Search results for "Modulus"
showing 10 items of 491 documents
Elastic Properties of Barium Zirconate Titanate Ceramics
2011
In the paper the influence of zirconium admixture on the structure and material constants of polycrystalline ferroelectric materials BaZrxTi1-xO3 (BZT) was examined. The barium zirconate titanate samples were prepared by a conventional solid state reaction method. A single phase with perovskite structure of the samples, was identified by an X-Ray diffraction technique at room temperature. The performed EDS study revealed that the samples were perfectly sintered and the material was chemically homogeneous. The dependence of shear modulus G on sample composition is similar to the respective dependence of Young's modulus E, whereas the Poisson's ratio ν decreases with the increase in zirconium…
Stancu–Schurer–Kantorovich operators based on q-integers
2015
The goal of this paper is to introduce and study q analogue of Stancu-Schurer-Kantorovich operators. A convergence theorem using the well known Bohman-Korovkin criterion is proven and the rate of convergence involving the modulus of continuity is established. The estimate of the rate of convergence by means of the Lipshitz function is considered. Furthermore, we obtained a Voronovskaja type result for these operators. Also, we investigate the statistical approximation properties of these operators using Korovkin type statistical approximation theorem.
Modulus of continuity with respect to semigroups of analytic functions and applications
2016
Abstract Given a complex Banach space E , a semigroup of analytic functions ( φ t ) and an analytic function F : D → E we introduce the modulus w φ ( F , t ) = sup | z | 1 ‖ F ( φ t ( z ) ) − F ( z ) ‖ . We show that if 0 α ≤ 1 and F belongs to the vector-valued disc algebra A ( D , E ) , the Lipschitz condition M ∞ ( F ′ , r ) = O ( ( 1 − r ) 1 − α ) as r → 1 is equivalent to w φ ( F , t ) = O ( t α ) as t → 0 for any semigroup of analytic functions ( φ t ) , with φ t ( 0 ) = 0 and infinitesimal generator G , satisfying that φ t ′ and G belong to H ∞ ( D ) with sup 0 ≤ t ≤ 1 ‖ φ ′ ‖ ∞ ∞ , and in particular is equivalent to the condition ‖ F − F r ‖ A ( D , E ) = O ( ( 1 − r ) α ) as r …
On the continuity of discrete maximal operators in Sobolev spaces
2014
We investigate the continuity of discrete maximal operators in Sobolev space W 1;p (R n ). A counterexample is given as well as it is shown that the continuity follows under certain sucient assumptions. Especially, our research verifies that for the continuity in Sobolev spaces the role of the partition of the unity used in the construction of the maximal operator is very delicate.
Mappings of finite distortion: Removable singularities for locally homeomorphic mappings
2004
Let f be a locally homeomorphic mapping of finite distortion in dimension larger than two. We show that when the distortion of f satisfies a certain subexponential integrability condition, small sets are removable. The smallness is measured by a weighted modulus.
Theory of heterogeneous viscoelasticity
2015
We review a new theory of viscoelasticity of a glass-forming viscous liquid near and below the glass transition. In our model we assume that each point in the material has a specific viscosity, which varies randomly in space according to a fluctuating activation free energy. We include a Maxwellian elastic term and assume that the corresponding shear modulus fluctuates as well with the same distribution as that of the activation barriers. The model is solved in coherent-potential approximation (CPA), for which a derivation is given. The theory predicts an Arrhenius-type temperature dependence of the viscosity in the vanishing-frequency limit, independent of the distribution of the activatio…
Analysis of different geometrical features to achieve close-to-bone stiffness material properties in medical device: A feasibility numerical study
2021
Background and objective: In orthopedic medical devices, elasto-plastic behavior differences between bone and metallic materials could lead to mechanical issues at the bone-implant interface, as stress shielding. Those issue are mainly related to knee and hip arthroplasty, and they could be responsible for implant failure. To reduce mismatching-related adverse events between bone and prosthesis mechanical properties, modifying the implant's internal geometry varying the bulk stiffness and density could be the right approach. Therefore, this feasibility study aims to assess which in-body gap geometry improves, by reducing, the bulk stiffness. Methods: Using five finite element models, a unia…
KNOWN RESIDUAL STRESS SPECIMENS USING OPPOSED INDENTATION
2009
In order to test new theories for residual stress measurement or to test the effects of residual stress on fatigue, fracture, and stress corrosion cracking, a known stress test specimen was designed and then fabricated, modeled, and experimentally validated. To provide a unique biaxial stress state, a 60 mm diameter 10 mm thick disk of 316L stainless steel was plastically compressed through the thickness with an opposing 15 mm diameter hard steel indenters in the center of the disk. For validation, the stresses in the specimen were first mapped using time-of-flight neutron diffraction and Rietveld full pattern analysis. Next, the hoop stresses were mapped on a cross section of two disks usi…
Testing of “Global Young's Modulus E” on a rehabilitated masonry bell tower in Venice
2017
Abstract This paper shows the effectiveness of the techniques chosen for the rehabilitation of the historic “Sant'Andrea” masonry bell-tower in Venice. The achieved rehabilitation projects based on the indenting technique consisting in removing and replacing bricks in bad conditions, and on the isolation of the bells at the belfry quote, respect all the constraints represented by the aesthetic and structural features of the building. Moreover, the experimental analyses used to define the existing state of the structure are described in detail. The tower is also an interesting case study for the validation of the proposed method to determine the global young's modulus in a rehabilitated maso…
A full body musculoskeletal model based on flexible multibody simulation approach utilised in bone strain analysis during human locomotion
2011
Load-induced strains applied to bone can stimulate its development and adaptation. In order to quantify the incident strains within the skeleton, in vivo implementation of strain gauges on the surfaces of bone is typically used. However, in vivo strain measurements require invasive methodology that is challenging and limited to certain regions of superficial bones only such as the anterior surface of the tibia. Based on our previous study [Al Nazer et al. (2008) J Biomech. 41:1036-1043], an alternative numerical approach to analyse in vivo strains based on the flexible multibody simulation approach was proposed. The purpose of this study was to extend the idea of using the flexible multibod…