorporate the full information of HYDI for aligning mDWI

Nonlinear shell problem formulation accounting for through-the-thickness stretching and its finite element implementation

We discuss a theoretical formulation of shell model accounting for through-the-thickness stretching, which allows for large deformations and direct use of 3d constitutive equations. Three different possibilities for implementing this model within the framework of the finite element method are examined: one leading to 7 nodal parameters and the remaining two to 6 nodal parameters. The 7-parameter shell model with no simplification of kinematic terms is compared to the 7-parameter shell model which exploits usual simplifications of the Green–Lagrange strains. Two different ways of implementing the incompatible mode method for reducing the number of parameters to 6 are presented. One implementation uses an additive decomposition of the strains and the other an additive decomposition of the deformation gradient. Several numerical examples are given to illustrate performance of the shell elements developed herein

Finite element model set-up of colorectal tissue for analyzing surgical scenarios

Finite Element Analysis (FEA) has gained an extensive application in the medical field, such as soft tissues simulations. In particular, colorectal simulations can be used to understand the interaction with the surrounding tissues, or with instruments used in surgical procedures. Although several works have been introduced considering small displacements, as a result of the forces exerted on adjacent tissues, FEA applied to colorectal surgical scenarios is still a challenge. Therefore, this work aims to provide a sensitivity analysis on three geometric models, taking in mind different bioengineering tasks. In this way, a set of simulations has been performed using three mechanical models named Linear Elastic, Hyper-Elastic with a Mooney-Rivlin material model, and Hyper-Elastic with a YEOH material model

Polarization Effects in Superfluid 4^4He

A theory of thermoelectric phenomena in superfluid $^4He$ is developed. It is found an estimation of the dipole moment of helium atom arising due to electron shell deformation caused by pushing forces from the side of its surrounding atoms. The corresponding electric signal generated in a liquid consisting of electrically neutral atoms by the ordinary sound waves is found extremely small. The second sound waves in superfluid $^4He$ generate the polarization of liquid induced by the relative accelerated motion of the superfluid and the normal component. The derived ratio of the amplitudes of temperature and electric polarization potential was proved to be practically temperature independent. Its magnitude is in reasonable correspondence with the experimental observations. The polarity of electric signal is determined by the sign of temperature gradient in accordance with the measurements. The problem of the roton excitations dipole moment is also discussed.Comment: 8 pages, no figure

A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth

Mollusk shells are an ideal model system for understanding the morpho-elastic basis of morphological evolution of invertebrates' exoskeletons. During the formation of the shell, the mantle tissue secretes proteins and minerals that calcify to form a new incremental layer of the exoskeleton. Most of the existing literature on the morphology of mollusks is descriptive. The mathematical understanding of the underlying coupling between pre-existing shell morphology, de novo surface deposition and morpho-elastic volume growth is at a nascent stage, primarily limited to reduced geometric representations. Here, we propose a general, three-dimensional computational framework coupling pre-existing morphology, incremental surface growth by accretion, and morpho-elastic volume growth. We exercise this framework by applying it to explain the stepwise morphogenesis of seashells during growth: new material surfaces are laid down by accretive growth on the mantle whose form is determined by its morpho-elastic growth. Calcification of the newest surfaces extends the shell as well as creates a new scaffold that constrains the next growth step. We study the effects of surface and volumetric growth rates, and of previously deposited shell geometries on the resulting modes of mantle deformation, and therefore of the developing shell's morphology. Connections are made to a range of complex shells ornamentations.Comment: Main article is 20 pages long with 15 figures. Supplementary material is 4 pages long with 6 figures and 6 attached movies. To be published in PLOS Computational Biolog

Large strain compressive response of 2-D periodic representative volume element for random foam microstructures

A numerical investigation has been conducted to determine the influence of Representative Volume Element (RVE) size and degree of irregularity of polymer foam microstructure on its compressive mechanical properties, including stiffness, plateau stress and onset strain of densification. Periodic two-dimensional RVEs have been generated using a Voronoi-based numerical algorithm and compressed. Importantly, self-contact of the foam’s internal microstructure has been incorporated through the use of shell elements, allowing simulation of the foam well into the densification stage of compression; strains of up to 80 percent are applied. Results suggest that the stiffness of the foam RVE is relatively insensitive to RVE size but tends to soften as the degree of irregularity increases. Both the shape of the plateau stress and the onset strain of densification are sensitive to both the RVE size and degree of irregularity. Increasing the RVE size and decreasing the degree of irregularity both tend to result in a decrease of the gradient of the plateau region, while increasing the RVE size and degree of irregularity both tend to decrease the onset strain of densification. Finally, a method of predicting the onset strain of densification to an accuracy of about 10 per cent, while reducing the computational cost by two orders of magnitude is suggested

A new shell formulation for graphene structures based on existing ab-initio data

An existing hyperelastic membrane model for graphene calibrated from ab-initio data (Kumar and Parks, 2014) is adapted to curvilinear coordinates and extended to a rotation-free shell formulation based on isogeometric finite elements. Therefore, the membrane model is extended by a hyperelastic bending model that reflects the ab-inito data of Kudin et al. (2001). The proposed formulation can be implemented straight-forwardly into an existing finite element package, since it does not require the description of molecular interactions. It thus circumvents the use of interatomic potentials that tend to be less accurate than ab-initio data. The proposed shell formulation is verified and analyzed by a set of simple test cases. The results are in agreement to analytical solutions and satisfy the FE patch test. The performance of the shell formulation for graphene structures is illustrated by several numerical examples. The considered examples are indentation and peeling of graphene and torsion, bending and axial stretch of carbon nanotubes. Adhesive substrates are modeled by the Lennard-Jones potential and a coarse grained contact model. In principle, the proposed formulation can be extended to other 2D materials.Comment: New examples are added and some typos are removed. The previous results are unchanged, International Journal of Solids and Structures (2017