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We propose a combined nodal integration and virtual element method for compressible and nearly incompressible elasticity, wherein the strain is averaged at the nodes from the strain of surrounding virtual elements. For the strain averaging procedure, a nodal averaging operator is constructed using a generalization to virtual elements of the node-based uniform strain approach for finite elements. We refer to the proposed technique as the node-based uniform strain virtual element method (NVEM). No additional degrees of freedom are introduced in this approach, thus resulting in a displacement-based formulation. A salient feature of the NVEM is that the stresses and strains become nodal variables just like displacements, which can be exploited in nonlinear simulations. Through several benchmark problems in compressible and nearly incompressible elasticity as well as in elastodynamics, we demonstrate that the NVEM is accurate, optimally convergent and devoid of volumetric locking.

In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical framework of the virtual element method. We adopt linear maximum-entropy basis functions for the discretization of field variables, although the proposed scheme is applicable to any linear meshfree approximant. In our approach, the weak form integrals are nodally integrated using nodal representative cells that carry the nodal displacements and state variables such as strains and stresses. The nodal integration is performed using the virtual element decomposition, wherein the bilinear form is decomposed into a consistency part and a stability part that ensure consistency and stability of the method. The performance of the proposed nodal integration scheme is assessed through benchmark problems in linear and nonlinear analyses of solids for small displacements and small-strain kinematics. Numerical results are presented for linear elastostatics and linear elastodynamics, and viscoelasticity. We demonstrate that the proposed nodally integrated meshfree method is accurate, converges optimally, and is more reliable and robust than a standard cell-based Gauss integrated meshfree method.

High frequency [1-500 MHz] measurements of the magnetoimpedance (MI) of glass-coated Co$_{69.4}$Fe$_{3.7}$B$_{15.9}$Si$_{11}$ microwires are carried out with various metal-to-wire diameter ratios. A twin-peak, anhysteretic behaviour is observed as a function of magnetic field. A maximum in the normalized impedance, $\Delta Z$/$Z$, appears at different values of the frequency $f$, 125, 140 and 85 MHz with the corresponding diameter ratio $p$ = 0.80, 0.55 and 0.32. We describe the measurement technique and interpret our results with a thermodynamic model that leads to a clearer view of the effects of $p$ on the maximum value of MI and the anisotropy field. The behavior of the real and imaginary components of impedance is also investigated; they display a resonance that becomes a function of the DC field $H_{DC}$ for values larger or equal to $H_{K}$ the circumferential anisotropy field for each $p $ value. These results are interpreted in terms of a rotation model of the outer shell magnetization., Comment: 8 pages, 8 figures, to appear in Sensors and Actuators (Elsevier)

High frequency [1-500 MHz] measurements of the Magneto-Impedance (MI) of glass-covered Co$_{69.4}$Fe$_{3.7}$B$_{15.9}$Si$_{11}$ microwires are carried out with various metal-to-wire diameter ratios. A twin-peak, anhysteretic behaviour is observed as a function of magnetic field. A maximum in $\Delta Z/Z$ appears at different values of the frequency $f$, 125, 140 and 85 MHz with the corresponding diameter ratio $p$ = 0.80, 0.55 and 0.32. We describe the measurement technique and interpret our results with a thermodynamic model that leads to a clearer view of the effects of $p$ on the maximum value of MI and the anisotropy field., Comment: 5 pages and 6 figures

Recent measurements of the magnetoimpedance (at a fixed frequency of 1 MHz) of cobalt-rich wires subjected to torsion stress show an asymmetry as a function of torsion angle stemming from residual anisotropies induced during wire fabrication. We interpret these measurements with a simple model based on the competition between a circumferential magnetic anisotropy and another one induced by torsional and residual stress. This allows extraction of the physical parameters of the wire and explains the positive and negative torsion cases. The agreement between theoretical and experimental results provides a firm support for the model describing the behaviour of the anisotropy field versus static magnetic field for all torsion angles., Comment: 6 pages and 3 eps figures. Revised version submitted to Phys. Rv B

A novel broad-band measurement method of the MI in thin films and ribbons is presented. It is based on the automated measurement of the reflection coefficient of a cell loaded with the sample. Illustrative results obtained with a permalloy multilayer thin film are presented and discussed., Comment: Paper submitted to International Conference on Magnetism (Rome 2003)

Giant magneto impedance (GMI) effect for as-cast Vitrovac$^{\textrm{\scriptsize\textregistered}}$ amorphous ribbons (Vacuumschmelze, Germany) in two configurations (parallel and normal to the ribbon axis) is studied over the frequency range [0.3-400 MHz] and under static magnetic fields -160 Oe $< H_{dc} < $+160 Oe. A variety of peak features and GMI ratio values, falling within a small field range, are observed and discussed., Comment: Paper submitted to International Conference on Magnetism 2003 (ICM Rome 2003)