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Displacement Field (displacement + field)
Selected AbstractsStrain field measurements of rubber by image analysis and design criteria for laminated rubber bearings (LRB)EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 4 2004Chamindalal Sujeewa Lewangamage Abstract Although seismic isolation rubber bearings in bridges and buildings have proven to be a very effective passive method for reducing earthquake-induced forces, a detailed mechanical modeling of the rubber that is used in bearings under large strains has not been established. Therefore, a 3D model of failure behavior and the design criteria for the safety evaluation of seismic isolation bearings have not yet been developed. This paper presents: (1) correlation-based template-matching algorithms to measure large strain fields of continua; (2) a failure criterion for rubber; and (3) the design criteria for the safety evaluation of laminated algorithms, data-validation algorithms were developed and implemented to eliminate possible unrealistic displacement vectors present in the measured displacement field. The algorithms were successfully employed in the strain field measurement of LRB and rubber materials that are subjected to failure. The measured local strains for rubber material at failure were used to develop a failure criterion for rubber. The validity of the proposed criterion was evaluated by applying it to the LRB; the criterion was introduced into a 3D finite element model of LRB, compared with the experimental results of bearings failure, and verified. Finally, design criteria are proposed for LRB for the safety evaluation. Copyright © 2003 John Wiley & Sons, Ltd. [source] Incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode I elastic,plastic displacement fieldsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 7 2007S. POMMIER ABSTRACT The mode I displacement field in the near crack tip region is assumed to be depicted by its partition into an elastic field and a plastic field. Then, each part of the displacement field is also assumed to be the product of a reference field, a function of space coordinates only, and of an intensity factor, function of the loading conditions. This assumption, classical in fracture mechanics, enables one to work at the global scale since fracture criteria can be formulated as a function of the stress intensity factors only. In the present case, the intensity factor of the plastic part of the displacement field measures crack tip plastic flow rate at the global scale. On the basis of these hypotheses, the energy balance equation and the second law of thermodynamics are written at the global scale, i.e. the scale of the K-dominance area. This enables one to establish a yield criterion and a plastic flow rule for the crack tip region. Then, assuming a relation between plastic flow in the crack tip region and fatigue crack growth allows an incremental model for fatigue crack growth to be built. A few examples are given to show the versatility of the model and its ability to reproduce memory effects associated with crack tip plasticity. [source] The continuous crack flexibility model for crack identificationFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 10 2001T. G. Chondros The presence of a crack in a structural member introduces a local flexibility that affects its dynamic response. Moreover, the crack will open and close in time depending on the loading conditions and vibration amplitude. The changes in dynamic characteristics can be measured and lead to an identification of the structural changes which eventually might lead to the detection of a structural flaw. The results of various independent evaluations of changes in the natural frequency of vibrations of cracked structural elements are reported. A crack model of a continuous flexibility, found with fracture mechanics methods using the displacement field in the vicinity of the crack developed recently is used here. The analytical results for the cracked elements behaviour based on the continuous crack flexibility vibration theory were correlated with numerical solutions, the lumped-crack beam vibration analysis and experimental results obtained on aluminium and steel beams with open cracks. [source] Surface deformation due to loading of a layered elastic half-space: a rapid numerical kernel based on a circular loading elementGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007E. Pan SUMMARY This study is motivated by a desire to develop a fast numerical algorithm for computing the surface deformation field induced by surface pressure loading on a layered, isotropic, elastic half-space. The approach that we pursue here is based on a circular loading element. That is, an arbitrary surface pressure field applied within a finite surface domain will be represented by a large number of circular loading elements, all with the same radius, in which the applied downwards pressure (normal stress) is piecewise uniform: that is, the load within each individual circle is laterally uniform. The key practical requirement associated with this approach is that we need to be able to solve for the displacement field due to a single circular load, at very large numbers of points (or ,stations'), at very low computational cost. This elemental problem is axisymmetric, and so the displacement vector field consists of radial and vertical components both of which are functions only of the radial coordinate r. We achieve high computational speeds using a novel two-stage approach that we call the sparse evaluation and massive interpolation (SEMI) method. First, we use a high accuracy but computationally expensive method to compute the displacement vectors at a limited number of r values (called control points or knots), and then we use a variety of fast interpolation methods to determine the displacements at much larger numbers of intervening points. The accurate solutions achieved at the control points are framed in terms of cylindrical vector functions, Hankel transforms and propagator matrices. Adaptive Gauss quadrature is used to handle the oscillatory nature of the integrands in an optimal manner. To extend these exact solutions via interpolation we divide the r -axis into three zones, and employ a different interpolation algorithm in each zone. The magnitude of the errors associated with the interpolation is controlled by the number, M, of control points. For M= 54, the maximum RMS relative error associated with the SEMI method is less than 0.2 per cent, and it is possible to evaluate the displacement field at 100 000 stations about 1200 times faster than if the direct (exact) solution was evaluated at each station; for M= 99 which corresponds to a maximum RMS relative error less than 0.03 per cent, the SEMI method is about 700 times faster than the direct solution. [source] Three-dimensional elastic earthquake modelling based on integrated seismological and InSAR data: the Mw= 7.2 Nuweiba earthquake, gulf of Elat/Aqaba 1995 NovemberGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2003G. Shamir SUMMARY The Nuweiba earthquake (1995 November 22; Mw= 7.2), the largest seismic event along the Dead Sea Transform (DST) in at least 160 yr, ruptured 45,50 km along the Aragonese segment of the left-stepping strike-slip fault system occupying the gulf of Elat/Aqaba (southern segment of the DST). The rupture initiated in a partly normal, low-slip first subevent near the southern end of the fault and propagated unilaterally north-northeastward as a high-slip, nearly pure sinistral second subevent, which was responsible for over 90 per cent of the total seismic moment. The source mechanism and slip distribution, derived from inversion of teleseismic broad-band waveforms, are used to construct a 3-D elastic model of the earthquake based on the boundary elements method, resulting in the full 3-D displacement and stress fields induced by the earthquake. In the absence of sufficient Global Positioning System data, the only other constraints on the geometry and slip distribution of the rupture are provided by interferometric synthetic aperture radar (InSAR) measurements spanning the coseismic and early post-seismic period. We calculate simulated interferograms by transforming the calculated surface displacement field into the satellite coordinate system and comparing them with the observed interferograms. The model parameters are then iteratively modified until a best-fitting model is obtained, providing a refined set of static source parameters for the mainshock. This model is then used to calculate the static Coulomb stress changes induced by the mainshock on the step-over faults, suggesting that the major (Mw, 5) aftershocks in the first eight post-seismic months were triggered by small changes (<1 bar) in the left-lateral Coulomb stress, with effective friction coefficient not higher than 0.2. Aftershock distribution and mechanisms indicate that the available Coulomb stress dropped below the frictional strength of the fault but was not complete. [source] Co-seismic slip from the 1995 July 30 Mw= 8.1 Antofagasta, Chile, earthquake as constrained by InSAR and GPS observationsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2002M. E. Pritchard Summary We analyse radar interferometric and GPS observations of the displacement field from the 1995 July 30 Mw= 8.1 Antofagasta, Chile, earthquake and invert for the distribution of slip along the co-seismic fault plane. Using a fixed fault geometry, we compare the use of singular-value decomposition and constrained linear inversion to invert for the slip distribution and find that the latter approach is better resolved and more physically reasonable. Separate inversions using only GPS data, only InSAR data from descending orbits, and InSAR data from both ascending and descending orbits without the GPS data illustrate the complimentary nature of GPS and the presently available InSAR data. The GPS data resolve slip near GPS benchmarks well, while the InSAR provides greater spatial sampling. The combination of ascending and descending InSAR data contributes greatly to the ability of InSAR to resolve the slip model, thereby emphasizing the need to acquire this data for future earthquakes. The rake, distribution of slip and seismic moment of our preferred model are generally consistent with previous seismic and geodetic inversions, although significant differences do exist. GPS data projected in the radar line-of-sight (LOS) and corresponding InSAR pixels have a root mean square (rms) difference of about 3 cm. Comparison of our predictions of vertical displacement and observed uplift from corraline algae have an rms of 10 cm. Our inversion and previous results reveal that the location of slip might be influenced by the 1987 Mw= 7.5 event. Our analysis further reveals that the 1995 slip distribution was affected by a 1988 Mw= 7.2 event, and might have influenced a 1998 Mw= 7.0 earthquake that occurred downdip of the 1995 rupture. Our slip inversion reveals a potential change in mechanism in the southern portion of the rupture, consistent with seismic results. Predictions of the satellite LOS displacement from a seismic inversion and a joint seismic/GPS inversion do not compare favourably with the InSAR observations. [source] Discrete numerical modelling of rockfill damsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2006R. Deluzarche Abstract The aim of this study is to obtain quantitative information on the behaviour of rockfill used in embankment dams, and particularly on the influence of block breakage on the displacement field, from a numerical analysis using the Distinct element method. A methodology is set up to define the resistance of the 2D particles so that the same probability of breaking blocks may be reproduced as in a 3D material. The model uses the discrete element code PFC2D (Itasca Consulting Group Inc., PFC2D (Particle Flow Code in Two Dimensions), Version 3.0, 2002) and considers breakable clusters of 2D balls. The different parameters are determined from experimental data obtained from laboratory tests performed on rock blocks. The model is validated by comparing the results of the simulation of shearing tests with actual triaxial tests on rockfill material published in the literature. The numerical analysis of block crushing in an actual dam is proposed in the last part of this paper. Copyright © 2006 John Wiley & Sons, Ltd. [source] A rate-dependent cohesive crack model based on anisotropic damage coupled to plasticityINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2006Per-Ola Svahn Abstract In quasi-brittle material the complex process of decohesion between particles in microcracks and localization of the displacement field into macrocracks is limited to a narrow fracture zone, and it is often modelled with cohesive crack models. Since the anisotropic nature of the decohesion process in separation and sliding is essential, it is particularly focused in this paper. Moreover, for cyclic and dynamic loading the unloading, load reversal (including crack closure) and rate dependency are essential features that are included in a new model. The modelling of degradation is based on a ,localized' version of anisotropic continuum damage coupled to inelasticity. The concept of strain energy equivalence between the states in the effective and nominal settings is adopted in order to define the free energy of the interface. The proposed fracture criterion is of the Mohr type, with a smooth transition of the failure and kinematics (slip and dilatation) characteristics between tension and shear. The chosen potential, of the Lemaitre-type, for evolution of the dissipative processes is additively decomposed into plastic and damage parts, and non-associative constitutive equations are obtained. The constitutive equations are integrated by applying the backward Euler rule and by using Newton iteration. The proposed model is assessed analytically and numerically and a typical calibration procedure for concrete is proposed. Copyright © 2006 John Wiley & Sons, Ltd. [source] Deformations caused by the movements of shear and tensile faultsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2001Guang Y. Sheu Abstract Earlier solutions of deformations resulting from the movements of shear and tensile faults in a half space (Bull. Seismol. Soc. Amer. 1985; 75:1135, 1992; 82:1018) have been revised in view of cross-anisotropic stress,strain relationships. The dislocation theory (Canad. J. Phys. 1958; 36:192) is reviewed and the displacement field due to a concentrated force in an anisotropic half space is solved analytically for developing the current research. A fault is simulated as a point source of strain nuclei in applying the dislocation theory. Data (Terr. Atmos. Oceanic Sci. 2000; 11(3):591, 631) that were used to study the Chi-Chi earthquake (ML=7.3; 1999/9/21 AM 1:47) are introduced to compare the solution with the isotropic results. Results indicate that the anisotropy of stress,strain relationships does affect the results of predicted deformations. Copyright © 2001 John Wiley & Sons, Ltd. [source] Kinematic and dynamic analysis of open-loop mechanical systems using non-linear recursive formulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2006Yunn-Lin Hwang Abstract In this paper, a non-linear recursive formulation is developed for kinematic and dynamic analysis of open-loop mechanical systems. The non-linear equations of motion are developed for deformable links that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars and matrices that depend on the spatial co-ordinates as well as the assumed displacement field, and these time invariant quantities represent the dynamic coupling between the rigid-body modes and elastic deformations. A new recursive formulation is presented for solving equations of motion for open-loop chains consisting of interconnected rigid and deformable open-loop mechanical systems. This formulation is expressed by the recursive relationships and the generalized non-linear equations for deformable mechanical systems to obtain a large system of loosely coupled equations of motion. The main processor program consists of three main modules: constraint module, mass module and force module. The constraint module is used to numerically evaluate the relationship between the absolute and joint accelerations. The mass module is used to numerically evaluate the system mass matrix as well as the non-linear Coriolis and centrifugal forces associated with the absolute, joint and elastic co-ordinates. Simultaneously, the force module is used to numerically evaluate the generalized external and elastic forces associated with the absolute, joint and elastic co-ordinates. Computational efficiency is achieved by taking advantage of the structure of the resulting system of loosely coupled equations. The solution techniques used in this investigation yield a much smaller operations count and can more efficiently implement in any computer. The algorithms and solutions presented in this paper are illustrated by using an industrial robotic manipulator system. The numerical results using this formulation are also presented and discussed in this paper. Copyright © 2006 John Wiley & Sons, Ltd. [source] Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracksINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010Flavio V. Souza Abstract Multiscale computational techniques play a major role in solving problems related to viscoelastic composites due to the complexities inherent to these materials. In this paper, a numerical procedure for multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks is proposed in which the (global scale) homogenized viscoelastic incremental constitutive equations have the same form as the local-scale viscoelastic incremental constitutive equations, but the homogenized tangent constitutive tensor and the homogenized incremental history-dependent stress tensor at the global scale depend on the amount of damage accumulated at the local scale. Furthermore, the developed technique allows the computation of the full anisotropic incremental constitutive tensor of viscoelastic solids containing evolving cracks (and other kinds of heterogeneities) by solving the micromechanical problem only once at each material point and each time step. The procedure is basically developed by relating the local-scale displacement field to the global-scale strain tensor and using first-order homogenization techniques. The finite element formulation is developed and some example problems are presented in order to verify the approach and demonstrate the model capabilities. Copyright © 2009 John Wiley & Sons, Ltd. [source] Computational aspects in 2D SBEM analysis with domain inelastic actionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2010T. Panzeca Abstract The Symmetric Boundary Element Method, applied to structures subjected to temperature and inelastic actions, shows singular domain integrals. In the present paper the strong singularity involved in the domain integrals of the stresses and tractions is removed, and by means of a limiting operation, this traction is evaluated on the boundary. First the weakly singular domain integral in the Somigliana Identity (S.I.) of the displacements is regularized and the singular integral is transformed into a boundary one using the Radial Integration Method; subsequently, using the differential operator applied to the displacement field, the S.I. of the tractions inside the body is obtained and through a limit operation its expression is evaluated on the boundary. The latter operation makes it possible to substitute the strongly singular domain integral in a strongly singular boundary one, defined as a Cauchy Principal Value, with which the related free term is associated. The expressions thus obtained for the displacements and the tractions, in which domain integrals are substituted by boundary integrals, were utilized in the Galerkin approach, for the evaluation in closed form of the load coefficients connected to domain inelastic actions. This strategy makes it possible to evaluate the load coefficients avoiding considerable difficulties due to the geometry of the solid analyzed; the obtained coefficients were implemented in the Karnak.sGbem calculus code. Copyright © 2009 John Wiley & Sons, Ltd. [source] A continuum-to-atomistic bridging domain method for composite latticesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Mei Xu Abstract The bridging domain method is an overlapping domain decomposition approach for coupling finite element continuum models and molecular mechanics models. In this method, the total energy is decomposed into atomistic and continuum parts by complementary weight functions applied to each part of the energy in the coupling domain. To enforce compatibility, the motions of the coupled atoms are constrained by the continuum displacement field using Lagrange multipliers. For composite lattices, this approach is suboptimal because the internal modes of the lattice are suppressed by the homogeneous continuum displacement field in the coupling region. To overcome this difficulty, we present a relaxed bridging domain method. In this method, the atom set is divided into primary and secondary atoms; the relative motions between them are often called the internal modes. Only the primary atoms are constrained in the coupling region, which succeed in allowing these internal modes to fully relax. Several one- and two-dimensional examples are presented, which demonstrate improved accuracy over the standard bridging domain method. Copyright © 2009 John Wiley & Sons, Ltd. [source] Two-level multiscale enrichment methodology for modeling of heterogeneous platesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2009Caglar OskayArticle first published online: 15 JUN 200 Abstract A new two-level multiscale enrichment methodology for analysis of heterogeneous plates is presented. The enrichments are applied in the displacement and strain levels: the displacement field of a Reissner,Mindlin plate is enriched using the multiscale enrichment functions based on the partition of unity principle; the strain field is enriched using the mathematical homogenization theory. The proposed methodology is implemented for linear and failure analysis of brittle heterogeneous plates. The eigendeformation-based model reduction approach is employed to efficiently evaluate the non-linear processes in case of failure. The capabilities of the proposed methodology are verified against direct three-dimensional finite element models with full resolution of the microstructure. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009A. El Kacimi Abstract In this paper, we investigate a numerical approach based on the partition of unity finite element method, for the time-harmonic elastic wave equations. The aim of the proposed work is to accurately model two-dimensional elastic wave problems with fewer elements, capable of containing many wavelengths per nodal spacing, and without refining the mesh at each frequency. The approximation of the displacement field is performed via the standard finite element shape functions, enriched by superimposing pressure and shear plane wave basis, which incorporate knowledge of the wave propagation. A variational framework able to handle mixed boundary conditions is described. Numerical examples dealing with the radiation and the scattering of elastic waves by a circular body are presented. The results show the performance of the proposed method in both accuracy and efficiency. Copyright © 2008 John Wiley & Sons, Ltd. [source] Adaptive superposition of finite element meshes in non-linear transient solid mechanics problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2007Z. Yue Abstract An s-adaptive finite element procedure is developed for the transient analysis of 2-D solid mechanics problems with material non-linearity due to progressive damage. The resulting adaptive method simultaneously estimates and controls both the spatial error and temporal error within user-specified tolerances. The spatial error is quantified by the Zienkiewicz,Zhu error estimator and computed via superconvergent patch recovery, while the estimation of temporal error is based on the assumption of a linearly varying third-order time derivatives of the displacement field in conjunction with direct numerical time integration. The distinguishing characteristic of the s-adaptive procedure is the use of finite element mesh superposition (s-refinement) to provide spatial adaptivity. Mesh superposition proves to be particularly advantageous in computationally demanding non-linear transient problems since it is faster, simpler and more efficient than traditional h-refinement schemes. Numerical examples are provided to demonstrate the performance characteristics of the s-adaptive method for quasi-static and transient problems with material non-linearity. Copyright © 2007 John Wiley & Sons, Ltd. [source] Two-scale method for shear bands: thermal effects and variable bandwidthINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2007Pedro M. A. Areias Abstract A method for the analysis of shear bands using local partition of unity is developed in the framework of the extended finite element method (XFEM). Enrichments are introduced for both the displacement field and the thermal field. The shear band width is determined by minimizing the plastic work. A coupled finite strain thermo-elastoplastic constitutive law is used. The enrichment is injected into the mesh when the material law becomes unstable. The criterion based on a complete stability analysis for materials in the finite strain regime including heat conduction, strain hardening, strain rate hardening and thermal softening is presented. A mixed continuous quadrilateral element is employed. The method is applied to the Nesterenko experiments, which exhibit multiple propagating shear bands and other problems. Copyright © 2007 John Wiley & Sons, Ltd. [source] A second-order homogenization procedure for multi-scale analysis based on micropolar kinematicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2007Ragnar Larsson Abstract The paper presents a higher order homogenization scheme based on non-linear micropolar kinematics representing the macroscopic variation within a representative volume element (RVE) of the material. On the microstructural level the micro,macro kinematical coupling is introduced as a second-order Taylor series expansion of the macro displacement field, and the microstructural displacement variation is gathered in a fluctuation term. This approach relates strongly to second gradient continuum formulations, presented by, e.g. Kouznetsova et al. (Int. J. Numer. Meth. Engng 2002; 54:1235,1260), thus establishing a link between second gradient and micropolar theories. The major difference of the present approach as compared to second gradient formulations is that an additional constraint is placed on the higher order deformation gradient in terms of the micropolar stretch. The driving vehicle for the derivation of the homogenized macroscopic stress measures is the Hill,Mandel condition, postulating the equivalence of microscopic and macroscopic (homogenized) virtual work. Thereby, the resulting homogenization procedure yields not only a stress tensor, conjugated to the micropolar stretch tensor, but also the couple stress tensor, conjugated to the micropolar curvature tensor. The paper is concluded by a couple of numerical examples demonstrating the size effects imposed by the homogenization of stresses based on the micropolar kinematics. Copyright © 2006 John Wiley & Sons, Ltd. [source] Non-local damage model based on displacement averagingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005M. Jirásek Abstract Continuum damage models describe the changes of material stiffness and strength, caused by the evolution of defects, in the framework of continuum mechanics. In many materials, a fast evolution of defects leads to stress,strain laws with softening, which creates serious mathematical and numerical problems. To regularize the model behaviour, various generalized continuum theories have been proposed. Integral-type non-local damage models are often based on weighted spatial averaging of a strain-like quantity. This paper explores an alternative formulation with averaging of the displacement field. Damage is assumed to be driven by the symmetric gradient of the non-local displacements. It is demonstrated that an exact equivalence between strain and displacement averaging can be achieved only in an unbounded medium. Around physical boundaries of the analysed body, both formulations differ and the non-local displacement model generates spurious damage in the boundary layers. The paper shows that this undesirable effect can be suppressed by an appropriate adjustment of the non-local weight function. Alternatively, an implicit gradient formulation could be used. Issues of algorithmic implementation, computational efficiency and smoothness of the resolved stress fields are discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source] A spline strip kernel particle method and its application to two-dimensional elasticity problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003K. M. Liew Abstract In this paper we present a novel spline strip kernel particle method (SSKPM) that has been developed for solving a class of two-dimensional (2D) elasticity problems. This new approach combines the concepts of the mesh-free methods and the spline strip method. For the interpolation of the assumed displacement field, we employed the kernel particle shape functions in the transverse direction, and the B3 -spline function in the longitudinal direction. The formulation is validated on several beam and semi-infinite plate problems. The numerical results of these test problems are then compared with the existing solutions obtained by the exact or numerical methods. From this study we conclude that the SSKPM is a potential alternative to the classical finite strip method (FSM). Copyright © 2003 John Wiley & Sons, Ltd. [source] Strategies for computing goal-oriented a posteriori error measures in non-linear elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2002Fredrik Larsson Abstract We investigate the characteristics and performance of goal-oriented a posteriori error measures for a class of non-linear elasticity models, while restriction is made to small strain theory. The chosen error measure of the displacement field can be global or local (probing the chosen quantity in a specific spatial point). The error is computable with the aid of the solution of a dual problem whose data depend on the error measure. The main thrust of the paper is to evaluate the performance of a few different approximation strategies for computing the dual solution. The chosen strategies are compared in terms of accuracy, ease of implementation, reliability and cost-efficiency. A well-known numerical example, the Cook's membrane, is used for the numerical evaluations. Copyright © 2002 John Wiley & Sons, Ltd. [source] Free vibration of sandwich plates with laminated facesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2002W. X. Yuan Description is given of the development of a spline finite strip method for predicting the natural frequencies and modes of conventional rectangular sandwich plates. The faceplates are treated as being classically thin and may be of composite laminated construction. The core is modelled as a three-dimensional body. Finite strip stiffness and mass properties are based on a displacement field which represents eight fundamental through-thickness displacements as a series of products of longitudinal B-spline functions and crosswise Lagrangian or Hermitian polynominal shape functions. The solution procedure utilizes the efficient superstrip concept in conjunction with the extended Sturm sequence-bisection approach. A variety of applications of the developed analysis capability is described which demonstrates the nature of the convergence of the finite strip predictions of natural frequencies and the close comparison of these predictions with available results in the literature, and also the use of the capability in parametric studies. Copyright © 2002 John Wiley & Sons, Ltd. [source] Three-dimensional subzone-based reconstruction algorithm for MR elastographyMAGNETIC RESONANCE IN MEDICINE, Issue 5 2001Elijah E.W. Van Houten Abstract Accurate characterization of harmonic tissue motion for realistic tissue geometries and property distributions requires knowledge of the full three-dimensional displacement field because of the asymmetric nature of both the boundaries of the tissue domain and the location of internal mechanical heterogeneities. The implications of this for magnetic resonance elastography (MRE) are twofold. First, for MRE methods which require the measurement of a harmonic displacement field within the tissue region of interest, the presence of 3D motion effects reduces or eliminates the possibility that simpler, lower-dimensional motion field images will capture the true dynamics of the entire stimulated tissue. Second, MRE techniques that exploit model-based elastic property reconstruction methods will not be able to accurately match the observed displacements unless they are capable of accounting for 3D motion effects. These two factors are of key importance for MRE techniques based on linear elasticity models to reconstruct mechanical tissue property distributions in biological samples. This article demonstrates that 3D motion effects are present even in regular, symmetric phantom geometries and presents the development of a 3D reconstruction algorithm capable of discerning elastic property distributions in the presence of such effects. The algorithm allows for the accurate determination of tissue mechanical properties at resolutions equal to that of the MR displacement image in complex, asymmetric biological tissue geometries. Simulation studies in a realistic 3D breast geometry indicate that the process can accurately detect 1-cm diameter hard inclusions with 2.5× elasticity contrast to the surrounding tissue. Magn Reson Med 45:827,837, 2001. © 2001 Wiley-Liss, Inc. [source] The elastic echo problemMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2003Mongi Mabrouk Abstract We consider a homogeneous isotropic unbounded linear elastic medium ,,,3, having a free boundary ,. A forcing f(t,x) creates an incident displacement field u0(t,x). This primary field is scattered by , giving rise to a secondary field or echo, for which we determine the asymptotic behaviour in time. These results are obtained via the use of an tension of the time-dependent scattering theory of C. Wilcox. Copyright © 2003 John Wiley & Sons, Ltd. [source] The effect of a penalty term involving higher order derivatives on the distribution of phases in an elastic medium with a two-well elastic potentialMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2002M. Bildhauer Abstract We consider the problem of minimizing 0 Refined mixed finite element method for the elasticity problem in a polygonal domainNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2002M. Farhloul Abstract The purpose of this article is to study a mixed formulation of the elasticity problem in plane polygonal domains and its numerical approximation. In this mixed formulation the strain tensor is introduced as a new unknown and its symmetry is relaxed by a Lagrange multiplier, which is nothing else than the rotation. Because of the corner points, the displacement field is not regular in general in the vicinity of the vertices but belongs to some weighted Sobolev space. Using this information, appropriate refinement rules are imposed on the family of triangulations in order to recapture optimal error estimates. Moreover, uniform error estimates in the Lamé coefficient , are obtained for , large. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 323,339, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10009 [source] Tools for multiaxial validation of behavior laws chosen for modeling hyper-elasticity of rubber-like materialsPOLYMER ENGINEERING & SCIENCE, Issue 2 2002L. Chevalier We present an experimental approach to discriminate hyper-elastic models describing the mechanical behavior of rubber-like materials. An evaluation of the displacement field obtained by digital image correlation allows us to evaluate the heterogeneous strain field observed during these tests. We focus on the particular case of hyper-elastic models to simulate the behavior of some rubber-like materials. Assuming incompressibility of the material, the hyper-elastic potential is determined from tension and compression tests. A biaxial loading condition is obtained in a multiaxial testing machine and model predictions are compared with experimental results. [source] Dynamic stability of a porous rectangular platePROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Daniel Debowski The study is devoted to a axial compressed porous-cellular rectangular plate. Mechanical properties of the plate vary across is its thickness which is defined by the non-linear function with dimensionless variable and coefficient of porosity. The material model used in the current paper is as described by Magnucki, Stasiewicz papers. The middle plane of the plate is the symmetry plane. First of all, a displacement field of any cross section of the plane was defined. The geometric and physical (according to Hook's law) relationships are linear. Afterwards, the components of strain and stress states in the plate were found. The Hamilton's principle to the problem of dynamic stability is used. This principle was allowed to formulate a system of five differential equations of dynamic stability of the plate satisfying boundary conditions. This basic system of differential equations was approximately solved with the use of Galerkin's method. The forms of unknown functions were assumed and the system of equations was reduced to a single ordinary differential equation of motion. The critical load determined used numerically processed was solved. Results of solution shown in the Figures for a family of isotropic porous-cellular plates. The effect of porosity on the critical loads is presented. In the particular case of a rectangular plate made of an isotropic homogeneous material, the elasticity coefficients do not depend on the coordinate (thickness direction), giving a classical plate. The results obtained for porous plates are compared to a homogeneous isotropic rectangular plate. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A Finite Element Approach for the Simulation of Quasi-Brittle FracturePROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Oliver Hilgert In the context of a strong discontinuity approach, we propose a finite element formulation with an embedded displacement discontinuity. The basic assumption of the proposed approach is the additive split of the total displacement field in a continuous and a discontinuous part. An arbitrary crack splits the linear triangular finite element into two parts, namely a triangular and a quadrilateral part. The discontinuous part of the displacement field in the quadrilateral portion is approximated using linear shape functions. For these purposes, the quadrilateral portion is divided into two triangular parts which is in this way similar to the approach proposed in [5]. In contrast, the discretisation is different compared to formulations proposed in [1] and [3], where the discontinuous part of the displacement field is approximated using bilinear shape functions. The basic theory of the underlying finite element formulation and a cohesive interface model to simulate brittle fracture are presented. By means of representative numerical examples differences and similarities of the present formulation and the formulations proposed in [1] and [3] are highlighted. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Molecular dynamics simulation of crack tip blunting in opposing directions along a symmetrical tilt grain boundary of copper bicrystalFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 11 2007A. LUQUE ABSTRACT Mode I crack growth along some grain boundaries of copper embrittled by solute segregation shows strong anisotropy. For instance, growth along the direction on the symmetrical tilt boundary has been reported to occur by intergranular brittle fracture, whereas growth along the opposite sense occurs in a ductile manner. In this paper, we simulate such crack configurations using molecular dynamics (embedded atom method [EAM]) in 3-dimensional perfect bicrystalline samples of pure copper of the aforementioned orientation at room temperature. In both cases the response is ductile, crack opening taking place by dislocation emission from the crack tip. The critical stress intensity factors (SIFs) for dislocation emission have been calculated by matching the displacement fields of the atoms in the tip neighbourhood with the continuum elastic fields. They are of the same order of magnitude for both growth senses despite the different morphology of their respective blunted crack tips and of the patterns of dislocations constituting their plastic zones. Thus, it seems that, in agreement with published results of continuum crystalline plasticity for the same problem, the plastic anisotropy associated with the different orientation of the slip systems with respect to the crack cannot in this case explain the experimental behaviour observed with solute embrittled bicrystals. [source]
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