Search results for "Isotropic"
showing 10 items of 128 documents
Spatial symmetries of the local densities
2010
Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial cases are considered.
Surface processing of TlBr single crystals used for radiation detectors
2009
Abstract The processing method for obtaining the high-quality surfaces of TlBr single crystals, providing removal of a mechanically destroyed surface layer by chemical etching, is developed. The crystals grown from the melt of purified materials by the Bridgman–Stockbarger method were used for the experiments. The Vickers microhardness as a structure-sensitive technique was used in a study of the crystal quality and properties of the plastically deformed surface layer created by cutting. It was shown that even under highly accurate conditions of cutting, the depth of the work-hardened surface layer with a high density of dislocations, vacancies and other structural defects exceeds 20 μm. Th…
NON-LINEAR MECHANICAL, ELECTRICAL AND THERMAL PHENOMENA IN PIEZOELECTRIC CRYSTALS
2003
Mechanical, electrical and thermal phenomena occurring in piezoelectric crystals were examined by non-linear approximation. For this purpose, use was made of the thermodynamic function of state, which describes an anisotropic body. Considered was the Gibbs function. The calculations included strain tensor εij = f(σkl , En, T), induction vector Dm = f(σkl , En, T) and entropy S = f(σkl , En, T) as function of stress σkl , field strength En and temperature difference T. The equations obtained apply to anisotropic piezoelectric bodies provided that the “forces” σkl , En, T acting on the crystal are known. Механічні, електричні та термічні явища у п’єзоелектричних кристалах вивчаються у неліній…
Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields
2017
The quantum dynamics of a $\hat{\mathbf{J}}^2=(\hat{\mathbf{j}}_1+\hat{\mathbf{j}}_2)^2$-conserving Hamiltonian model describing two coupled spins $\hat{\mathbf{j}}_1$ and $\hat{\mathbf{j}}_2$ under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of $\hat{\mathbf{J}}^2$ is dynamically invariant and the Hamiltonian of the total system restricted to any one of such $(j_1+j_2)-|j_1-j_2|+1$ eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical…
Molecular correlation functions for uniaxial ellipsoids in the isotropic state
2006
We perform event-driven molecular dynamics simulations of a system composed by uniaxial hard ellipsoids for different values of the aspect-ratio and packing fraction . We compare the molecular orientational-dependent structure factors previously calculated within the Percus-Yevick approximation with the numerical results. The agreement between theoretical and numerical results is rather satisfactory. We also show that, for specific orientational quantities, the molecular structure factors are sensitive to the particle shape and can be used to distinguish prolate from oblate ellipsoids. A first-order theoretical expansion around the spherical shape and a geometrical analysis of the configura…
A cohesive boundary element approach to material degradation in three-dimensional polycrystalline aggregates
2013
A new three-dimensional grain-level formulation for intergranular degradation and failure in polycrystalline materials is presented. The polycrystalline microstructure is represented as a Voronoi tessellation and the boundary element method is used to express the elastic problem for each crystal of the aggregate. The continuity of the aggregate is enforced through suitable conditions at the intergranular interfaces. The grain-boundary model takes into account the onset and evolution of damage by means of an irreversible linear cohesive law, able to address mixed-mode failure conditions. Upon interface failure, a non-linear frictional contact analysis is introduced for addressing the contact…
A three-dimensional boundary element model for the analysis of polycrystalline materials at the microscale
2012
A three-dimensional multi-domain anisotropic boundary element formulation is presented for the analysis of polycrystalline microstructures. The formulation is naturally expressed in terms of intergranular displacements and tractions that play an important role in polycrystalline micromechanics, micro-damage and micro-cracking. The artificial morphology is generated by Hardcore Voronoi tessellation, which embodies the main statistical features of polycrystalline microstructures. Each crystal is modeled as an anisotropic elastic region and the integrity of the aggregate is restored by enforcing interface continuity and equilibrium between contiguous grains. The developed technique has been ap…
Design and use of a Fatigue Test Machine in Plane Bending for Composite Specimens and Bonded Joints
2011
Polymeric and composites materials are increasingly used in industry as structural parts, so that specific information on their mechanical properties "at long term" (creep, relaxation, fatigue) are requested. The design and implementation of these components also requires that they are permanently connected together to perform certain functions. The use of adhesives in structural joints has increased over recent years thanks to the continuous development by companies which provide the market with adhesive having better and better mechanical properties. The main areas relate to the aerospace, aeronautical and automotive industries, where requirements are required for lightness and reliabilit…
A new constructive method using the theory of invariants to obtain material behavior laws
2006
International audience; The aim of this paper is to present a constructive method to derive mechanical behavior laws using the Theory of Invariants and Continuum Thermodynamics. More precisely, we want to construct, in a general way, the state or dissipation potential in a polynomial form given a set of variables V and the material symmetry group S. For this purpose, we show how to obtain a set of generators for the S-invariant polynomials of V. Then, using the Grœbner basis concept, we write all the decompositions of a polynomial of a given degree.
Role of geometry and anisotropic diffusion for modelling PO2 profiles in working red muscle
1990
A 3-dimensional analytical model of O2 diffusion in heavily working muscle is proposed which considers anisotropic, myoglobin (Mb)-facilitated O2 diffusion inside the muscle fiber and a carrier-free layer separating erythrocytes and fiber. The model is used to study the effects of some commonly applied simplifying assumptions (reduced dimensionality, neglected anisotropy) on the resulting PO2 distributions: (1) In order not to underestimate PO2 drops near erythrocytes, modelling O2 transport in 3 dimensions is important. (2) For a capillary-to-fiber ratio of 1, the results from the 2-dimensional version of the present model and from a Krogh-type model which incorporates a carrier-free layer…