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Showing papers on "Linear elasticity published in 2004"


Journal ArticleDOI
TL;DR: This paper introduces and analyze a finite element method for elasticity problems with interfaces and proposes a general approach that can handle both perfectly and imperfectly bonded interfaces without modifications of the code.

791 citations


Proceedings Article
17 May 2004
TL;DR: This method extends the warped stiffness finite element approach for linear elasticity and combines it with a strain-state-based plasticity model and produces realistic animations of a wide spectrum of materials at interactive rates that have typically been simulated off-line thus far.
Abstract: In this paper we present a fast and robust approach for simulating elasto-plastic materials and fracture in real time. Our method extends the warped stiffness finite element approach for linear elasticity and combines it with a strain-state-based plasticity model. The internal principal stress components provided by the finite element computation are used to determine fracture locations and orientations. We also present a method to consistently animate and fracture a detailed surface mesh along with the underlying volumetric tetrahedral mesh. This multi-resolution strategy produces realistic animations of a wide spectrum of materials at interactive rates that have typically been simulated off-line thus far.

524 citations


Journal ArticleDOI
TL;DR: In this article, an instability criterion based on bifurcation analysis is incorporated into the finite element calculation to predict homogeneous dislocation nucleation, which is superior to that based on the critical resolved shear stress in terms of its accuracy of prediction for both the nucleation site and slip character of the defect.
Abstract: Nanoscale contact of material surfaces provides an opportunity to explore and better understand the elastic limit and incipient plasticity in crystals. Homogeneous nucleation of a dislocation beneath a nanoindenter is a strain localization event triggered by elastic instability of the perfect crystal at finite strain. The finite element calculation, with a hyperelastic constitutive relation based on an interatomic potential, is employed as an efficient method to characterize such instability. This implementation facilitates the study of dislocation nucleation at length scales that are large compared to atomic dimensions, while remaining faithful to the nonlinear interatomic interactions. An instability criterion based on bifurcation analysis is incorporated into the finite element calculation to predict homogeneous dislocation nucleation. This criterion is superior to that based on the critical resolved shear stress in terms of its accuracy of prediction for both the nucleation site and the slip character of the defect. Finite element calculations of nanoindentation of single crystal copper by a cylindrical indenter and predictions of dislocation nucleation are validated by comparing with direct molecular dynamics simulations governed by the same interatomic potential. Analytic 2D and 3D linear elasticity solutions based on the Stroh formalism are used to benchmark the finite element results. The critical configuration of homogeneous dislocation nucleation under a spherical indenter is quantified with full 3D finite element calculations. The prediction of the nucleation site and slip character is verified by direct molecular dynamics simulations. The critical stress state at the nucleation site obtained from the interatomic potential is in quantitative agreement with ab initio density functional theory calculation.

234 citations


Journal ArticleDOI
TL;DR: In this article, a method for modeling the growth of multiple cracks in linear elastic media is presented, which uses the extended finite element method for arbitrary discontinuities and does not require remeshing as the cracks grow; the method also treats the junction of cracks.
Abstract: SUMMARY A method for modelling the growth of multiple cracks in linear elastic media is presented. Both homogeneous and inhomogeneous materials are considered. The method uses the extended finite element method for arbitrary discontinuities and does not require remeshing as the cracks grow; the method also treats the junction of cracks. The crack geometries are arbitrary with respect to the mesh and are described by vector level sets. The overall response of the structure is obtained until complete failure. A stability analysis of competitive cracks tips is performed. The method is applied to bodies in plane strain or plane stress and to unit cells with 2‐10 growing cracks (although the method does not limit the number of cracks). It is shown to be efficient and accurate for crack coalescence and percolation problems. Copyright ! 2004 John Wiley & Sons, Ltd.

225 citations


Journal ArticleDOI
TL;DR: In this article, a generalized continuum representation of two-dimensional periodic cellular solids is obtained by treating these materials as micropolar continua, and the effects of shear deformation of the cell walls on the elastic constants are also discussed.

183 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of surface energy on the effective elastic properties was analyzed for elastic composite materials containing spherical nanocavities at dilute concentration, and closed-form solutions of the effective shear modulus and bulk modulus were obtained.
Abstract: The effect of surface energy on the effective elastic properties was analyzed for elastic composite materials containing spherical nanocavities at dilute concentration. Closed-form solutions of the effective shear modulus and bulk modulus were obtained, which turn out to be a function of the surface energy and size of the nanocavity. The dependence of the elastic response on size of the nanocavity in composite materials is different from the classic results obtained in the linear elasticity theory, suggesting the importance of the surface energy of the nanocavity in analyzing the deformation of nanoscale structures.

176 citations


Journal ArticleDOI
TL;DR: In this paper, the experimental inputs related to the constitutive model of the powder and the powder/tooling friction are determined, and the calibration techniques were developed based on a series of simple mechanical tests including diametrical compression, simple compression, and die compaction using an instrumented die.

168 citations


Journal ArticleDOI
TL;DR: VBFM has the potential to increase the robustness and reliability of micromanipulation and biomanipulation tasks where force sensing is essential for success and is demonstrated for both a microcantilever beam and a microgripper.
Abstract: This paper demonstrates a method to visually measure the force distribution applied to a linearly elastic object using the contour data in an image. The force measurement is accomplished by making use of the result from linear elasticity that the displacement field of the contour of a linearly elastic object is sufficient to completely recover the force distribution applied to the object. This result leads naturally to a deformable template matching approach where the template is deformed according to the governing equations of linear elasticity. An energy minimization method is used to match the template to the contour data in the image. This technique of visually measuring forces we refer to as vision-based force measurement (VBFM). VBFM has the potential to increase the robustness and reliability of micromanipulation and biomanipulation tasks where force sensing is essential for success. The effectiveness of VBFM is demonstrated for both a microcantilever beam and a microgripper. A sensor resolution of less than +/-3 nN for the microcantilever and +/-3 mN for the microgripper was achieved using VBFM. Performance optimizations for the energy minimization problem are also discussed that make this algorithm feasible for real-time applications.

153 citations


Book
18 Jun 2004
TL;DR: In this paper, the authors propose a method for the conservation of angular momentum in the context of linear elastic materials, and derive the strong form from the weak form of a tetrahedral element.
Abstract: Preface.Nomenclature.1 Displacements, Strain, Stress and Energy.1.1 The Reference State.1.2 The Spatial State.1.3 Strain Measures.1.4 Principal Strains.1.5 Velocity.1.6 Objective Tensors.1.7 Balance Laws.1.7.1 Conservation of mass.1.7.2 Conservation of momentum.1.7.3 Conservation of angular momentum.1.7.4 Conservation of energy.1.7.5 Entropy inequality.1.7.6 Closure.1.8 Localization of the Balance Laws.1.8.1 Conservation of mass.1.8.2 Conservation of momentum.1.8.3 Conservation of angular momentum.1.8.4 Conservation of energy.1.8.5 Entropy inequality.1.9 The Stress Tensor.1.10 The Balance Laws in Material Coordinates.1.10.1 Conservation of mass.1.10.2 Conservation of momentum.1.10.3 Conservation of angular momentum.1.10.4 Conservation of energy.1.10.5 Entropy inequality.1.11 The Weak Form of the Balance of Momentum.1.11.1 Formulation of the boundary conditions (material coordinates).1.11.2 Deriving the weak form from the strong form (material coordinates).1.11.3 Deriving the strong form from the weak form (material coordinates).1.11.4 The weak form in spatial coordinates.1.12 The Weak Form of the Energy Balance.1.13 Constitutive Equations.1.13.1 Summary of the balance equations.1.13.2 Development of the constitutive theory.1.14 Elastic Materials.1.14.1 General form.1.14.2 Linear elastic materials.1.14.3 Isotropic linear elastic materials.1.14.4 Linearizing the strains.1.14.5 Isotropic elastic materials.1.15 Fluids.2 Linear Mechanical Applications.2.1 General Equations.2.2 The Shape Functions.2.2.1 The 8-node brick element.2.2.2 The 20-node brick element.2.2.3 The 4-node tetrahedral element.2.2.4 The 10-node tetrahedral element.2.2.5 The 6-node wedge element.2.2.6 The 15-node wedge element.2.3 Numerical Integration.2.3.1 Hexahedral elements.2.3.2 Tetrahedral elements.2.3.3 Wedge elements.2.3.4 Integration over a surface in three-dimensional space.2.4 Extrapolation of Integration Point Values to the Nodes.2.4.1 The 8-node hexahedral element.2.4.2 The 20-node hexahedral element.2.4.3 The tetrahedral elements.2.4.4 The wedge elements.2.5 Problematic Element Behavior.2.5.1 Shear locking.2.5.2 Volumetric locking.2.5.3 Hourglassing.2.6 Linear Constraints.2.6.1 Inclusion in the global system of equations.2.6.2 Forces induced by linear constraints.2.7 Transformations.2.8 Loading.2.8.1 Centrifugal loading.2.8.2 Temperature loading.2.9 Modal Analysis.2.9.1 Frequency calculation.2.9.2 Linear dynamic analysis.2.9.3 Buckling.2.10 Cyclic Symmetry.2.11 Dynamics: The alpha-Method.2.11.1 Implicit formulation.2.11.2 Extension to nonlinear applications.2.11.3 Consistency and accuracy of the implicit formulation.2.11.4 Stability of the implicit scheme.2.11.5 Explicit formulation.2.11.6 The consistent mass matrix.2.11.7 Lumped mass matrix.2.11.8 Spherical shell subject to a suddenly applied uniform pressure.3 Geometric Nonlinear Effects.3.1 General Equations.3.2 Application to a Snapping-through Plate.3.3 Solution-dependent Loading.3.3.1 Centrifugal forces.3.3.2 Traction forces.3.3.3 Example: a beam subject to hydrostatic pressure.3.4 Nonlinear Multiple Point Constraints.3.5 Rigid Body Motion.3.5.1 Large rotations.3.5.2 Rigid body formulation.3.5.3 Beam and shell elements.3.6 Mean Rotation.3.7 Kinematic Constraints.3.7.1 Points on a straight line.3.7.2 Points in a plane.3.8 Incompressibility Constraint.4 Hyperelastic Materials.4.1 Polyconvexity of the Stored-energy Function.4.1.1 Physical requirements.4.1.2 Convexity.4.1.3 Polyconvexity.4.1.4 Suitable stored-energy functions.4.2 Isotropic Hyperelastic Materials.4.2.1 Polynomial form.4.2.2 Arruda-Boyce form.4.2.3 The Ogden form.4.2.4 Elastomeric foam behavior.4.3 Nonhomogeneous Shear Experiment.4.4 Derivatives of Invariants and Principal Stretches.4.4.1 Derivatives of the invariants.4.4.2 Derivatives of the principal stretches.4.4.3 Expressions for the stress and stiffness for three equal eigenvalues.4.5 Tangent Stiffness Matrix at Zero Deformation.4.5.1 Polynomial form.4.5.2 Arruda-Boyce form.4.5.3 Ogden form.4.5.4 Elastomeric foam behavior.4.5.5 Closure.4.6 Inflation of a Balloon.4.7 Anisotropic Hyperelasticity.4.7.1 Transversely isotropic materials.4.7.2 Fiber-reinforced material.5 Infinitesimal Strain Plasticity.5.1 Introduction.5.2 The General Framework of Plasticity.5.2.1 Theoretical derivation.5.2.2 Numerical implementation.5.3 Three-dimensional Single Surface Viscoplasticity.5.3.1 Theoretical derivation.5.3.2 Numerical procedure.5.3.3 Determination of the consistent elastoplastic tangent matrix.5.4 Three-dimensional Multisurface Viscoplasticity: the Cailletaud Single Crystal Model.5.4.1 Theoretical considerations.5.4.2 Numerical aspects.5.4.3 Stress update algorithm.5.4.4 Determination of the consistent elastoplastic tangent matrix.5.4.5 Tensile test on an anisotropic material.5.5 Anisotropic Elasticity with a von Mises-type Yield Surface.5.5.1 Basic equations.5.5.2 Numerical procedure.5.5.3 Special case: isotropic elasticity.6 Finite Strain Elastoplasticity.6.1 Multiplicative Decomposition of the Deformation Gradient.6.2 Deriving the Flow Rule.6.2.1 Arguments of the free-energy function and yield condition.6.2.2 Principle of maximum plastic dissipation.6.2.3 Uncoupled volumetric/deviatoric response.6.3 Isotropic Hyperelasticity with a von Mises-type Yield Surface.6.3.1 Uncoupled isotropic hyperelastic model.6.3.2 Yield surface and derivation of the flow rule.6.4 Extensions.6.4.1 Kinematic hardening.6.4.2 Viscoplastic behavior.6.5 Summary of the Equations.6.6 Stress Update Algorithm.6.6.1 Derivation.6.6.2 Summary.6.6.3 Expansion of a thick-walled cylinder.6.7 Derivation of Consistent Elastoplastic Moduli.6.7.1 The volumetric stress.6.7.2 Trial stress.6.7.3 Plastic correction.6.8 Isochoric Plastic Deformation.6.9 Burst Calculation of a Compressor.7 Heat Transfer.7.1 Introduction.7.2 The Governing Equations.7.3 Weak Form of the Energy Equation.7.4 Finite Element Procedure.7.5 Time Discretization and Linearization of the Governing Equation.7.6 Forced Fluid Convection.7.7 Cavity Radiation.7.7.1 Governing equations.7.7.2 Numerical aspects.References.Index.

150 citations


Journal ArticleDOI
TL;DR: The linear elastic model is very suitable for estimating wall Young's modulus from micromanipulation experiments on single suspension-cultured tomato cells, and is a powerful method for determining cell wall material properties.

140 citations


Journal ArticleDOI
TL;DR: The results of this study demonstrate that similar values for the cell modulus can be obtained from three models of increasing complexity, however, the viscoelastic and biphasic models generate additional material properties that are important for characterizing the transient response of compressed chondrocytes.

Book ChapterDOI
26 Sep 2004
TL;DR: This work introduces a new approach to simultaneously identify mesh topology and spring stiffness values and shows that uniform distributions of spring stiffness constants fails to simulate linear elastic deformations.
Abstract: Mass-spring systems are of special interest for soft tissue modeling in surgical simulation due to their ease of implementation and real-time behavior. However, the parameter identification (masses, spring constants, mesh topology) still remains a challenge. In previous work, we proposed an approach based on the training of mass-spring systems according to known reference models. Our initial focus was the determination of mesh topology in 2D. In this paper, we extend the method to 3D. Furthermore, we introduce a new approach to simultaneously identify mesh topology and spring stiffness values. Linear elastic FEM deformation computations are used as reference. Additionally, our results show that uniform distributions of spring stiffness constants fails to simulate linear elastic deformations.

Book ChapterDOI
TL;DR: This chapter presents different algorithms for modeling soft tissue deformation in the context of surgery simulation, which make radical simplifications about tissue material property, tissue visco-elasticity and tissue anatomy.
Abstract: This chapter presents different algorithms for modeling soft tissue deformation in the context of surgery simulation These algorithms make radical simplifications about tissue material property, tissue visco-elasticity and tissue anatomy The chapter describes the principles and the components of a surgical simulator It also presents the process of building a patient-specific hepatic surgery simulator from a set of medical images The different stages of computation leading to the creation of a volumetric tetrahedral mesh from a medical image are especially emphasized Later, it describes the five main hypotheses that are made in the proposed soft tissue models Moreover, the main equations of isotropic and transversally anisotropic linear elasticity in continuum mechanics are also presented The discretization of these equations is presented that are based on finite element modeling The simple linear tetrahedron element is presented that provide closed form expressions of local and global stiffness matrices After describing the types of boundary conditions existing in surgery simulation, the static and dynamic equilibrium equations in their matrix form are derived The chapter introduces a first model of soft tissue; it is based on the off-line inversion of the stiffness matrix and can be computed very efficiently as long as no topology change is required A second soft tissue model allows to perform cutting and tearing but with less efficiency as the previous model A combination of the two previous models, called “hybrid model” is also presented in the chapter It also introduces an extension of the second soft tissue model that implements large displacement elasticity

Journal ArticleDOI
TL;DR: In this article, the authors measured the four independent linear elastic engineering constants of the orthotropic MFC actuator under short-circuit electrical boundary conditions using standard tensile testing procedures, and used these experimental results to characterize the nonlinear tensile and shear stress-strain behavior and Poisson effects.
Abstract: The Macro Fiber Composite (MFC) actuator, developed at the NASA Langley Research Center, offers much higher flexibility and induced strain levels (~2000μσ, peak-to-peak) than its monolithic piezoceramic predecessors. The focus of this work is twofold; to measure the four independent linear elastic engineering constants of the orthotropic MFC actuator under short-circuit electrical boundary conditions using standard tensile testing procedures, and to use these experimental results to characterize the nonlinear tensile and shear stress–strain behavior and Poisson effects using various plastic deformation models. The results can then be readily incorporated into the piezoelectric constitutive equation and ultimately into structural actuation models that accurately consider nonlinear mechanical behavior.

Journal ArticleDOI
TL;DR: In this paper, a linear elastic and progressive damage approach was used to predict the strength of unnotched and notched laminate laminates in tension and compression conditions, and the results showed that the linear elastic model either significantly underestimated (first-ply failure approach) or overestimated (last-plummer failure approach).

Journal ArticleDOI
19 Feb 2004
TL;DR: Stiffness relationship of Hertzian contact for linear elastic materials is shown to be a special case of the general theory presented in this paper, and potential applications to fixturing are discussed.
Abstract: In this paper, nonlinear stiffness of contact for soft fingers, commonly used in robotic grasping and manipulation, under a normal load is studied. Building upon previous research results of soft-finger contact expressed in the power-law equation, the equation for the nonlinear stiffness of soft contact was derived. This new theory relates the approach displacement (or the vertical depression) of soft fingertips with respect to the normal force applied. The nonlinear contact stiffness is found to be the product of an exponent and the ratio of the normal force versus approach displacement. Stiffness relationship of Hertzian contact for linear elastic materials is shown to be a special case of the general theory presented in this paper. Experimental results are used to validate the theoretical analysis. In addition, potential applications to fixturing are discussed.

Journal ArticleDOI
TL;DR: In this article, an extension of the classical asymptotic homogenization theory was proposed for the scalar problem of antiplane shear, which was extended to three-dimensional linear elasticity.
Abstract: Classical effective descriptions of heterogeneous materials fail to capture the influence of the spatial scale of the heterogeneity on the overall response of components. This influence may become important when the scale at which the effective continuum fields vary approaches that of the microstructure of the material and may then give rise to size effects and other deviations from the classical theory. These effects can be successfully captured by continuum theories that include a material length scale, such as strain gradient theories. However, the precise relation between the microstructure, on the one hand, and the length scale and other properties of the effective modeling, on the other, are usually unknown. A rigorous link between these two scales of observation is provided by an extension of the classical asymptotic homogenization theory, which was proposed by Smyshlyaev and Cherednichenko (J. Mech. Phys. Solids 48:1325‐1358, 2000) for the scalar problem of antiplane shear. In the present contribution, this method is extended to three-dimensional linear elasticity. It requires the solution of a series of boundary value problems on the periodic cell that characterizes the microstructure. A finite element solution strategy is developed for this purpose. The resulting fields can be used to determine the effective higherorder elasticity constants required in the Toupin-Mindlin strain gradient theory. The method has been applied to a matrix-inclusion composite, showing that higher-order terms become more important as the stiffness contrast between inclusion and matrix increases.

Journal ArticleDOI
TL;DR: It is shown that the homogeneous least-squares functional is elliptic and continuous in the H({\rm div};\,\Omega)^d \times H^1(\Omega]^d$ norm, which immediately implies optimal error estimates for finite element subspaces of the L2 norm.
Abstract: This paper develops least-squares methods for the solution of linear elastic problems in both two and three dimensions. Our main approach is defined by simply applying the L2 norm least-squares principle to a stress-displacement system: the constitutive and the equilibrium equations. It is shown that the homogeneous least-squares functional is elliptic and continuous in the $H({\rm div};\,\Omega)^d \times H^1(\Omega)^d$ norm. This immediately implies optimal error estimates for finite element subspaces of $H({\rm div};\,\Omega)^d \times H^1(\Omega)^d$. It admits optimal multigrid solution methods as well if Raviart--Thomas finite element spaces are used to approximate the stress tensor. Our method does not degrade when the material properties approach the incompressible limit. Least-squares methods that impose boundary conditions weakly and use an inverse norm are also considered. Numerical results for a benchmark test problem of planar elasticity are included in order to illustrate the robustness of our ...

Journal ArticleDOI
TL;DR: In this paper, the application of the method of fundamental solutions to the Cauchy problem in two-dimensional isotropic linear elasticity is investigated, where the resulting system of linear algebraic equations is ill-conditioned and therefore its solution is regularised by employing the first-order Tikhonov functional, while the choice of the regularisation parameter is based on the L-curve method.

Journal ArticleDOI
TL;DR: In this article, an integrated micromechanical and structural framework for the nonlinear viscoelastic analysis of laminated composite materials and structures is presented. And the effect of physical aging on creep is also examined.

Journal ArticleDOI
TL;DR: In this paper, a discontinuous Galerkin method for linear elasticity is proposed, which derives from the Hellinger-Reissner variational principle with the addition of stabilization terms analogous to those previously considered by others for the Navier-Stokes equations and a scalar Poisson equation.
Abstract: We analyze a discontinuous Galerkin method for linear elasticity. The discrete formulation derives from the Hellinger-Reissner variational principle with the addition of stabilization terms analogous to those previously considered by others for the Navier-Stokes equations and a scalar Poisson equation. For our formulation, we first obtain convergence in a mesh-dependent norm and in the natural mesh-independent BD norm. We then prove a generalization of Korn's second inequality which allows us to strengthen our results to an optimal, mesh-independent BV estimate for the error.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the regularization and numerical solution of geometric inverse problems related to linear elasticity with minimal assumptions on the geometry of the solution, and they considered the probably severely ill-posed reconstruction problem of a two-dimensional inclusion from a single boundary measurement.
Abstract: In this paper, we investigate the regularization and numerical solution of geometric inverse problems related to linear elasticity with minimal assumptions on the geometry of the solution. In particular, we consider the probably severely ill-posed reconstruction problem of a two-dimensional inclusion from a single boundary measurement. In order to avoid parametrizations, which would introduce a priori assumptions on the geometric structure of the solution, we employ the level set method for the numerical solution of the reconstruction problem. With this approach, we construct an evolution of shapes with a normal velocity chosen depending on the shape derivative of the corresponding least-squares functional in order to guarantee its descent. Moreover, we analyse penalization by perimeter as a regularization method, based on recent results on the convergence of Neumann problems and a generalization of Golab's theorem. The behaviour of the level set method and of the regularization procedure in the presence of noise are tested in several numerical examples. It turns out that reconstructions of good quality can be obtained only for simple shapes or for unreasonably low noise levels. However, it seems reasonable that the quality of reconstructions improves by using more than a single boundary measurement, which is an interesting topic for future research.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the depinning transition occurring in dislocation assemblies and showed that the deformations of a dislocation assembly cannot be described by local elastic interactions with a constant tension or stiffness.
Abstract: We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low-angle grain boundaries interacting with a disordered stress landscape provided by solute atoms, or by other immobile dislocations present in nonactive slip systems. Using linear elasticity, we compute the stress originated by small deformations of these assemblies and the corresponding energy cost in two and three dimensions. Contrary to the case of isolated dislocation lines, which are usually approximated as elastic strings with an effective line tension, the deformations of a dislocation assembly cannot be described by local elastic interactions with a constant tension or stiffness. A nonlocal elastic kernel results as a consequence of long-range interactions between dislocations. In light of this result, we revise statistical depinning theories of dislocation assemblies and compare the theoretical results with numerical simulations and experimental data.

Journal ArticleDOI
TL;DR: In this article, a mechanistic-empirical framework for evaluating permanent deformation in flexible pavements is presented, which uses rational material properties and can be used as an analysis tool, as a companion to the design method.
Abstract: This paper presents a mechanistic-empirical framework for evaluating permanent deformation in flexible pavements. The procedure uses rational material properties and can be used as an analysis tool, as a companion to the design method. The material properties required are (1) the stress dependent modulus of the pavement layers, asphalt concrete and granular base/subbase, and (2) the relation between the accumulated and the resilient strain with the number of load repetitions and stress level. The procedure is a compromise between simple and advanced approaches, between linear elasticity and nonlinear incremental finite element approaches. In addition to this improvement, the proposed procedure uses the “actual” temperature distribution in the asphalt layer at every hour in the whole design period. It is evaluated by computing the rut depth in well-designed pavements. All the results for the pavement response under different conditions are within the expected ranges.

Journal ArticleDOI
TL;DR: In this article, a 3D Voronoi cell finite element model is developed for analyzing heterogeneous materials containing a dispersion of ellipsoidal inclusions or voids in the matrix.
Abstract: In this paper a three-dimensional Voronoi cell finite element model is developed for analyzing heterogeneous materials containing a dispersion of ellipsoidal inclusions or voids in the matrix. The paper starts with a description of 3D tessellation of a domain with ellipsoidal heterogeneities, to yield a 3D mesh of Voronoi cells containing the heterogeneities. A surface based tessellation algorithm is developed to account for the shape and size of the ellipsoids in point based tessellation methods. The 3D Voronoi cell finite element model, using the assumed stress hybrid formulation, is developed for determining stresses and displacements in a linear elastic material domain. Special stress functions that introduce classical Lame functions in ellipsoidal coordinates are implemented to enhance solution convergence. Numerical methods for implementation of algorithms and yielding stable solutions are discussed. Numerical examples are conducted with inclusions and voids to demonstrate the effectiveness of the model.

Journal ArticleDOI
TL;DR: In this article, a nonlinear model for inextensible rods from three-dimensional nonlinear elasticity was derived, passing to the limit as the diameter of the rod goes to zero.
Abstract: Using a variational approach we rigorously deduce a nonlinear model for inextensible rods from three-dimensional nonlinear elasticity, passing to the limit as the diameter of the rod goes to zero. The theory obtained is analogous to the Foppl–von Karman theory for plates. We also derive an asymptotic expansion of the solution and compare it to a similar expansion which Murat and Sili obtained starting from three-dimensional linear elasticity.

Journal ArticleDOI
TL;DR: In this article, a universal biaxial testing device (UBTD) was used to investigate the response of aluminum honeycomb under various combinations of large shear and compressive strains in its tubular direction.
Abstract: A new custom-built universal biaxial testing device (UBTD) is introduced and successfully used to investigate the response of aluminum honeycomb under various combinations of large shear and compressive strains in its tubular direction. At the macroscopic level, different characteristic regimes are identified in the measured shear and normal stress-strain curves: elastic I, elastic II, nucleation, softening, and crushing. The first elastic regime shows a conventional linear elastic response, whereas the second elastic regime is nonlinear due to the generation of elastic buckles in the honeycomb microstructure. Nucleation is the point at which the cellular structure loses its load carrying capacity as a result of plastic collapse. It precedes a rapid drop of stress levels in the softening regime as pronounced plastic collapse bands emerge in the microstructure. Formation and growth of plastic folds dominate the microstructural response in the crushing phase. The mechanical features of this phase are long stress plateaus for both the corresponding shear and compressive stress-strain curses. Based on these observations, honeycomb plasticity is established by making analogies of plastic hinge lines and folding systems in the cellular microstructure with dislocations and slip line systems in a solid lattice, respectively. The initial yield surface is found to take the form of an ellipse in stress space, while the crushing behavior is described by a linear envelope along with a nonassociated flow rule based on total strain increments.

Journal ArticleDOI
TL;DR: An analytical model for determining adhesive stress distributions within the adhesive-bonded single-lap composite joints was developed in this article, where the adhesive was assumed to be very thin and the adhesive stresses are assumed constant through the bondline thickness.
Abstract: An analytical model for determining adhesive stress distributions within the adhesive-bonded single-lap composite joints was developed. ASTM D3165 ‘‘Strength Properties of Adhesives in Shear by Tension Loading of Single-Lap-Joint Laminated Assemblies’’ test specimen geometry was followed in the model derivation. In the model derivation, the composite adherends were assumed linear elastic while the adhesive was assumed elastic-perfectly plastic following von Mises yield criterion. Laminated Anisotropic Plate Theory was applied in the derivation of the governing equations of the bonded laminates. The adhesive was assumed to be very thin and the adhesive stresses are assumed constant through the bondline thickness. The entire coupled system of equations was determined through the kinematics relations and force equilibrium of the adhesive and the adherends. The overall system of governing equations was solved analytically with appropriate boundary conditions. Computer software Maple V was used as the solution...

Journal ArticleDOI
TL;DR: In this article, the authors presented an analytical solution for the stress field at a notch root in a plate of arbitrary thickness, based on two recently developed analysis methods for the in-plane stresses at notch root under plane-stress or plane strain conditions, and the out-of-plane stress at a three-dimensional notch root.
Abstract: This paper presents an analytical solution, substantiated by extensive finite element calculations, for the stress field at a notch root in a plate of arbitrary thickness. The present approach builds on two recently developed analysis methods for the in-plane stresses at notch root under plane-stress or plane strain conditions, and the out-of-plane stresses at a three-dimensional notch root. The former solution (Filippi et al., 2002) considered the plane problem and gave the in-plane stress distributions in the vicinity of a V-shaped notch with a circular tip. The latter solution by Kotousov and Wang (2002a), which extended the generalized plane-strain theory by Kane and Mindlin to notches, provided an expression for the out-of-plane constraint factor based on some modified Bessel functions. By combining these two solutions, both valid under linear elastic conditions, closed form expressions are obtained for stresses and strain energy density in the neighborhood of the V-notch tip. To demonstrate the accuracy of the newly developed solutions, a significant number of fully three-dimensional finite element analyses have been performed to determine the influences of plate thickness, notch tip radius, and opening angle on the variability of stress distributions, out-of-plane stress constraint factor and strain energy density. The results of the comprehensive finite element calculations confirmed that the in-plane stress concentration factor has only a very weak variability with plate thickness, and that the present analytical solutions provide very satisfactory correlation for the out-of-plane stress concentration factor and the strain constraint factor.

Journal ArticleDOI
TL;DR: It is shown that the deformation of the surface in a microindentation test can be used along with FD data to estimate material properties, as well as residual stress, in soft tissue structures that can be regarded as a plate under tension on an elastic foundation.
Abstract: Microindentation methods are commonly used to determine material properties of soft tissues at the cell or even sub-cellular level. In determining properties from force-displacement (FD) data, it is often assumed that the tissue is initially a stress-free, homogeneous, linear elastic half-space. Residual stress, however, can strongly influence such results. In this paper, we present a new microindentation method for determining both elastic properties and residual stress in soft tissues that, to a first approximation, can be regarded as a pre-stressed layer embedded in or adhered to an underlying relatively soft, elastic foundation. The effects of residual stress are shown using two linear elastic models that approximate specific biological structures. The first model is an axially loaded beam on a relatively soft, elastic foundation (i.e., stress-fiber embedded in cytoplasm), while the second is a radially loaded plate on a foundation (e.g., cell membrane or epithelium). To illustrate our method, we use a nonlinear finite element (FE) model and experimental FD and surface contour data to find elastic properties and residual stress in the early embryonic chick heart, which, in the region near the indenter tip, is approximated as an isotropic circular plate under tension on a foundation. It is shown that the deformation of the surface in a microindentation test can be used along with FD data to estimate material properties, as well as residual stress, in soft tissue structures that can be regarded as a plate under tension on an elastic foundation. This method may not be as useful, however, for structures that behave as a beam on a foundation.