George Akhras

Finite strip analysis of anisotropic laminated composite plates using higher-order shear deformation theory

Abstract In the present study, a finite strip method for the elastic analysis of anisotropic laminated composite plates is developed according to higher-order shear deformation theory. This theory accounts for the parabolic distribution of the transverse shear strains through the thickness of the plate and for zero transverse shear stresses on the plate surfaces. In comparison with the finite strip method based on first-order shear deformation theory, the present method gives improved results while using approximately the same number of degrees of freedom. It also eliminates the need for shear correction factors in calculating the transverse shear stiffness.

Comprehensive three dimensional hysteretic magnetomechanical model and its validation with experimental ⟨110⟩ single-crystal iron-gallium behavior

A unique modeling approach is introduced, which can track the hysteretic evolution of volume fractions of magnetic moments in several directions and has the potential to predict the magnetomechanical behavior accurately along several important crystallographic directions. The model is benchmarked against the [110] oriented single-crystal Fe82Ga18 experimental magnetomechanical behavior. The different physical effects such as flipping of moments between easy directions versus gradual rotation of moments from easy toward the noneasy directions can be captured by this model. The ability of this model to capture these effects along with hysteresis, some of which are lacking in the previous models, are explained.

Progressive Failure Analysis of Composite Plates by the Finite Strip Method

Abstract In the present study, a finite strip method for the progressive failure of anisotropic composite laminates is developed based on the higher-order shear deformation theory and Lees strength criterion. This method produces results in a good agreement with existing analytical and numerical solutions. The effects of fibre orientation and the number of plies on the load-carrying capacity are also investigated in numerical examples.

Stability analysis of anisotropic laminated composite plates by finite strip method

Abstract The finite strip method has been applied to the stability analysis of rectangular shear-deformable composite laminates. However, for the plates with two opposite simply supported sides, the existing analysis was restricted to the symmetrical cross-ply laminates under compression loading. In the present study, by selecting proper displacement functions and including the coupling between different series terms, the finite strip method is extended to the stability analysis of any anisotropic laminated plates under arbitrary in-plane loading. Furthermore, a number of numerical results are presented to show the effects of thickness, fibre orientation and stacking sequence on the buckling loads.

A three dimensional rate equation model for the dynamical sensing effect of magnetostrictive Galfenol

A three-dimensional computational model for the dynamical sensing response of Galfenol magnetostrictive devices based on the rate equations is developed. The sensing model calculates the fraction of magnetic moments oriented along each of the energetically preferred directions of the crystal as a function of time, which can then be used to determine the time evolution of the total magnetization. Results from this 3D sensing model are compared to quasistatic loading experiments for the validation and extraction of phenomenological parameters. Using these extracted parameters, calculations are made for the dynamical sensing response. Thermodynamic effects are also incorporated into the model by a Boltzmann distribution of the magnetic moments in the crystal. Good quantitative agreement between the model and experiment at low magnetic bias fields and qualitative agreement at higher magnetic bias fields is obtained.

Modelling the quasistatic and dynamical sensing response of Galfenol-based magnetostrictive devices

A computational model for the quasistatic and dynamical response of Galfenol based magnetostrictive devices in the sensing configuration is presented. The model calculates the fraction of magnetic moments oriented along the preferred orientations within the crystal as a function of time using a self-consistent rate equation technique. These magnetic moment fractions are then used to determine the total magnetization as a function of time. The model is compared to experiments for uniaxial, compressive, and quasistatic loading. Predictive calculations are presented for dynamical loading. Eddy currents and finite transition times lead to increasing hysteresis as the frequency increases.

Modeling the dynamical response of ferromagnetic shape memory alloy actuators using a dissipative Euler–Lagrange equation

A phenomenological dynamical model of ferromagnetic shape memory alloy based actuators is developed. The parameters of effective mass density, viscosity, and elasticity are defined and used in a dissipative Euler–Lagrange equation to determine the martensite variant fraction and strain as a function of time. These three parameters are determined by fitting our simulations to recent experiments on a NiMnGa based actuator. In addition to the simplicity of only three fitting parameters to model martensite variant evolution, the present model is a convenient formulation of the problem because it incorporates self-consistently all stresses and loads in the system.

One and three dimensional models for the dynamical sensing response of Galfenol with applications to energy harvesting

One and three-dimensional computational models for the dynamical sensing response of Galfenol based magnetostrictive devices are developed. The sensing model calculates the fraction of magnetic moments oriented along each of the energetically preferred directions of the crystal as a function of time, which can then be used to determine the time evolution of the total magnetization. Results from the sensing model are compared to quasi-static loading experiments for validation and extraction of phenomenological parameters. As a sample application, the sensing model is incorporated into an AC energy harvesting circuit to predict the magnetization and energy harvested under dynamical loading conditions.

Modeling a Galfenol based stress sensor capable of sensing up to three axial stresses

A three dimensional rate equation model can be used to calculate the magnetization response in a Galfenol sample under the application of any or all components of stress (axial and shear) [P. Weetman and G. Akhras, J. Appl. Phys. 109, 043902 (2011)]. For a Galfenol based stress sensor, one is essentially interested in the inverse of that calculation: from magnetization measurements, determine which stresses are acting on the system. A conceptual design of a Galfenol based three dimensional dynamical sensor is presented. One assumes the time-varying magnetization and its time derivative in all three directions can be measured for different external magnetic bias fields at different points in time. It is shown that the rate equation model can be used to calculate all the stresses acting on the system from knowledge of the magnetization and the time derivative of magnetization. The necessary calculations are presented and then applied to a sample set of magnetization values, which were generated from a bench...

Preliminary model of a 3D dynamically loaded Galfenol based stress sensor using rate equations

The Villari effect of magnetostrictive materials, a change in magnetization due to an external stress, is used for sensing applications. For a dynamically loaded sensor, one measures the time-varying magnetization on the material. The question is, from these measurements, could information be extracted about all the applied stresses (the three axial and the three shear) on the material? In a previously developed rate-equation model [P. Weetman and G. Akhras, SPIE Proceedings Vol. 7644, 76440R], essentially the inverse of this problem was discussed where the input was a set of known stresses and the output was the calculated resulting magnetizations. A preliminary conceptual design of a Galfenol based 3D dynamical sensor is presented. In the proposed prototype sensing device, one can measure the time-varying magnetization and its derivative in all three directions. Incorporating the previously developed 3D rate equation model, a new model is developed pertaining to this sensor. It will be shown that, under certain conditions, all stresses can be found from the magnetization measurements. The required calculations are presented and then performed on a sample set of magnetization data for validation. From this model, the implications to future sensing devices are discussed as well as suggestions on improvements to the model and the prototype.