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Isotropic Material (isotropic + material)
Selected AbstractsA homogenization method for estimating the bearing capacity of soils reinforced by columnsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2005B. Jellali Abstract The ultimate bearing capacity problem of a strip foundation resting on a soil reinforced by a group of regularly spaced columns is investigated in the situation when both the native soil and reinforcing material are purely cohesive. Making use of the yield design homogenization approach, it is shown that such a problem may be dealt with as a plane strain yield design problem, provided that the reinforced soil macroscopic strength condition has been previously determined. Lower and upper bound estimates for such a macroscopic criterion are obtained, thus giving evidence of the reinforced soil strong anisotropy. Performing the upper bound kinematic approach on the homogenized bearing capacity problem, by using the classical Prandtl's failure mechanism, makes it then possible to derive analytical upper bound estimates for the reinforced foundation bearing capacity, as a function of the reinforced soil parameters (volume fraction and cohesion ratio), as well as of the relative extension of the reinforced area. It is shown in particular that such an estimate is closer to the exact value of the ultimate bearing capacity, than that derived from a direct analysis which implicitly assumes that the reinforced soil is an isotropic material. Copyright © 2005 John Wiley & Sons, Ltd. [source] Integrated layout design of multi-component systemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2009Jihong Zhu Abstract A new integrated layout optimization method is proposed here for the design of multi-component systems. By introducing movable components into the design domain, the components layout and the supporting structural topology are optimized simultaneously. The developed design procedure mainly consists of three parts: (i) Introduction of non-overlap constraints between components. The finite circle method (FCM) is used to avoid the components overlaps and also overlaps between components and the design domain boundaries. (ii) Layout optimization of the components and supporting structure. Locations and orientations of the components are assumed as geometrical design variables for the optimal placement while topology design variables of the supporting structure are defined by the density points. Meanwhile, embedded meshing techniques are developed to take into account the finite element mesh change caused by the component movements. (iii) Consistent material interpolation scheme between element stiffness and inertial load. The commonly used solid isotropic material with penalization model is improved to avoid the singularity of localized deformation in the presence of design dependent loading when the element stiffness and the involved inertial load are weakened by the element material removal. Finally, to validate the proposed design procedure, a variety of multi-component system layout design problems are tested and solved on account of inertia loads and gravity center position constraint. Solutions are compared with traditional topology designs without component. Copyright © 2008 John Wiley & Sons, Ltd. [source] Mechanical and fracture properties for predicting cracking in semi-sweet biscuitsINTERNATIONAL JOURNAL OF FOOD SCIENCE & TECHNOLOGY, Issue 4 2005Qasim Saleem Summary Mechanical and fracture properties required for predicting crack development in semi-sweet (,rich tea') biscuits have been experimentally determined. Pilot-scale biscuits of different fat concentrations were prepared and studied with commercial biscuits at different moisture contents. Bending modulus, fracture stress and strain were measured using three-point bending tests. All biscuit types showed considerable dependence on moisture content over a range of 4,12%. Young's modulus and failure stress showed a uniform decrease and failure strain showed an increase with increasing moisture content. For pilot-scale biscuits of different fat concentrations, an increase in fat level caused a decrease in modulus and failure stress values; however, the failure strains were very similar for all the fat types. The testing of the samples with top surface up and top surface down revealed that the sample orientation does not affect the measured parameters. The measured parameters also did not show any directional dependence within the plane, thus assuring that the assumption of an isotropic material would be valid for modelling. The mechanical and fracture properties measured in this study will serve as a very useful set of data to predict the stress state and cracking of the checked biscuits. [source] Asymptotic analysis of elastic curved rodsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2007Rostislav Vodák Abstract We consider a sequence of curved rods which consist of isotropic material and which are clamped on the lower base or on both bases. We study the asymptotic behaviour of the stress tensor and displacement under the assumptions of linearized elasticity when the cross-sectional diameter of the rods tends to zero and the body force is given in the particular form. The analysis covers the case of a non-smooth limit line of centroids. We show how the body force and the choice of the approximating curved rods can affect the strong convergence and the limit form of the stress tensor for the curved rods clamped on both bases. Copyright © 2006 John Wiley & Sons, Ltd. [source] On interaction of electromagnetic waves with infinite bianisotropic layered slabMATHEMATISCHE NACHRICHTEN, Issue 9-10 2007Tengiz Buchukuri Abstract A stratified general bianisotropic medium is considered, consisting of several infinite slabs either between two half-spaces filled with isotropic material, or grounded. The slab is illuminated by an incident plane wave from one of the half-spaces. The excited electromagnetic field inside the bianisotropic slab and in the isotropic domains is described. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Electrically switchable exhibition of circular Bragg phenomenon by an isotropic slabMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 11 2006Akhlesh Lakhtakia Abstract A slab of an isotropic material with structural chirality in the thickness direction and with either 43m or 23 point group symmetry exhibits the circular Bragg phenomenon in the optical regime, only on the application of a low-frequency electric field across its two faces. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 2148,2153, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21941 [source] On parallel solution of linear elasticity problems.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 3 2002Part II: Methods, some computer experiments Abstract This is the second part of a trilogy on parallel solution of the linear elasticity problem. We consider the plain case of the problem with isotropic material, including discontinuous coefficients, and with homogeneous Dirichlet boundary condition. The discretized problem is solved by the preconditioned conjugate gradient (pcg) method. In the first part of the trilogy block- diagonal preconditioners based on the separate displacement component part of the elasticity equations were analysed. The preconditioning systems were solved by the pcg-method, i.e. inner iterations were performed. As preconditioner, we used modified incomplete factorization MIC(0), where possibly the element matrices were modified in order to give M -matrices, i.e. in order to guarantee the existence of the MIC(0) factorization. In the present paper, the second part, full block incomplete factorization preconditioners are presented and analysed. In order to avoid inner/outer iterations we also study a variant of the block-diagonal method and of the full block method, where the matrices of the inner systems are just replaced by their MIC(0)-factors. A comparison is made between the various methods with respect to rate of convergence and work per unknown. The fastest methods are implemented by message passing utilizing the MPI system. In the third part of the trilogy, we will focus on the use of higher-order finite elements. Copyright © 2002 John Wiley & Sons, Ltd. [source] On predicting elastic moduli and natural frequencies of multi-phase composites with randomly distributed short fibersPOLYMER COMPOSITES, Issue 1 2000Lu-Ping Chao This study presents a formulation to determine the overall stiffness of an n -phase short fiber composite to include the inclusions' aspect ratio ranging from less than one to greater than one. The Mori-Tanaka theory is initially employed to investigate the overall stress-strain relation of a multi-phase short-fiber-reinforced composite material, particularly whether or not the fibers and the matrix are isotropic, cubic, or transversely isotropic material. The effective stiffness tensor of a multi-phase composite is then denoted as a function of the matrix's elastic moduli, the n -phases' inclusions' elastic moduli, the n -phases' inclusions' Eshelby tensor, and the n -phases' inclusions' volume fractions. Utilizing the equivalent inclusion method allows us to model inclusions of n -phases that consist of fictitious eigenstrains. In addition, the corresponding Eshelby tensors' values for ellipsoidal inclusion embedded in the isotropic matrix with the variation of aspect ratio are presented. Numerical results of the proposed formulation in solving a two-phase composite closely correspond to the Halpin-Tsai Equation. Results presented herein provide valuable information on the appropriate manufacturing requirements of multi-phase composite materials or the design and optimization of multi-phase composite structures. [source] Simulation of polycrystalline ferroelectrics based on discrete orientation distribution functionsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Ingo Kurzhöfer Ferroelectric materials exhibit a spontaneous polarization, which can be reversed by an applied electric field of sufficient magnitude. The resulting nonlinearities are expressed by characteristic dielectric and butterfly hysteresis loops. These effects are correlated to the structure of the crystal and especially to the axis of spontaneous polarization in case of single crystals. We start with a representative meso scale, where the domains consist of unit cells with equal spontaneous polarization. Each domain is modeled within a coordinate invariant formulation for an assumed transversely isotropic material as presented in [10], in this context see also [8]. In this investigation we obtain the macroscopic polycrystalline quantities via a simple homogenization procedure, where discrete orientation distribution functions are used to approximate the different domains. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Stress Concentration Factors and Weight Functions in Thin Notched Structures of Equibiaxial Anisotropic Materials,ADVANCED ENGINEERING MATERIALS, Issue 7 2010Michael Heinzelmann In notched structures, the influence of the notch on the structural strength of the component can be described by a stress concentration factor or,in the presence of cracks,a weight function. Numerous stress concentration factor and weight function solutions are available to the engineer, but regrettably almost exclusively for isotropic materials. In the present study, stress concentration factors and weight functions are calculated for equibiaxial anisotropic materials. The geometry under investigation is a flat plate in tension containing a central hole. The calculated results show that the elastic anisotropic material behavior can significantly influence the magnitude of both stress concentration factors and weight functions. [source] Influence of anisotropy on a limit load of weld strength overmatched middle cracked tension specimensFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 5 2003S. ALEXANDROV ABSTRACT A plane-strain upper bound limit load solution for weld strength overmatched middle cracked tension specimens (M(T) specimens), is found. It is assumed that the weld material is isotropic, but the base material is orthotropic and its axes of orthotropy are straight and parallel to the axes of symmetry of the specimen. A quadratic orthotropic yield criterion is adopted. The solution is based on a simple discontinuous kinematically admissible velocity field and is an extension of the corresponding solution for the specimen made of isotropic materials. These two solutions are compared to demonstrate the influence of anisotropy on the magnitude of the limit load. [source] Numerical modeling of creep and creep damage in thin plates of arbitrary shape from materials with different behavior in tension and compression under plane stress conditionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2009A. Zolochevsky Abstract A constitutive model for describing the creep and creep damage in initially isotropic materials with characteristics dependent on the loading type, such as tension, compression and shear, has been applied to the numerical modeling of creep deformation and creep damage growth in thin plates under plane stress conditions. The variational approach of establishing the basic equations of the plane stress problem under consideration has been introduced. For the solution of two-dimensional creep problems, the fourth-order Runge,Kutta,Merson's method of time integration, combined with the Ritz method and R-functions theory, has been used. Numerical solutions to various problems have been obtained, and the processes of creep deformation and creep damage growth in thin plates of arbitrary shape have been investigated. The influence of tension,compression asymmetry on the stress,strain state and damage evolution, with time, in thin plates of arbitrary shape, has been discussed. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical finite element formulation of the Schapery non-linear viscoelastic material modelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004Rami M. Haj-Ali Abstract This study presents a numerical integration method for the non-linear viscoelastic behaviour of isotropic materials and structures. The Schapery's three-dimensional (3D) non-linear viscoelastic material model is integrated within a displacement-based finite element (FE) environment. The deviatoric and volumetric responses are decoupled and the strain vector is decomposed into instantaneous and hereditary parts. The hereditary strains are updated at the end of each time increment using a recursive formulation. The constitutive equations are expressed in an incremental form for each time step, assuming a constant incremental strain rate. A new iterative procedure with predictor,corrector type steps is combined with the recursive integration method. A general polynomial form for the parameters of the non-linear Schapery model is proposed. The consistent algorithmic tangent stiffness matrix is realized and used to enhance convergence and help achieve a correct convergent state. Verifications of the proposed numerical formulation are performed and compared with a previous work using experimental data for a glassy amorphous polymer PMMA. Copyright © 2003 John Wiley & Sons, Ltd. [source] Buckling analysis for delaminated composites using plate bending elements based on higher-order zig-zag theoryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002Jun-Sik Kim Abstract A finite element based on the efficient higher-order zig-zag theory with multiple delaminations is developed. The bending part of the formulation is constructed from the concept of DKQ element. Unlike conventional elements, a developed element has its reference in the bottom surface which simplifies zig-zag terms on formulation. Exact patch solutions are developed on elements which have the bottom reference system. The present element passes proper bending patch tests in the arbitrary mesh configurations in isotropic materials. Zig-zag formulation is adopted to model laminated plates with multiple delaminations. To assess the accuracy and efficiency of the present element based on higher-order zig-zag theory with multiple delaminations, the linear buckling problem of laminated plates with multiple delaminations has been analysed. The results have been compared with three-dimensional elasticity solutions. The present element works as an efficient tool for analysing the behaviour of the laminated composites with multiple delaminations. Copyright © 2002 John Wiley & Sons, Ltd. [source] Liquid-crystalline thermosets by the curing of dimeric liquid-crystalline epoxyimine monomers with 2,4-toluene diisocyanateJOURNAL OF POLYMER SCIENCE (IN TWO SECTIONS), Issue 16 2003David Ribera Abstract We studied the curing processes of several series of dimeric liquid-crystalline epoxyimine monomers with 2,4-toluene diisocyanate (TDI) alone or with added catalytic proportions of 4-(N,N -dimethylamino)pyridine. We obtained isotropic materials or liquid-crystalline thermosets with different degrees of order, which depended on the structures of the monomers. To fix ordered networks, we had to do the curing in two steps when TDI was used alone as the curing agent. However, when a tertiary amine was added in catalytic proportions, the ordered networks were fixed in just one step. In this way, we were able to fix both nematic and smectic mesophases. The significance of the polarization of the mesogen for obtaining liquid-crystalline thermosets was demonstrated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2521,2530, 2003 [source] Eigen-frequencies in thin elastic 3-D domains and Reissner,Mindlin plate modelsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2002Monique Dauge Abstract The eigen-frequencies of elastic three-dimensional thin plates are addressed and compared to the eigen-frequencies of two-dimensional Reissner,Mindlin plate models obtained by dimension reduction. The qualitative mathematical analysis is supported by quantitative numerical data obtained by the p-version finite element method. The mathematical analysis establishes an asymptotic expansion for the eigen-frequencies in power series of the thickness parameter. Such results are new for orthotropic materials and for the Reissner,Mindlin model. The 3-D and R,M asymptotics have a common first term but differ in their second terms. Numerical experiments for clamped plates show that for isotropic materials and relatively thin plates the Reissner,Mindlin eigen-frequencies provide a good approximation to the three-dimensional eigen-frequencies. However, for some anisotropic materials this is no longer the case, and relative errors of the order of 30 per cent are obtained even for relatively thin plates. Moreover, we showed that no shear correction factor is known to be optimal in the sense that it provides the best approximation of the R,M eigen-frequencies to their 3-D counterparts uniformly (for all relevant thicknesses range). Copyright © 2002 John Wiley & Sons, Ltd. [source] Re-entrant corner problems for isotropic materials and layered compositesPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005E. Schnack Modern materials like composites in different types require new methods in computational fracture mechanics. Besides of classical fracture mechanics we have to solve the asymptotic solution around crack tips. This can be done on the basis of the Kondratievs theorem with the Pietrov-Galerkin method to solve the unknown eigenvalues for those problems. Additionally, we have to de.ne instead classical modes I, II and III, mode I* up to mode IV* to interpret the computational results for the unknown eigenvalues. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Improving realism of a surgery simulator: linear anisotropic elasticity, complex interactions and force extrapolationCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 3 2002Guillaume Picinbono Abstract In this article, we describe the latest developments of the minimally invasive hepatic surgery simulator prototype developed at INRIA. The goal of this simulator is to provide a realistic training test bed to perform laparoscopic procedures. Therefore, its main functionality is to simulate the action of virtual laparoscopic surgical instruments for deforming and cutting tridimensional anatomical models. Throughout this paper, we present the general features of this simulator including the implementation of several biomechanical models and the integration of two force-feedback devices in the simulation platform. More precisely, we describe three new important developments that improve the overall realism of our simulator. First, we have developed biomechanical models, based on linear elasticity and finite element theory, that include the notion of anisotropic deformation. Indeed, we have generalized the linear elastic behaviour of anatomical models to ,transversally isotropic' materials, i.e. materials having a different behaviour in a given direction. We have also added to the volumetric model an external elastic membrane representing the ,liver capsule', a rather stiff skin surrounding the liver, which creates a kind of ,surface anisotropy'. Second, we have developed new contact models between surgical instruments and soft tissue models. For instance, after detecting a contact with an instrument, we define specific boundary constraints on deformable models to represent various forms of interactions with a surgical tool, such as sliding, gripping, cutting or burning. In addition, we compute the reaction forces that should be felt by the user manipulating the force-feedback devices. The last improvement is related to the problem of haptic rendering. Currently, we are able to achieve a simulation frequency of 25,Hz (visual real time) with anatomical models of complex geometry and behaviour. But to achieve a good haptic feedback requires a frequency update of applied forces typically above 300,Hz (haptic real time). Thus, we propose a force extrapolation algorithm in order to reach haptic real time. Copyright © 2002 John Wiley & Sons, Ltd. [source] | ||||||||||||||||