Effects of phase inhomogeneity and boundary conditions on the dynamic response of SMA wire actuators

This paper reports the simulation results from the dynamic analysis of a Shape Memory Alloy (SMA) actuator. The emphasis is on understanding the dynamic behavior under various loading rates and boundary conditions, resulting in complex scenarios such as thermal and stress gradients. Also, due to the polycrystalline nature of SMA wires, presence of microstructural inhomogeneity is inevitable. Probing the effect of inhomogeneity on the dynamic behavior can facilitate the prediction of life and characteristics of SMA wire actuator under varieties of boundary and loading conditions. To study the effect of these factors, an initial boundary value problem of SMA wire is formulated. This is subsequently solved using finite element method. The dynamic response of the SMA wire actuator is analyzed under mechanical loading and results are reported. Effect of loading rate, micro-structural inhomogeneity and thermal boundary conditions on the dynamic response of SMA wire actuator is investigated and the simulation results are reported.

Modified lattice model for mode-I fracture analysis of notched plain concrete beam using probabilistic approach

A modified lattice model using finite element method has been developed to study the mode-I fracture analysis of heterogeneous materials like concrete. In this model, the truss members always join at points where aggregates are located which are modeled as plane stress triangular elements. The truss members are given the properties of cement mortar matrix randomly, so as to represent the randomness of strength in concrete. It is widely accepted that the fracture of concrete structures should not be based on strength criterion alone, but should be coupled with energy criterion. Here, by incorporating the strain softening through a parameter ‘α’, the energy concept is introduced. The softening branch of load-displacement curves was successfully obtained. From the sensitivity study, it was observed that the maximum load of a beam is most sensitive to the tensile strength of mortar. It is seen that by varying the values of properties of mortar according to a normal random distribution, better results can be obtained for load-displacement diagram.

Implementation of a phase array diffuse optical tomographic imager

Diffuse optical tomography (DOT) using near-infrared (NIR) light is a promising tool for noninvasive imaging of deep tissue. This technique is capable of quantitative reconstructions of absorption coefficient inhomogeneities of tissue. The motivation for reconstructing the optical property variation is that it, and, in particular, the absorption coefficient variation, can be used to diagnose different metabolic and disease states of tissue. In DOT, like any other medical imaging modality, the aim is to produce a reconstruction with good spatial resolution and accuracy from noisy measurements. We study the performance of a phase array system for detection of optical inhomogeneities in tissue. The light transport through a tissue is diffusive in nature and can be modeled using diffusion equation if the optical parameters of the inhomogeneity are close to the optical properties of the background. The amplitude cancellation method that uses dual out-of-phase sources (phase array) can detect and locate small objects in turbid medium. The inverse problem is solved using model based iterative image reconstruction. Diffusion equation is solved using finite element method for providing the forward model for photon transport. The solution of the forward problem is used for computing the Jacobian and the simultaneous equation is solved using conjugate gradient search. The simulation studies have been carried out and the results show that a phase array system can resolve inhomogeneities with sizes of 5 mm when the absorption coefficient of the inhomogeneity is twice that of the background tissue. To validate this result, a prototype model for performing a dual-source system has been developed. Experiments are carried out by inserting an inhomogeneity of high optical absorption coefficient in an otherwise homogeneous phantom while keeping the scattering coefficient same. The high frequency (100 MHz) modulated dual out-of-phase laser source light is propagated through the phantom. The interference of these sources creates an amplitude null and a phase shift of 180° along a plane between the two sources with a homogeneous object. A solid resin phantom with inhomogeneities simulating the tumor is used in our experiment. The amplitude and phase changes are found to be disturbed by the presence of the inhomogeneity in the object. The experimental data (amplitude and the phase measured at the detector) are used for reconstruction. The results show that the method is able to detect multiple inhomogeneities with sizes of 4 mm. The localization error for a 5 mm inhomogeneity is found to be approximately 1 mm.

Diffuse optical tomographic imager using a single light source

Near-infrared diffuse optical tomography (DOT) technique has the capability of providing good quantitative reconstruction of tissue absorption and scattering properties with additional inputs such as input and output modulation depths and correction for the photon leakage. We have calculated the two-dimensional (2D) input modulation depth from three-dimensional (3D) diffusion to model the 2D diffusion of photons. The photon leakage when light traverses from phantom to the fiber tip is estimated using a solid angle model. The experiments are carried for single (5 and 6 mm) as well as multiple inhomogeneities (6 and 8 mm) with higher absorption coefficient in a homogeneous phantom. Diffusion equation for photon transport is solved using finite element method and Jacobian is modeled for reconstructing the optical parameters. We study the development and performance of DOT system using modulated single light source and multiple detectors. The dual source methods are reported to have better reconstruction capabilities to resolve and localize single as well as multiple inhomogeneities because of its superior noise rejection capability. However, an experimental setup with dual sources is much more difficult to implement because of adjustment of two out of phase identical light probes symmetrically on either side of the detector during scanning time. Our work shows that with a relatively simpler system with a single source, the results are better in terms of resolution and localization. The experiments are carried out with 5 and 6 mm inhomogeneities separately and 6 and 8 mm inhomogeneities both together with absorption coefficient almost three times as that of the background. The results show that our experimental single source system with additional inputs such as 2D input/output modulation depth and air fiber interface correction is capable of detecting 5 and 6 mm inhomogeneities separately and can identify the size difference of multiple inhomogeneities such as 6 and 8 mm. The localization error is zero. The recovered absorption coefficient is 93% of inhomogeneity that we have embedded in experimental phantom.

Gap model of one-way cyclic lateral load on vertical files in soft clay

For the analysis and design of pile foundation used for coastal structures the prediction of cyclic response, which is influenced by the nonlinear behavior, gap (pile soil separation) and degradation (reduction in strength) of soil becomes necessary. To study the effect of the above parameters a nonlinear cyclic load analysis program using finite element method is developed, incorporating the proposed gap and degradation model and adopting an incremental-iterative procedure. The pile is idealized using beam elements and the soil by number of elastoplastic sub-element springs at each node. The effect of gap and degradation on the load-deflection behavior. elasto-plastic sub-element and resistance of the soil at ground-line have been clearly depicted in this paper.

Structure and deformation correlation of closed-cell aluminium foam subject to uniaxial compression

We report the results of an experimental and numerical study conducted on a closed-cell aluminium foam that was subjected to uniaxial compression with lateral constraint. X-ray computed tomography was utilized to gain access into the three-dimensional (3-D) structure of the foam and some aspects of the deformation mechanisms. A series of advanced 3-D image analyses are conducted on the 3-D images aimed at characterizing the strain localization regions. We identify the morphological/geometrical features that are responsible for the collapse of the cells and the strain localization. A novel mathematical approach based on a Minkowski tensor analysis along with the mean intercept length technique were utilized to search for signatures of anisotropy across the foam sample and its evolution as a function of loading. Our results show that regions with higher degrees of anisotropy in the undeformed foam have a tendency to initiate the onset of cell collapse. Furthermore, we show that strain hardening occurs predominantly in regions with large cells and high anisotropy. We combine the finite element method with the tomographic images to simulate the mechanical response of the foam. We predict further deformation in regions where the foam is already deformed. Crown Copyright (C) 2012 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved.

An invariant subspace-based approach to the random eigenvalue problem of systems with clustered spectrum

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non-unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal-based reduced-order model of the system. Copyright (C) 2012 John Wiley & Sons, Ltd.

Effect of isothermal aging and electromigration on the microstructural evolution of solder interconnections during thermomechanical loading

The effect of different pre-aging treatments on the microstructural evolution of lead-free solder and growth of interfacial intermetallic compound layers under thermal cycling has been investigated in this work. The results show that there are distinct differences in the microstructural changes between samples with no pretreatment, samples that have experienced thermal annealing at 125A degrees C for 750 h before thermal cycling, and those that have had direct current (DC) stressing for 750 h as pretreatment. The microstructural evolution of the solder matrix is rationalized by utilizing the science of microstructures and analysis of the influence of electron flow on the precipitation phenomena. The finite-element method is utilized to understand the loading conditions imposed on the solder interconnections during cyclic stressing. The growth of intermetallic reaction layers is further analyzed by utilizing quantitative thermodynamic calculations coupled with kinetic analysis. The latter is based on the changes in the intrinsic diffusion fluxes of elements induced by current flow and alloying elements present in the system. With this concurrent approach the differences seen in thermal cycling behavior between the different pre-aging treatments can be explained.

Size-dependent free flexural vibration behavior of functionally graded nanoplates

In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method. The field variables are approximated by non-uniform rational B-splines. The nonlocal constitutive relation is based on Eringen's differential form of nonlocal elasticity theory. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG plate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of the FG nanoplate. From the detailed numerical study it is seen that the fundamental frequency decreases with increasing gradient index and characteristic internal length. (c) 2012 Elsevier B.V. All rights reserved.

An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. (C) 2012 Elsevier B.V. All rights reserved.

Wave propagation in a porous composite beam: Porosity determination, location and quantification

A wave-based method is developed to quantify the defect due to porosity and also to locate the porous regions, in a composite beam-type structure. Wave propagation problem for a porous laminated composite beam is modeled using spectral finite element method (SFEM), based on the modified rule of mixture approach, which is used to include the effect of porosity on the stiffness and density of the composite beam structure. The material properties are obtained from the modified rule of mixture model, which are used in a conventional SFEM to develop a new model for solving wave propagation problems in porous laminated composite beam. The influence of the porosity content on the group speed and also the effect of variation in theses parameters on the time responses are studied first, in the forward problem. The change in the time responses with the change in the porosity of the structure is used as a parameter to find the porosity content in a composite beam. The actual measured response from a structure and the numerically obtained time responses are used for the estimation of porosity, by solving a nonlinear optimization problem. The effect of the length of the porous region (in the propagation direction), on the time responses, is studied. The damage force indicator technique is used to locate the porous region in a beam and also to find its length, using the measured wave propagation responses. (C) 2012 Elsevier Ltd. All rights reserved.

Flux density calibration in diffuse optical tomographic systems

The solution of the forward equation that models the transport of light through a highly scattering tissue material in diffuse optical tomography (DOT) using the finite element method gives flux density (Phi) at the nodal points of the mesh. The experimentally measured flux (U-measured) on the boundary over a finite surface area in a DOT system has to be corrected to account for the system transfer functions (R) of various building blocks of the measurement system. We present two methods to compensate for the perturbations caused by R and estimate true flux density (Phi) from U-measured(cal). In the first approach, the measurement data with a homogeneous phantom (U-measured(homo)) is used to calibrate the measurement system. The second scheme estimates the homogeneous phantom measurement using only the measurement from a heterogeneous phantom, thereby eliminating the necessity of a homogeneous phantom. This is done by statistically averaging the data (U-measured(hetero)) and redistributing it to the corresponding detector positions. The experiments carried out on tissue mimicking phantom with single and multiple inhomogeneities, human hand, and a pork tissue phantom demonstrate the robustness of the approach. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE) DOI: 10.1117/1.JBO.18.2.026023]

Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part II: comparison and validation

The analytical solutions for the coupled diffusion equations that are encountered in diffuse fluorescence spectroscopy/ imaging for regular geometries were compared with the well-established numerical models, which are based on the finite element method. Comparison among the analytical solutions obtained using zero boundary conditions and extrapolated boundary conditions (EBCs) was also performed. The results reveal that the analytical solutions are in close agreement with the numerical solutions, and solutions obtained using EBCs are more accurate in obtaining the mean time of flight data compared to their counterpart. The analytical solutions were also shown to be capable of providing bulk optical properties through a numerical experiment using a realistic breast model. (C) 2013 Optical Society of America

Friction Welding of Thixocast A356 Aluminium Alloy

In this paper, a numerical model for friction welding of thixo-cast materials is developed, which includes a coupling of thermal effect and plastic deformation using a finite element method (FEM). As the constitutive equations for flow behavior of materials for a thixo-cast material are expected to be different from those of conventionally cast material of the same alloy, the necessary material data are experimentally determined from isothermal hot compression tests of the A356 thixocast alloy. The Johnson-Cook model has been employed to represent the flow behavior of the thixocast A356 alloy. The purpose of this FEM analysis is to provide better understanding of the friction welding process of thixo-cast material, and to obtain optimized process parameters before an actual welding is carried out.

A fully discrete C-0 interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation

A fully discrete C-0 interior penalty finite element method is proposed and analyzed for the Extended Fisher-Kolmogorov (EFK) equation u(t) + gamma Delta(2)u - Delta u + u(3) - u = 0 with appropriate initial and boundary conditions, where gamma is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in gamma and as a consequence we derive a priori error estimates that are robust in gamma. (C) 2013 Elsevier B.V. All rights reserved.