Showing papers on "Linear elasticity published in 2005"
TL;DR: In this paper, a Hookeanelastic model is used to compute the additional effect of bulk mechanical forces on electrode stability. But the authors assume that the surface tension resists the amplification of surface roughness at cathodes and show that instability at lithium/liquid interfaces cannot be prevented by surface forces alone.
Abstract: Department of Chemical Engineering, University of California, Berkeley, California 94720-1462, USAPast theories of electrode stability assume that the surface tension resists the amplification of surface roughness at cathodes andshow that instability at lithium/liquid interfaces cannot be prevented by surface forces alone @Electrochim. Acta, 40, 599 ~1995!#.This work treats interfacial stability in lithium/polymer systems where the electrolyte is solid. Linear elasticity theory is employedto compute the additional effect of bulk mechanical forces on electrode stability. The lithium and polymer are treated as Hookeanelastic materials, characterized by their shear moduli and Poisson’s ratios. Two-dimensional displacement distributions that satisfyforce balances across a periodically deforming interface are derived; these allow computation of the stress and surface-tensionforces. The incorporation of elastic effects into a kinetic model demonstrates regimes of electrolyte mechanical properties whereamplification of surface roughness can be inhibited. For a polymer material with Poisson’s ratio similar to poly~ethylene oxide!,interfacial roughening is mechanically suppressed when the separator shear modulus is about twice that of lithium.© 2005 The Electrochemical Society. @DOI: 10.1149/1.1850854# All rights reserved.Manuscript submitted January 16, 2004; revised manuscript received July 29, 2004. Available electronically January 11, 2005.
1,195 citations
Book•
24 May 2005
TL;DR: Linear Elastic Stress-Strain Relations Elastic Constants Based on Micromechanics, Plane Stress, Global Coordinate System, Elastic Constant Based on Global Coordinated System, Laminate Analysis - Part I- Laminate analysis - Part II- Effective Elastic Constant of a Laminate- Failure Theories of a Laminating System, Homogenization of Composite Materials, to Damage Mechanics of composite Materials as discussed by the authors.
Abstract: Linear Elastic Stress-Strain Relations- Elastic Constants Based on Micromechanics- Plane Stress- Global Coordinate System- Elastic Constants Based on Global Coordinate System- Laminate Analysis - Part I- Laminate Analysis - Part II- Effective Elastic Constants of a Laminate- Failure Theories of a Lamina- to Homogenization of Composite Materials- to Damage Mechanics of Composite Materials
851 citations
TL;DR: In this article, the compressive response of polyester urethane open-cell foams with relative densities of about 0.025 was analyzed using experiments coupled with several levels of modeling.
438 citations
TL;DR: In this paper, a review is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters or buried objects such as cracks.
Abstract: This review is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters or buried objects such as cracks. These inverse problems are considered mainly for three-dimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e., fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded.
411 citations
TL;DR: The authors used finite element procedures combined with knowledge of individual phase moduli, in combination with a cement paste microstructure development model, to predict elastic moduli as a function of degree of hydration, as measured by loss on ignition.
351 citations
TL;DR: In this paper, a shear-lag model for carbon nanotube-reinforced polymer composites using a multiscale approach is developed for axisymmetric problems, and the resulting formulas are derived in closed forms.
258 citations
TL;DR: An experimental and a theoretical study of the radial elasticity of multiwalled carbon nanotubes as a function of external radius is reported, finding a radial Young modulus strongly decreasing with increasing radius and reaching an asymptotic value of 30+/-10 GPa.
Abstract: We report an experimental and a theoretical study of the radial elasticity of multiwalled carbon nanotubes as a function of external radius. We use atomic force microscopy and apply small indentation amplitudes in order to stay in the linear elasticity regime. The number of layers for a given tube radius is inferred from transmission electron microscopy, revealing constant ratios of external to internal radii. This enables a comparison with molecular dynamics results, which also shed some light onto the applicability of Hertz theory in this context. Using this theory, we find a radial Young modulus strongly decreasing with increasing radius and reaching an asymptotic value of 30 � 10 GPa.
223 citations
TL;DR: This work introduces an extension of the linear elastic tensor-mass method allowing fast computation of non-linear and visco-elastic mechanical forces and deformations for the simulation of biological soft tissue and develops a simulation tool for the planning of cryogenic surgical treatment of liver cancer.
158 citations
01 Jun 2005
TL;DR: In this paper, the authors describe the motion of a system: geometry and kinematics, and describe the fundamental laws of dynamics, including the Cauchy stress-tensor and the Schrodinger equation.
Abstract: Part I. Fundamental Concepts in Continuum Mechanics: 1. Describing the motion of a system: geometry and kinematics 2. The fundamental law of dynamics 3. The Cauchy stress-tensor. Applications 4. Real and virtual powers 5. Deformation tensor. Deformation rate tensor. Constitutive laws 6. Energy equations. Shock equations Part II. Physics of Fluids: 7. General properties of Newtonian fluids 8. Flows of perfect fluids 9. Viscous fluids and thermohydraulics 10. Magnetohydrodynamics and inertial confinement of plasmas 11. Combustion 12. Equations of the atmosphere and of the ocean Part III. Solid Mechanics: 13. The general equations of linear elasticity 14. Classical problems of elastostatics 15. Energy theorems. Duality. Variational formulations 16. Introduction to nonlinear constitutive laws and to homogenization Part IV. Introduction to Wave Phenomena: 17. Linear wave equations in mechanics 18. The soliton equation: the Korteweg-de Vries equations 19. The nonlinear Schrodinger equation Appendix A.
135 citations
Book•
01 May 2005TL;DR: In this article, the authors describe the motion of a system: geometry and kinematics, and describe the fundamental laws of dynamics, including the Cauchy stress-tensor and the Schrodinger equation.
Abstract: Part I. Fundamental Concepts in Continuum Mechanics: 1. Describing the motion of a system: geometry and kinematics 2. The fundamental law of dynamics 3. The Cauchy stress-tensor. Applications 4. Real and virtual powers 5. Deformation tensor. Deformation rate tensor. Constitutive laws 6. Energy equations. Shock equations Part II. Physics of Fluids: 7. General properties of Newtonian fluids 8. Flows of perfect fluids 9. Viscous fluids and thermohydraulics 10. Magnetohydrodynamics and inertial confinement of plasmas 11. Combustion 12. Equations of the atmosphere and of the ocean Part III. Solid Mechanics: 13. The general equations of linear elasticity 14. Classical problems of elastostatics 15. Energy theorems. Duality. Variational formulations 16. Introduction to nonlinear constitutive laws and to homogenization Part IV. Introduction to Wave Phenomena: 17. Linear wave equations in mechanics 18. The soliton equation: the Korteweg-de Vries equations 19. The nonlinear Schrodinger equation Appendix A.
130 citations
01 Mar 2005
TL;DR: In this paper, a hexagonal chiral honeycomb was proposed as a truss-like internal structure for adaptive wing box configurations, which exhibited negative Poisson's ratio behavior under a large range of strain.
Abstract: In this paper a concept of hexagonal chiral honeycomb is proposed as a truss-like internal structure for adaptive wing box configurations. In contrast with classical centresym-metric cellular structures like rectangular or hexagonal grids, the proposed honeycomb did not present inversion symmetry, and featured an in-plane negative Poisson's ratio behaviour. The cellular structure considered exhibited this Poisson's ratio behaviour under a large range of strain. A set of numerical (finite element, FE) simulations have been carried out in order to correct the initial theoretical predictions to take into account axial, shear and elastic deformations of all elements composing the unit cell when subjected to uniaxial loading. The homogenized linear elastic mechanical properties were then introduced in an FE wing box model of a racecar wing coupled to a panel code to simulate unidirectional static fluid—structure coupling between the wing box and the flow surrounding the airfoil. The cellular solid prop...
TL;DR: In this article, the elastic and failure mechanical properties of hydrogen-free tetrahedral amorphous carbon (ta-C) MEMS structures were investigated via in situ direct and local displacement measurements by a method that integrates atomic force microscopy (AFM) with digital image correlation (DIC).
Abstract: The elastic and failure mechanical properties of hydrogen-free tetrahedral amorphous carbon (ta-C) MEMS structures were investigated via in situ direct and local displacement measurements by a method that integrates atomic force microscopy (AFM) with digital image correlation (DIC). On-chip MEMS-scale specimens were tested via a custom-designed apparatus that was integrated with an AFM to conduct in situ uniaxial tension tests. Specimens 10 µm and 50 µm wide and of 1.5 µm average thickness were used to measure the elastic properties while 340 µm wide tension specimens with a central elliptical perforation resulting in a stress concentration factor of 27 were tested to investigate local effects on material strength. The Young's modulus, Poisson's ratio and tensile strength were measured as 759 ± 22 GPa, 0.17 ± 0.03 and 7.3 ± 1.2 GPa, respectively. In an effort to understand the effect of local defects and assess the true material strength, the local failure stress at sharp central elliptical notches with a stress concentration factor of 27 was measured to be 11.4 ± 0.8 GPa. The AFM/DIC method provided for the first time local displacement fields in the vicinity of microscale perforations and these displacement fields were in accordance with those predicted by linear elasticity.
Abstract: A tool for studying links between continuum plasticity and dislocation theory within a field framework is presented A finite element implementation of the geometrically linear version of a recently proposed theory of field dislocation mechanics (J Mech Phys Solids 49 (2001) 761; Proc Roy Soc 459 (2003) 1343; J Mech Phys Solids 52 (2004) 301) represents the main idea behind the tool The constitutive ingredients of the theory under consideration are simply elasticity and a specification of dislocation velocity and nucleation The set of equations to be approximated are non-standard in the context of solid mechanics applications It comprises the standard second-order equilibrium equations, a first-order div–curl system for the elastic incompatibility, and a first-order, wave-propagative system for the evolution of dislocation density The latter two sets of equations require special treatment as the standard Galerkin method is not adequate, and are solved utilizing a least-squares finite element strategy The implementation is validated against analytical results of the classical elastic theory of dislocations and analytical results of the theory itself Elastic stress fields of dislocation distributions in generally anisotropic media of finite extent, deviation from elastic response, yield-drop, and back-stress are shown to be natural consequences of the model The development of inhomogeneity, from homogeneous initial conditions and boundary conditions corresponding to homogeneous deformation in conventional plasticity, is also demonstrated To our knowledge, this work represents the first computational implementation of a theory of dislocation mechanics where no analytical results, singular solutions in particular, are required to formulate the implementation In particular, a part of the work is the first finite element implementation of Kroner's linear elastic theory of continuously distributed dislocations in its full generality
TL;DR: A force balance condition to predict quasistatic crack paths in anisotropic brittle materials is derived from an analysis of diffuse interface continuum models that describe both short-scale failure and macroscopic linear elasticity.
Abstract: A force balance condition to predict quasistatic crack paths in anisotropic brittle materials is derived from an analysis of diffuse interface continuum models that describe both short-scale failure and macroscopic linear elasticity. The path is uniquely determined by the directional anisotropy of the fracture energy, independent of details of the failure process. The derivation exploits the gradient dynamics and translation symmetry properties of this class of models to define a generalized energy-momentum tensor whose integral around an arbitrary closed path enclosing the crack tip yields all forces acting on this tip, including Eshelby's configurational forces, cohesive forces, and dissipative forces. Numerical simulations are in very good agreement with analytic predictions.
TL;DR: A stable mixed finite element method for linear elasticity in three dimensions is described and it is shown that this method can be generalized to 2D and 3D spaces.
Abstract: We describe a stable mixed finite element method for linear elasticity in three dimensions.
TL;DR: In this article, a discrete theory of crystal elasticity and dislocations in crystal lattices is proposed, based on algebraic topology and differential calculus such as chain complexes and homology groups, differential forms and operators.
Abstract: This article is concerned with the development of a discrete theory of crystal elasticity and dislocations in crystals. The theory is founded upon suitable adaptations to crystal lattices of elements of algebraic topology and differential calculus such as chain complexes and homology groups, differential forms and operators, and a theory of integration of forms. In particular, we define the lattice complex of a number of commonly encountered lattices, including body-centered cubic and face-centered cubic lattices. We show that material frame indifference naturally leads to discrete notions of stress and strain in lattices. Lattice defects such as dislocations are introduced by means of locally lattice-invariant (but globally incompatible) eigendeformations. The geometrical framework affords discrete analogs of fundamental objects and relations of the theory of linear elastic dislocations, such as the dislocation density tensor, the equation of conservation of Burgers vector, Kroner's relation and Mura's formula for the stored energy. We additionally supply conditions for the existence of equilibrium displacement fields; we show that linear elasticity is recovered as the Γ-limit of harmonic lattice statics as the lattice parameter becomes vanishingly small; we compute the Γ-limit of dilute dislocation distributions of dislocations; and we show that the theory of continuously distributed linear elastic dislocations is recovered as the Γ-limit of the stored energy as the lattice parameter and Burgers vectors become vanishingly small.
TL;DR: In this article, the connection between gradient theory and nonlocal theory is discussed for elasticity as well as for micropolar elasticity, and Nonsingular solutions for the elastic fields of screw and edge dislocations are given.
Abstract: In this paper we consider and compare special classes of static theories of gradient elasticity, nonlocal elasticity, gradient micropolar elasticity and nonlocal micropolar elasticity with only one gradient coefficient. Equilibrium equations are presented but higher-order boundary conditions are not of concern here, since they are not required for the problems considered. The connection between gradient theory and nonlocal theory is discussed for elasticity as well as for micropolar elasticity. Nonsingular solutions for the elastic fields of screw and edge dislocations are given. Both the elastic deformation (distortion, strain, bend-twist) and the force and couple stress tensors do not possess any singularity unlike ‘classical’ theories. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
TL;DR: A model of elastic properties of articular cartilage based on its microstructure is developed, demonstrating that the axial elastic modulus decreases from the deep zone to the articular surface, a result that is in good agreement with experimental findings.
TL;DR: In this article, the authors proposed a new concept based on a Taylor expansion of the constitutively dependent quantities with respect to the center of the element, which is called hourglass stabilization part of the residual force vector.
TL;DR: In this paper, the authors define the minimal kinematic boundary conditions such that only the desired overall strain is imposed on the volume element, with no other undesirable constraints, and prove that such conditions result in a unique solution for the linear elastic case, and that the uniqueness for nonlinear problems is dependent on the pointwise positive definiteness of the incremental stiffness tensor.
Abstract: In simulations of representative volume elements (RVEs) of materials with disordered microstructures, commonly used rigid and periodic boundary conditions (BCs) introduce additional constraints, causing: (i) boundary effects, (ii) unrealistic stiff response, (iii) artificial wavelengths in the solution fields, and (iv) suppression of solutions with localized deformation that otherwise may occur in the simulation. In this paper we define the minimal kinematic boundary conditions such that only the desired overall strain is imposed on the RVE, with no other undesirable constraints. We prove that such BCs result in a unique solution for the linear elastic case, and that the uniqueness for nonlinear problems is dependent on the pointwise positive definiteness of the incremental stiffness tensor. Upon incorporating the minimal BCs into the finite element framework, we consider, as an example, two-dimensional, linear elastic, disordered polycrystals and perform a systematic study of the effects of boundary conditions while varying the RVE size and controlling the sampling error. The results demonstrate that the minimal BCs, applicable to a RVE of any shape, are superior to other BCs, in that they give more realistic overall behaviour, reduce the required size of the RVE, and eliminate the superficial wavelengths in the solution field, ubiquitous in simulations with other boundary conditions.
TL;DR: In this paper, the scaling center is located at the crack tip and the scaled boundary finite element solution converges to the Williams expansion, and the coefficients of Williams expansion including the stress intensity factor and the T-stress can be determined directly without further processing.
TL;DR: In this article, a study was undertaken to characterise the mechanical properties of cancellous bone from the human cervical spine from eight male cadavers (aged 40 − 79 yrs) subjected to quasi-static and dynamic compression.
Book•
08 Feb 2005
TL;DR: In this paper, the authors present a theoretical analysis of the Reissner Variational Theorem and its application in the context of plate and plate-and-sandwich construction.
Abstract: Part 1 - Plates and Panels of Isotropic Materials:- 1. Equations of Linear Elasticity in Cartesian Coordinates. 2. Derivation of the Governing Equations for Isotropic Rectangular Plates. 3. Solutions to Problems of Isotropic Rectangular Plates. 4. Thermal Stress in Plates. 5. Circular Isotropic Plates. 6. Buckling of Isotropic Columns and Plates. 7. Vibrations of Isotropic Beams and Plates. 8. Theorem of Minimum Potential Energy, Hamilton's Principle and Their Applications. 9. Reissner's Variational Theorem and Its Applications. Part 2 - Plates and Panels of Composite Materials:- 10. Anisotropic Elasticity and Composite Laminate Theory. 11. Plates and Panels of Composite Materials. 12. Elastic Instability (Buckling) of Composite Plates. 13. Linear and Nonlinear Vibration of Composite Plates. 14. Energy Methods for Composite Material Structures. Part 3 - Plates and Panels of Sandwich Construction:- 15. Governing Equations for Plates and Panels of Sandwich Construction. 16. Elastic Instability (Buckling) of Sandwich Plates. 17. Structural Optimization to Obtain Minimum Weight Sandwich Panels. Part 4 - Plates Using Smart (Piezoelectric) Materials: 18. Piezoelectric Materials. 19. Piezoelectric Effects. 20. Use of Minimum Potential Energy to Analyze a Piezoelectric Beam. Author Index. Subject Index
TL;DR: In this article, a micromechanical finite element calculation was performed in order to investigate the influence of matrix plasticity and temperature dependent mechanical and thermal properties on the formation of thermal residual stresses in unidirectional carbon fiber epoxy composites.
TL;DR: A mixed formulation of a spectral element approximation of the linear elasticity system is presented and perfectly matched layers (PMLs) are constructed for modeling unbounded domains.
Abstract: In this paper, we present a mixed formulation of a spectral element approximation of the linear elasticity system. After studying the main features of this approach, we construct perfectly matched layers (PMLs) for modeling unbounded domains. Then, algorithmic issues are discussed and numerical results are given.
TL;DR: In this article, a two-dimensional finite element analysis of composite bonded single-lap joints was presented, where six-node interface elements compatible with eight-node isoparametric plane solid elements were placed between the adherends and the adhesive, at the midplane of the adhesive and at the interfaces between different oriented layers of the adhereds.
TL;DR: In this article, the application of the method of fundamental solutions to the Cauchy problem in three-dimensional isotropic linear elasticity is investigated, where the resulting system of linear algebraic equations is ill-conditioned and therefore, its solution is regularized by employing the first-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method.
Abstract: The application of the method of fundamental solutions to the Cauchy problem in three-dimensional isotropic linear elasticity is investigated. The resulting system of linear algebraic equations is ill-conditioned and therefore, its solution is regularized by employing the first-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method. Numerical results are presented for both under- and equally-determined Cauchy problems in a piece-wise smooth geometry. The convergence, accuracy, and stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain, and decreasing the amount of noise added into the input data, respectively, are analysed.
TL;DR: An extension of the discrete element modeling (DEM) approach, or clustered DEM, was used to simulate the hollow cylinder tensile (HCT) test, in which various material phases (e.g., aggregates, mastic) are modeled with bonded clusters of discrete elements as mentioned in this paper.
Abstract: An extension of the discrete element modeling (DEM) approach, or clustered DEM, was used to simulate the hollow cylinder tensile (HCT) test, in which various material phases (e.g., aggregates, mastic) are modeled with bonded clusters of discrete elements. The basic principle of the HCT test is the application of internal pressure to the inner cavity of a hollow cylinder specimen, which produces circumferential strain. In the present study an experimental program was conducted to measure the complex modulus of asphalt concrete mixtures at various loading rates and temperatures. The HCT test was then modeled with a two-dimensional, linear elastic DEM simulation. The current approach uses the correspondence principle to bridge between the elastic simulation and viscoelastic response. The two-dimensional morphology of the asphalt concrete mixture was captured with a high-resolution scanner, enhanced with image-processing techniques, and reconstructed into an assembly of discrete elements. The mixture complex moduli predicted in the HCT simulations were found to be in good agreement with experimental measurements across a range of test temperatures and loading frequencies for the coarse-grained mixtures investigated. Ongoing work in the area of viscoelastic constitutive modeling, fracture modeling, and three-dimensional tomography and modeling will extend the capabilities of this promising technique for fundamental studies of asphalt concrete and other particulate composites.
TL;DR: In this article, a meshless method based on the local Petrov-Galerkin approach is proposed for stress analysis in two-dimensional (2D), anisotropic and linear elastic/viscoelastic solids with continuously varying material properties.
Abstract: A meshless method based on the local Petrov–Galerkin approach is proposed for stress analysis in two-dimensional (2D), anisotropic and linear elastic/viscoelastic solids with continuously varying material properties. The correspondence principle is applied for non-homogeneous, anisotropic and linear viscoelastic solids where the relaxation moduli are separable in space and time. The inertial dynamic term in the governing equations is considered too. A unit step function is used as the test functions in the local weak-form. It leads to local boundary integral equations (LBIEs). The analyzed domain is divided into small subdomains with a circular shape. The moving least squares (MLS) method is adopted for approximating the physical quantities in the LBIEs. For time-dependent problems, the Laplace-transform technique is utilized. Several numerical examples are given to verify the accuracy and the efficiency of the proposed method.