Papers by Keyword: Anisotropic Elasticity

Abstract: An Atomic Finite Element Analysis is developed in this paper. At atomic scale, the interatomic bonding forces of Van der Waals and the covalent chemical bond are taken into account. The methodology is applied to study the behavior of carbon nanotubes, whose development has experienced strong growth in recent years and that can be used for quality mechanical reinforcement. These carbon nanotubes are formed by repeating zigzag carbon-carbon bonds. Development of atomic finite element method (AFEM) methodology can be traced back to the homogenized elastic properties of various graphene structures (single-layer graphene sheet, Zig-zag single-walled carbon nanotubes, triple-layer graphene sheet).

Abstract: The development of multi-scale modeling methods reveals to be of undeniable practical importance, especially to describe and predict the mechanical properties of structural materials. The present work aims to relate the atomic scale with the macro-scale performances. To this purpose a model of a crystalline structure based on the Atomic Finite Element Method (AFEM) is developed. The interatomic bonding forces of Van der Waals, the Coulomb electrostatic force and the covalent chemical bond are taken into account. It is then applied to Portlandite (CH) as well as to graphene (triple-layer graphene sheet, TLGSs). Elastic modulus of these structures based on AFEM is determined. Then, modeling of a single crystal can be traced back to the homogenized elastic properties of polycrystals. Elastic constants and elastic modulus by AFEM algorithm are in quite good agreement with literature experiment. These modeling method and algorithm provide some basic reference to other hexagonal structures.

Abstract: Semiconductor nanostructures are interesting objects for many microelectronic and optoelectronic applications. Nevertheless, to use them, it is necessary to control their size, their density and their spatial distribution. In the last decade, many researches have been done to control these parameters. One of these researches is the elaboration of a functional substrate inducing a lateral self-organization of nanostructures. The organization driving force is the strain field induced on the surface by a buried dislocations network. The purpose of this work is the numerical resolution, in the case of anisotropic elasticity, of the problem of a misfit dislocation located between an infinite substrate and two-layer composite. The elastic fields of stresses are calculated for various orientations of the Burgers vector, by inversion of 30x30 arrays of linear equations. The composite NiSi2/Si / (001) GaAs, that made the object of several investigations, is treated like example.

Abstract: The dislocation-induced birefringence of Silicon Carbide (SiC) is analytically and quantitatively modelled by using the adequate SiC data. A good agreement can be obtained between theory and experiment, provided that a background residual (uniaxial) stress is added to the local dislocation-induced stress. Observations are compatible with or predictable from the Burgers vector values, so that birefringence reveals an interesting tool for probing the nature of the dislocations associated, e.g., to micropipes, also faster than and complementary to the more involved transmission electron microscopy (TEM) technique.

Abstract: Averaging the anisotropy of each crystal, the macroscopic behavior of polycrystalline materials is isotropic and homogenous in terms of elastic deformation. However, the anisotropic property of each crystal influences on the local stress field ahead of a crack tip if the crack size is not large enough in comparison with the grain diameter. This brings about the change in the crack driving force (CDF) such as stress intensity factors. In the present study, in order to investigate the cause and magnitude of the change in the CDF, the finite element analysis is performed. The calculations are carried out for a single crystal model, a bi-crystal model, and a polycrystal model containing a transgranular or an intergranular semi-circular crack. The results implied that the magnitude of CDF is dependent not only on the crystal orientation but also on the deformation-constraint caused by the difference in elastic modulus of grains near the crack tip. The statistical scatter of CDF due to the random crystal orientation in a polycrystal is examined by a Monte Carlo simulation. The variation in the SIF becomes small as the crack size increases.

Abstract: By employing the Stroh formalism for plane anisotropic thermoelasticity, closed-form solutions for the orders of stress and heat flux singularities of multi-material wedges have been obtained. Several different boundary conditions are considered in this paper such as insulated or isothermal as well as free-free or fixed-fixed or free-fixed or fixed-free wedge boundaries. The solutions show that the singular orders are influenced by the wedge configurations (n wedge angles), boundary conditions, elastic constants and heat conduction coefficients, but are independent of the thermal moduli.

Abstract: The equivalence between anisotropic and isotropic elasticity is investigated in this study for two-dimensional deformation under certain conditions. That is, the isotropic elasticity can be reconstructed in the same framework of the anisotropic elasticity, when the interface between dissimilar media lies along a straight line. Therefore, many known solutions for an anisotropic bimaterial can be regarded as valid even for a bimaterial, in which one or both of the constituent materials are isotropic. The usefulness of the equivalence is that the solutions for singularities and cracks in an anisotropic/isotropic bimaterial can easily be obtained without solving the boundary value problems directly. Conservation integrals also have the similar analogy between anisotropic and isotropic elasticity so that J integral and J-based mutual integral M are expressed in the same complex forms for anisotropic and isotropic materials, when both end points of the integration paths are on the straight interface. The method of analytic continuation and Schwarz-Neumann's alternating technique are applied to singularity problems in an anisotropic or isotropic 'trimaterial', which denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. The method of analytic continuation is alternatively applied across the two parallel interfaces in order to derive the trimaterial solution in a series form from the corresponding homogeneous solution. The trimaterial solution studied here can be applied to a variety of problems, e.g. a bimaterial (including a half-plane problem), a finite thin film on semi-infinite substrate, and a finite strip of thin film, etc. Some examples are presented to verify the usefulness of the obtained solutions.