Search results for: matrix inverse method

Authors: Shatadru Das, Natarajan Vijayarangan

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In this paper, a system and method for generating and recovering an authorization code has been designed and analyzed. The system creates an authorization code by accepting a base-sentence from a user. Based on the characters present in this base-sentence, the system computes a base-sentence matrix. The system also generates a plurality of patterns. The user can either select the pattern from the multiple patterns suggested by the system or can create his/her own pattern. The system then performs multiplications between the base-sentence matrix and the selected pattern matrix at different stages in the path forward, for obtaining a strong authorization code. In case the user forgets the base sentence, the system has a provision to manage and retrieve 'forgotten authorization code'. This is done by fragmenting the base sentence into different matrices and storing the fragmented matrices into a repository after computing matrix multiplication with a security question-answer approach and with a secret key provided by the user.

Keywords: easy authentication, key retrieval, memorable passwords, strong password generation

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Authors: Balwinder Singh

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The present research is a paper on the characterization of aluminum alloy-6063 hybrid metal matrix composites using three different reinforcement materials (SiC, red mud, and fly ash) through stir casting method. The red mud was used in solid form, and particle size range varies between 103-150 µm. During this investigation, fly ash is received from Guru Nanak Dev Thermal Plant (GNDTP), Bathinda. The study has been done by using Taguchi’s L9 orthogonal array by taking fraction wt.% (SiC 5%, 7.5%, and 10% and Red Mud and Fly Ash 2%, 4%, and 6%) as input parameters with their respective levels. The study of the mechanical properties (tensile strength, impact strength, and microhardness) has been done by using Analysis of Variance (ANOVA) with the help of MINITAB 17 software. It is revealed that silicon carbide is the most significant parameter followed by red mud and fly ash affecting the mechanical properties, respectively. The fractured surface morphology of the composites using Field Emission Scanning Electron Microscope (FESEM) shows that there is a good mixing of reinforcement particles in the matrix. Energy-dispersive X-ray spectroscopy (EDS) was performed to know the presence of the phases of the reinforced material.

Keywords: reinforcement, silicon carbide, fly ash, red mud

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Authors: Hamsasew Hankebo Lemago, Dóra Hessz, Zoltán Erdélyi, Imre Miklós Szilágyi

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Metal oxide inverse opals are a unique class of photocatalysts with a hierarchical structure that mimics the natural opal gemstone. They are composed of a network of interconnected pores, which provides a large surface area and efficient pathways for the transport of light and reactants. Atomic layer deposition (ALD) is a versatile technique for the synthesis of high-precision metal oxide thin films, including inverse opals. ALD allows for precise control over the thickness, composition, and morphology of the synthesized films, making it an ideal technique for the fabrication of photocatalysts with tailored properties. In this study, we report the synthesis of TiO2, ZnO, and Al2O3 inverse opal photocatalysts using thermal or plasma-enhanced ALD. The synthesized photocatalysts were characterized using a variety of techniques, including scanning electron microscopy (SEM)-energy dispersive X-ray spectroscopy (EDX), X-ray diffraction (XRD), Raman spectroscopy, photoluminescence (PL), ellipsometry, and UV-visible spectroscopy. The results showed that the ALD-synthesized metal oxide inverse opals had a highly ordered structure and a tunable pore size. The PL spectroscopy results showed low recombination rates of photogenerated electron-hole pairs, while the ellipsometry and UV-visible spectroscopy results showed tunable optical properties and band gap energies. The photocatalytic activity of the samples was evaluated by the degradation of methylene blue under visible light irradiation. The results showed that the ALD-synthesized metal oxide inverse opals exhibited high photocatalytic activity, even under visible light irradiation. The composites photocatalysts showed even higher activity than the individual metal oxide inverse opals. The enhanced photocatalytic activity of the composites can be attributed to the synergistic effect between the different metal oxides. For example, Al2O3 can act as a charge carrier scavenger, which can reduce the recombination of photogenerated electron-hole pairs. The ALD-synthesized metal oxide inverse opals and their composites are promising photocatalysts for a variety of applications, such as wastewater treatment, air purification, and energy production. For example, they can be used to remove organic pollutants from wastewater, decompose harmful gases in the air, and produce hydrogen fuel from water.

Keywords: ALD, metal oxide inverse opals, composites, photocatalysis

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Authors: Malay Bhattacharyya, Saparya Suresh

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The Correlation Structure associated with a portfolio is subjected to vary across time. Studying the structural breaks in the time-dependent Correlation matrix associated with a collection had been a subject of interest for a better understanding of the market movements, portfolio selection, etc. The current paper proposes a methodology for testing the change in the time-dependent correlation structure of a portfolio in the high dimensional data using the techniques of generalized inverse, singular valued decomposition and multivariate distribution theory which has not been addressed so far. The asymptotic properties of the proposed test are derived. Also, the performance and the validity of the method is tested on a real data set. The proposed test performs well for detecting the change in the dependence of global markets in the context of high dimensional data.

Keywords: correlation structure, high dimensional data, multivariate distribution theory, singular valued decomposition

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Authors: M. Adabi, A. Amadeh

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Electrodeposition is known as a relatively economical and simple technique commonly used for preparation of metallic and composite coatings. Electrodeposited composite coatings produced by dispersion of particles into the metal matrix show better properties than pure metallic coatings. In recent years, many researches were carried out on Ni matrix coatings reinforced by ceramic particles such as Ni-SiC, Ni-Al2O3, Ni-WC, Ni-CeO2, Ni-ZrO2, Ni-TiO2 to improve their corrosion and wear resistance. However, little effort has been made on incorporation of metal particles into Ni matrix. Therefore, the aim of this work was to produce Ni–Al composite coating on 6061 aluminum alloy by pulse plating and to investigate the effects of electrodeposition parameters, e.g. concentration Al particles in the electrolyte and current density, on composition and corrosion resistance of the composite coatings. The morphology and corrosion behavior of the coated 6061 Al alloys were studied by means of scanning electron microscope (SEM) equipped with energy dispersive X-ray spectrometer (EDS) and potentiodynamic polarization method, respectively. The results indicated that the addition of Al particles up to 50 g L-1 increased the amount of co-deposited Al particles in nickel matrix. It is also observed that the incorporation of Al particles decreased with increasing current density. Meanwhile, the corrosion resistance of the coatings shows an increment by increasing the content of Al particles into nickel matrix.

Keywords: Ni-Al composite coating, current density, corrosion resistance

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Khalil Ibrahim, Ahmed Ramadan, Mohamed Fanni, Yo Kobayashi, Ahmed Abo-Ismail, Masakatus G. Fujie

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This paper deals with the design process and the dynamic control simulation of a new type of 4-DOFs parallel mechanism that can be used as an endoscopic surgical manipulator. The proposed mechanism, 2-PUU_2-PUS, is designed based on the screw theory and the parallel virtual chain type synthesis method. Based on the structure analysis of the 4-DOF parallel mechanism, the inverse position equation is studied using the inverse analysis theory of kinematics. The design and the stress analysis of the mechanism are investigated using SolidWorks software. The virtual prototype of the parallel mechanism is constructed, and the dynamic simulation is performed using ADAMS TM software. The system model utilizing PID and PI controllers has been built using MATLAB software. A more realistic simulation in accordance with a given bending angle and point to point control is implemented by the use of both ADAMS/MATLAB software. The simulation results showed that this control method has solved the coordinate control for the 4-DOF parallel manipulator so that each output is feedback to the four driving rods. From the results, the tracking performance is achieved. Other control techniques, such as intelligent ones, are recommended to improve the tracking performance and reduce the numerical truncation error.

Keywords: parallel mechanisms, medical robotics, tracjectory control, virtual chain type synthesis method

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Authors: Juan M. Rodriguez-Diaz

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The precision of parameter estimators in the Gaussian linear model is traditionally accounted by the variance-covariance matrix of the asymptotic distribution. However, this measure can underestimate the true variance, specially for small samples. Traditionally, optimal design theory pays attention to this variance through its relationship with the model's information matrix. For this reason it seems convenient, at least in some cases, adapt the optimality criteria in order to get the best designs for the actual variance structure, otherwise the loss in efficiency of the designs obtained with the traditional approach may be very important.

Keywords: correlated observations, information matrix, optimality criteria, variance-covariance matrix

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Authors: Iyai Davies, Olivier L. C. Haas

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In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.

Keywords: infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability

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Authors: Jiazhen Chen, Yue Sun, Joanne Yip, Kit-Lun Yick

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The design of sports bras poses a considerable challenge due to the difficulty in accurately predicting the wearing result after computer-aided design (CAD). It needs repeated physical try-on or virtual try-on to obtain a comfortable pressure range during motion. Specifically, in the context of running, the exact support area and force exerted on the breasts remain unclear. Consequently, obtaining an effective method to design the sports bra pads shape becomes particularly challenging. This predicament hinders the successful creation and production of sports bras that cater to women's health needs. The purpose of this study is to propose an effective method to obtain the 3D shape of sports bra pads and to understand the relationship between the supporting force and the 3D shape parameters of the pads. Firstly, the static 3D shape of the sports bra pad and human motion data (Running) are obtained by using the 3D scanner and advanced 4D scanning technology. The 3D shape of the sports bra pad is parameterised and simplified by Free-form Deformation (FFD). Then the sub-models of sports bra and human body are constructed by segmenting and meshing them with MSC Apex software. The material coefficient of sports bras is obtained by material testing. The Marc software is then utilised to establish a dynamic contact model between the human breast and the sports bra pad. To realise the reverse design of the sports bra pad, this contact model serves as a forward model for calculating the inverse problem. Based on the forward contact model, the inverse problem of the 3D shape parameters of the sports bra pad with the target bra-wearing pressure range as the boundary condition is solved. Finally, the credibility and accuracy of the simulation are validated by comparing the experimental results with the simulations by the FE model on the pressure distribution. On the one hand, this research allows for a more accurate understanding of the support area and force distribution on the breasts during running. On the other hand, this study can contribute to the customization of sports bra pads for different individuals. It can help to obtain sports bra pads with comfortable dynamic pressure.

Keywords: sports bra design, breast motion, running, inverse problem, finite element dynamic model

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Authors: Vigen Arakelian

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This paper deals with the study of devices for displacement of the mould base of blow-molding machines. The displacement of the mould in the studied case is carried out by a linear actuator, which ensures the descent of the mould base and by extension springs, which return the letter in the initial position. The aim of this paper is to study the inverse dynamics of the device for displacement of the mould base of blow-molding machines and to determine its optimum parameters for higher rate of production. In the other words, it is necessary to solve the inverse dynamic problem to find the equation of motion linking applied forces with displacements. This makes it possible to determine the stiffness coefficient of the spring to turn the mold base back to the initial position for a given time. The obtained results are illustrated by a numerical example. It is shown that applying a spring with stiffness returns the mould base of the blow molding machine into the initial position in 0.1 sec.

Keywords: design, mechanisms, dynamics, blow-molding machines

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Authors: Ju-Hong Lee, Ching-Wei Liao, Kun-Che Lee

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This paper deals with the problem of using antenna sensors for adaptive beamforming in the presence of random steering mismatch. We present an efficient adaptive array beamformer with robustness to deal with the considered problem. The robustness of the proposed beamformer comes from the efficient designation of the steering vector. Using the received array data vector, we construct an appropriate correlation matrix associated with the received array data vector and a correlation matrix associated with signal sources. Then, the eigenvector associated with the largest eigenvalue of the constructed signal correlation matrix is designated as an appropriate estimate of the steering vector. Finally, the adaptive weight vector required for adaptive beamforming is obtained by using the estimated steering vector and the constructed correlation matrix of the array data vector. Simulation results confirm the effectiveness of the proposed method.

Keywords: adaptive beamforming, antenna array, linearly constrained minimum variance, robustness, steering vector

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: M. Rehan, H. Mashaly, H. Emam, A. Abou El-Kheir, S. Mowafi

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In this work, we will study a simple highly efficient technique to impart multi functional properties to different fabric substrates by in situ Ag NPs incorporation into fabric matrix. Ag NPs as a coloration and antimicrobial agent were prepared in situ incorporation into fabric matrix (Cotton and Wool) by using trisodium citrate as reducing and stabilizing agent. The Ag NPs treated fabric (Cotton and Wool) showed different color because of localized surface Plasmon resonance (LSPR) property of Ag NPs. The formation of Ag NPs was confirmed by UV/Vis spectra for the supernatant solutions and The Ag NPs treated fabric (Cotton and Wool) were characterized by scanning electron microscopy (SEM) and X-ray photo electron spectroscopy (XPS). The dependence of color properties characterized by colorimetric, fastness and antibacterial properties evaluated by Escherichia coli using counting method and the reaction parameters were studied. The results indicate that, the in situ Ag NPs incorporation into fabric matrix approach can simultaneously impart colorant and antimicrobial properties into different fabric substrates.

Keywords: Ag NPs, coloration, antibacterial, wool, cotton fabric

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Authors: Yoshio Kurosawa

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To reduce the interior noise of cars in high-frequency region, sound proof materials are laminated with the body panels and the interior trims. Therefore, sound proof properties of the laminates play an important role for the efficient acoustical design. A program code which predicts both sound absorption properties and sound insulation properties of the laminates are developed. This program code is used for transfer matrix method by Biot theory. This report described the outline of this program code, and the calculation results almost agreed with the experimental results.

Keywords: porous media, transmission loss, Biot theory, transfer matrix method

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Authors: M. P. Nanda Kumar, K. Dheeraj

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The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.

Keywords: inverse optimal control, radial basis function, neural network, controller design

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Authors: Amar Partap Singh Pharwaha, Balkrishan Jindal

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In this paper, a new method is developed for hiding image in a digital image with multilayer security. In the proposed method, the secret image is encrypted in the first instance using a flexible matrix based symmetric key to add first layer of security. Then another layer of security is added to the secret data by encrypting the ciphered data using Pythagorean Theorem method. The ciphered data bits (4 bits) produced after double encryption are then embedded within digital image in the spatial domain using Least Significant Bits (LSBs) substitution. To improve the image quality of the stego-image, an improved form of pixel adjustment process is proposed. To evaluate the effectiveness of the proposed method, image quality metrics including Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE), entropy, correlation, mean value and Universal Image Quality Index (UIQI) are measured. It has been found experimentally that the proposed method provides higher security as well as robustness. In fact, the results of this study are quite promising.

Keywords: Pythagorean theorem, pixel adjustment, ciphered data, image hiding, least significant bit, flexible matrix

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Authors: Kourosh Modarresi

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The Netflix problem has brought the topic of “Recommendation Systems” into the mainstream of computer science, mathematics, and statistics. Though much progress has been made, the available algorithms do not obtain satisfactory results. The success of these algorithms is rarely above 5%. This work is based on the belief that the main challenge is to come up with “scalable personalization” models. This paper uses an adaptive regularization of inverse singular value decomposition (SVD) that applies adaptive penalization on the singular vectors. The results show far better matching for recommender systems when compared to the ones from the state of the art models in the industry.

Keywords: convex optimization, LASSO, regression, recommender systems, singular value decomposition, low rank approximation

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Authors: Xiaobao Han, Huacong Li, Jia Li

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For dynamic decoupling of linear parameter varying system, a robust dominance pre-compensator design method is given. The parameterized pre-compensator design problem is converted into optimal problem constrained with parameterized linear matrix inequalities (PLMI); To solve this problem, firstly, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameterized Lyapunov function (PLF) and pre-compensator. Then the problem was reduced to a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a newly constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator was achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation of a turbofan engine PLPV model.

Keywords: linear parameter varying (LPV), parameterized Lyapunov function (PLF), linear matrix inequalities (LMI), diagonal dominance pre-compensator

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Authors: Mohamed Ali Al Shaari, Khalid M. El Fitori

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In the field of Quran Studies known as Ghareeb A Quran (the study of the meanings of strange words and structures in Holy Quran), it is difficult to distinguish some pragmatic meanings from conceptual meanings. One who wants to study this subject may need to look for a common usage between any two words or more; to understand general meaning, and sometimes may need to look for common differences between them, even if there are synonyms (word sisters). Some of the distinguished scholars of Arabic linguistics believe that there are no synonym words, they believe in varieties of meaning and multi-context usage. Based on this viewpoint, our method was designed to look for synonyms of a word, then the differences that distinct the word and their synonyms. There are many available books that use such a method e.g. synonyms books, dictionaries, glossaries, and some books on the interpretations of strange vocabulary of the Holy Quran, but it is difficult to look up words in these written works. For that reason, we proposed a logical entity, which we called Differences Matrix (DM). DM groups the synonyms words to extract the relations between them and to know the general meaning, which defines the skeleton of all word synonyms; this meaning is expressed by a word of its sisters. In Differences Matrix, we used the sisters(words) as titles for rows and columns, and in the obtained cells we tried to define the row title (word) by using column title (her sister), so the relations between sisters appear, the expected result is well defined groups of sisters for each word. We represented the obtained results formally, and used the defined groups as a base for building the ontology of the Holy Quran synonyms.

Keywords: Quran, synonyms, differences matrix, ontology

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Authors: S. Benkraouda, Z. Djelloul-Khedda, B. Yagoubi

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we present a method for early detection of forest fires from a thermal infrared satellite image, using the image matrix of the probability of belonging. The principle of the method is to compare a theoretical mathematical model to an experimental model. We considered that each line of the image matrix, as an embodiment of a non-stationary random process. Since the distribution of pixels in the satellite image is statistically dependent, we divided these lines into small stationary and ergodic intervals to characterize the image by an adequate mathematical model. A standard deviation was chosen to generate random variables, so each interval behaves naturally like white Gaussian noise. The latter has been selected as the mathematical model that represents a set of very majority pixels, which we can be considered as the image background. Before modeling the image, we made a few pretreatments, then the parameters of the theoretical Gaussian model were extracted from the modeled image, these settings will be used to calculate the probability of each interval of the modeled image to belong to the theoretical Gaussian model. The high intensities pixels are regarded as foreign elements to it, so they will have a low probability, and the pixels that belong to the background image will have a high probability. Finally, we did present the reverse of the matrix of probabilities of these intervals for a better fire detection.

Keywords: forest fire, forest fire detection, satellite image, normal distribution, theoretical gaussian model, thermal infrared matrix image

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Authors: Benyelles Zakaria, Yousfi Djaafar, Karoui Moussa Sofiane

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Agriculture is fundamental and remains an important objective in the Algerian economy, based on traditional techniques and structures, it generally has a purpose of consumption. Collection of agricultural statistics in Algeria is done using traditional methods, which consists of investigating the use of land through survey and field survey. These statistics suffer from problems such as poor data quality, the long delay between collection of their last final availability and high cost compared to their limited use. The objective of this work is to develop a processing chain for a reliable inventory of agricultural land by trying to develop and implement a new method of extracting information. Indeed, this methodology allowed us to combine data from remote sensing and field data to collect statistics on areas of different land. The contribution of remote sensing in the improvement of agricultural statistics, in terms of area, has been studied in the wilaya of Sidi Bel Abbes. It is in this context that we applied a method for extracting information from satellite images. This method is called the non-negative matrix factorization, which does not consider the pixel as a single entity, but will look for components the pixel itself. The results obtained by the application of the MNF were compared with field data and the results obtained by the method of maximum likelihood. We have seen a rapprochement between the most important results of the FMN and those of field data. We believe that this method of extracting information from satellite data leads to interesting results of different types of land uses.

Keywords: blind source separation, hyper-spectral image, non-negative matrix factorization, remote sensing

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Authors: Emine Tuğba Akyüz

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In this study, the analysis of Hadamard matrices, which is a special type of matrix, was made under three headings: norms, singular values, condition number. Six norm types was applied to Hadamard matrices and the relationship between the results and the size of the matrix has been studied. As a result of the investigation when 2-norm was used on the problem Hx =f, the equation ‖x‖_2= ‖f‖_2/√n was shown (H is n-dimensional Hadamard matrix). Related with this, the relationship between the the singular value of H and 2-norm and eigenvalues was shown. Then, the evaluation of condition number for Hx =f was made.

Keywords: condition number, Hadamard matrix, norm, singular value

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Authors: Pezhman Taghipour Birgani, Mehdi Shekarzadeh

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In this paper, the propagation of lamb waves in three-layer joints is investigated using global matrix method. Theoretical boundary value problem in three-layer adhesive joints with perfect bond and traction free boundary conditions on their outer surfaces is solved to find a combination of frequencies and modes with the lowest attenuation. The characteristic equation is derived by applying continuity and boundary conditions in three-layer joints using global matrix method. Attenuation and phase velocity dispersion curves are obtained with numerical solution of this equation by a computer code for a three-layer joint, including an aluminum repair patch bonded to the aircraft aluminum skin by a layer of viscoelastic epoxy adhesive. To validate the numerical solution results of the characteristic equation, wave structure curves are plotted for a special mode in two different frequencies in the adhesive joint. The purpose of present paper is to find a combination of frequencies and modes with minimum attenuation in high and low frequencies. These frequencies and modes are recognizable by transducers in inspections with Lamb waves because of low attenuation level.

Keywords: three-layer adhesive joints, viscoelastic, lamb waves, global matrix method

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Authors: Hussaini Doko Ibrahim, Hamilton Cyprian Chinwenyi, Henrietta Nkem Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of the conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax=b, where A is a real n×n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3×3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi, and conjugate gradient methods), respectively. From the results obtained, we discovered that the conjugate gradient method converges faster to exact solutions in fewer iterative steps than the two other methods, which took many iterations, much time, and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, gauss-seidel, Jacobi, algorithm

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Authors: Ratchada Sopakayang, Gerhard A. Holzapfel

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In this study, a new constitutive model is developed to describe the hyperelastic behavior of collagenous tissues with a parallel arrangement of collagen fibers such as ligaments and tendons. The model is formulated using a continuum approach incorporating the structural changes of the main tissue components: collagen fibers, proteoglycan-rich matrix and fiber-matrix interaction. The mechanical contribution of the interaction between the fibers and the matrix is simply expressed by a coupling term. The structural change of the collagen fibers is incorporated in the constitutive model to describe the activation of the fibers under tissue straining. Finally, the constitutive model can easily describe the stress-stretch nonlinearity which occurs when a ligament/tendon is axially stretched. This study shows that the interaction between the fibers and the matrix contributes to the mechanical tissue response. Therefore, the model may lead to a better understanding of the physiological mechanisms of ligaments and tendons under axial loading.

Keywords: constitutive model, fiber-matrix, hyperelasticity, interaction, ligament, tendon

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Authors: Ling Zhang, Feng Liu

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A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern A of order n is called spectrally arbitrary if the complex matrices in the ray pattern class of A give rise to all possible nth degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern. We call that a spectrally arbitrary ray pattern A of order n is minimally spectrally arbitrary if any nonzero entry of A is replaced, then A is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.

Keywords: spectrally arbitrary, nilpotent matrix , ray patterns, sign patterns

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Authors: Dhaladhuli Pranavi, Amirtham Rajagopal

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There are various failure modes in ceramic matrix composites; notable ones are fiber breakage, matrix cracking and fiber matrix debonding. Crack nucleation and propagation in microstructure of such composites requires an understanding of interaction of crack with the multiple inclusion heterogeneous system and interfaces. In order to assess structural integrity, the material parameters especially of the interface that governs the crack growth should be determined. In the present work, a nonlocal phase field approach is proposed to model the crack interface interaction in such composites. Nonlocal approaches help in understanding the complex mechanisms of delamination growth and mitigation and operates at a material length scale. The performance of the proposed formulation is illustrated through representative numerical examples. The model proposed is implemented in the framework of the finite element method. Several parametric studies on interface crack interaction are conducted. The proposed model is easy and simple to implement and works very well in modeling fracture in composite systems.

Keywords: composite, interface, nonlocal, phase field

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Authors: W. Sun, W. Wen, J. Lu, A. A. Becker

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In this work, methods for determining creep properties which can be used to represent the full life until failure from miniature specimen creep tests based on analytical solutions are presented. Examples used to demonstrate the application of the methods include a miniature rectangular thin beam specimen creep test under three-point bending and a miniature two-material tensile specimen creep test subjected to a steady load. Mathematical expressions for deflection and creep strain rate of the two specimens were presented for the Kachanov-Rabotnov creep damage model. On this basis, an inverse procedure was developed which has potential applications for deriving the full life creep damage constitutive properties from a very small volume of material, in particular, for various microstructure constitutive  regions, e.g. within heat-affected zones of power plant pipe weldments. Further work on validation and improvement of the method is addressed.

Keywords: creep damage property, miniature specimen, inverse approach, finite element modeling

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Authors: Gülçin Tekin, Fethi Kadıoğlu

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In this study, the dynamic analysis of viscoelastic plates with variable thickness is examined. The solutions of dynamic response of viscoelastic thin plates with variable thickness have been obtained by using the functional analysis method in the conjunction with the Gâteaux differential. The four-node serendipity element with four degrees of freedom such as deflection, bending, and twisting moments at each node is used. Additionally, boundary condition terms are included in the functional by using a systematic way. In viscoelastic modeling, Three-parameter Kelvin solid model is employed. The solutions obtained in the Laplace-Carson domain are transformed to the real time domain by using MDOP, Dubner & Abate, and Durbin inverse transform techniques. To test the performance of the proposed mixed finite element formulation, numerical examples are treated.

Keywords: dynamic analysis, inverse laplace transform techniques, mixed finite element formulation, viscoelastic plate with variable thickness

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