Showing papers on "Continuum mechanics published in 2005"

Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films

Abstract: Atoms at a free surface experience a different local environment than do atoms in the bulk of a material. As a result, the energy associated with these atoms will, in general, be different from that of the atoms in the bulk. The excess energy associated with surface atoms is called surface free energy. In traditional continuum mechanics, such surface free energy is typically neglected because it is associated with only a few layers of atoms near the surface and the ratio of the volume occupied by the surface atoms and the total volume of material of interest is extremely small. However, for nano-size particles, wires and films, the surface to volume ratio becomes significant, and so does the effect of surface free energy. In this paper, a framework is developed to incorporate the surface free energy into the continuum theory of mechanics. Based on this approach, it is demonstrated that the overall elastic behavior of structural elements (such as particles, wires, films) is size-dependent. Although such size-dependency is negligible for conventional structural elements, it becomes significant when at least one of the dimensions of the element shrinks to nanometers. Numerical examples are given in the paper to illustrate quantitatively the effects of surface free energy on the elastic properties of nano-size particles, wires and films.

Wave propagation in carbon nanotubes via nonlocal continuum mechanics

Abstract: Wave propagation in carbon nanotubes (CNTs) is studied with two nonlocal continuum mechanics models: elastic Euler-Bernoulli and Timoshenko beam models [Philos. Mag. 41, 744 (1921)]. The small-scale effect on CNTs wave propagation dispersion relation is explicitly revealed for different CNTs wave numbers and diameters by theoretical analyses and numerical simulations. The asymptotic phase velocities and frequency are also derived from nonlocal continuum mechanics. The scale coefficient in nonlocal continuum mechanics is roughly estimated for CNTs from the obtained asymptotic frequency. In addition, the applicability and comparison of the two nonlocal elastic beam models to CNTs wave propagation are explored through numerical simulations. The research findings are proved effective in predicting small-scale effect on CNTs wave propagation with a qualitative validation study based on the published experimental reports in this field.

A continuum mechanics-based non-orthogonal constitutive model for woven composite fabrics

Abstract: A non-orthogonal constitutive model is developed to characterize the anisotropic material behavior of woven composite fabrics under large deformation. A convected coordinate system, whose in-plane axes are coincident with the weft and warp yarns of woven fabrics, are embedded in the shell elements. Contravariant stress components and covariant strain components in a constitutive relation are introduced into the convected coordinate system. The transformations between the contravariant/covariant components and the Cartesian components of the stress and strain tensors provide an approach for deriving the global non-orthogonal constitutive relations for woven composite fabrics. By taking advantage of the tensile–shear decoupling in the constitutive equation under the convected coordinate system, the material characterization of woven fabrics is simplified. As an essential part for these transformations, a fiber orientation model is developed, by using some fundamental continuum mechanics concepts, to trace the yarn reorientation of woven fabrics during deformation. The proposed material characterization approach is demonstrated on a balanced plain weave composite fabric. The equivalent material properties are obtained by matching with experimental data of tensile and bias extension tests on the woven composite fabric. Model validation is provided by comparing numerical results with experimental data of bias extension test and shear test. The development of this non-orthogonal model is critical to the ultimate goal, i.e. using numerical simulations to optimize the forming of woven composite fabric sheets.

Peridynamic modeling of membranes and fibers

Abstract: The peridynamic theory of continuum mechanics allows damage, fracture, and long-range forces to be treated as natural components of the deformation of a material. In this paper, the peridynamic approach is applied to small thickness two- and one-dimensional structures. For membranes, a constitutive model is described appropriate for rubbery sheets that can form cracks. This model is used to perform numerical simulations of the stretching and dynamic tearing of membranes. A similar approach is applied to one-dimensional string like structures that undergrow stretching, bending, and failure. Long-range forces similar to van der Waals interactions at the nanoscale influence the equilibrium configurations of these structures, how they deform, and possibly self-assembly.

Fundamentals of structural geology

Abstract: 1. Motivations and opportunities 2. Structural mapping techniques and tools 3. Characterizing structures using differential geometry 4. Physical quantities, fields, dimensions and scaling 5. Deformation and flow 6. Force, traction and stress 7. Conservation of mass and momentum 8. Elastic deformation 9. Brittle behavior 10. Viscous flow 11. Rheological behavior 12. Model development and methodology Index.

Exact theory of kinkable elastic polymers

Abstract: The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection angles, many rod systems exhibit a high-curvature softening. The signature behavior of these rod systems is a kinking transition in which the bending is localized. Recent DNA cyclization experiments by Cloutier and Widom have offered evidence that the linear-elastic bending theory fails to describe the high-curvature mechanics of DNA. Motivated by this recent experimental work, we develop a simple and exact theory of the statistical mechanics of linear-elastic polymer chains that can undergo a kinking transition. We characterize the kinking behavior with a single parameter and show that the resulting theory reproduces both the low-curvature linear-elastic behavior which is already well described by the wormlike chain model, as well as the high-curvature softening observed in recent cyclization experiments.

Mathematical Modeling in Continuum Mechanics

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.

Trends in Continuum Mechanics of Porous Media

Abstract: Preface. 1. Introduction. 2. Volume Fraction Concept. 3. Kinematics. 1. Basic Relations. 2. Kinematics of Micropolar Constituents. 4. Balance Principles. 1. Balance of Mass. 2. Balance of Momentum and Moment of Momentum. 3. Balance of Energy. 5. Basic inequality (Entropy Principle) 1. Preliminaries. 2. Basic Inequality for Non-Polar Constituents and the Mixture Body. 6. Constitutive theory. 1. Preliminaries. 2. Closure Problems and Constraints. 3. Reformulation of the Entropy Inequality. 4. Exploitation of the Inequality for Ternary and Binary Capillary Porous Models. 5. Elastic Behaviour of the Solid Sceleton a. Finite Theories. b. Linear Theory. c. Other Approaches. 6. Elastic-Plastic Behaviour of the Solid Skeleton a. General Theory. b. Special Stress Strain Relations. 7. Viscous Behaviour of the Solid Skeleton. 8. Thermomechanical Behaviour of Porefluids. a. Inviscid Porefluids. b. Viscous Porefluids. 7. Fundamental Effects in Gas- and Liquid-Filled Porous Solids. 1. Introduction. 2. Basic Equations. 3. Uplift. 4. Friction. 5. Capillarity. a. Basic Relations. b. One-Dimensional Capillary Motion. c. Two-Dimensional Capillary Motion (an Example). 6. Effective Stresses. 7. Phase Transitions. a. Theorethical Foundation. b. Drying Processes. c. Freezing Processes. 8. Poroelasticity. 1. Introduction. 2. The Fundamental Field Equations for Poroelasticity. 3. Main Equations for an Incompressible Binary Model. 4. Basic Solutions for an Incompressible Binary Model. a. Fundamental Solution of the System of Equations of Steady Oscilliations in the Theory of Fluidsaturated Porous Media. b. On the Representations of Solutions in the Theory of Fluidsaturated Porous Media. 5. Wave Propagation. a. Plane Waves in a Semi-Infinite Liquidsaturated Porous medium. b. Propagation of Acceleration Waves in Saturated Porous Solids. c. Growth and Decay of Acceleration Waves. d. Dispersion and Attenuation of Surface Waves in a Saturated Porous Medium. e. Inhomogeneous Plane Waves, Mechanical Energy Flux, and Energy Dissipation in a Two-Phase Porous Medium. f. Propagation and Evolution of Wave Fronts in Saturated Porous Solids. 9. Poroplasticity for Metallic porous Solids. 1. Stress-Strain Realtion a. Rigid Ideal-Plastic Behaviour. b. Elastic-Plastic Behaviour with Hardening. 2. General Theorems for Saturated Porous Solids in the Rigid Ideal-Plastic Range. a. Preliminaries. b. The Uniqueness Theorem for Solutions of Boundary Value Problems. c. Minimum and Maximum Principles for Rigid Ideal-Plastic Behaviour. 10. Applications in Engineering and Biomechanics. 1. Soil Mechanics. a. Consolidation Problem and Localization Phenomena. b. Phase Transitions. c. Dynamics. 2. Chemical Engineering. a. Powder Compaction. b. Drying Processes. 3. Building Physics. a. Transport of Moisture. b. Heat Conduction in a Fluidsaturated Capillary-Porous Solid. 4. Biomechanics. 5. Some other Fields of Application. 11. Conclusions and Outlook. References. Author Index. Subject Index.

Finite element forming simulation for non-crimp fabrics using a non-orthogonal constitutive equation

Abstract: The forming behaviour of non-crimp fabric (NCF) was simulated using finite element (FE) analysis incorporating a non-orthogonal constitutive model. NCFs feature asymmetric shear behaviour caused by the stitching used to hold the tows together. This asymmetric shear property causes an asymmetric draping pattern of NCF, even when formed over a symmetrical hemispherical forming tool. Current work focuses on the feasibility of a continuum mechanics model to simulate the asymmetric forming behaviour of NCF. The constitutive equation consists of two parts: the tensile contribution from fibre reinforcement and the shear stiffness. For the fibre directional properties, a non-orthogonal equation originally developed for woven fabric was adopted. The shear stiffness was modelled through a constitutive equation incorporating picture-frame shear data. Both a picture-frame shear test and forming of NCF over a hemisphere tool were simulated by commercial finite element software with the current constitutive model implemented within a user material subroutine. The virtual picture-frame test confirmed the validity of the constitutive equation in simulating planar deformation behaviour of NCF. Furthermore, the numerical analysis of hemispherical forming suggests that increasing blank-holder force decreases the asymmetry of the draped pattern.

Mathematical Modeling in Continuum Mechanics

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.

Elements of Continuum Mechanics

Abstract: Introduction * Mathematical Preliminaries * Kinematics * The Balance Laws, Stress Tensors * Constitutive Relations * Torsion of a Circular Cylinder * Fluid Flow * Bending of Beams * Wave Propagation * Spherical and Cylindrical Pressure Vessels * Index * Supporting Materials.

Crack Path Prediction in Anisotropic Brittle Materials

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.

Continuum–discontinuum modelling of shear bands

Abstract: A methodology to model shear bands as strong discontinuities within a continuum mechanics context is presented. The loss of hyperbolicity of the IBVP is used as the criterion for switching from a classical continuum description of the constitutive behaviour to a traction–separation model acting at the discontinuity surface. The extended finite element method (XFEM) is employed for the spatial discretization of the governing equations. This enables the shear bands to be arbitrarily positioned within the mesh. Examples that study the shear band progression within a rate-independent material are presented. Copyright © 2005 John Wiley & Sons, Ltd.

Numerical Analysis of Nanotube Based NEMS Devices — Part II: Role of Finite Kinematics, Stretching and Charge Concentrations

Abstract: In this paper ci nonlinear analysis of nanotuhe based nano-electromechanical systems is reported. Assuming continuum mechanics, the complete nonlinear equation of the elastic line of the nanotube is derived and then numerically solved. In particular, we study singly and doubly clamped nanotubes under electrostatic actuation. The analysis emphasizes the importance of nonlinear kinematics effects in the prediction of the pull-in voltage of the device, a key design parameter. Moreover, the nonlinear behavior associated with finite kinematics (i.e., large deformations), neglected in previous studies, as well as charge concentrations at the tip of singly clamped nanotuhes, are investigated in detail. We show that nonlinear kinematics results in an important increase in the pull-in voltage of doubly clamped nanotube devices, but that it is negligible in the case of singly damped devices. Likewise, we demonstrate that charge concentration at the tip of singly clamped devices results in a significant reduction in pull-in voltage. By comparing numerical results to analytical predictions, closed form formulas are verified. These formulas provide a guide on the effect of the various geometrical variables and insight into the design of novel devices.

Continuum mechanics modeling and simulation of carbon nanotubes

Abstract: The understanding of the mechanics of atomistic systems greatly benefits from continuum mechanics. One appealing approach aims at deductively constructing continuum theories starting from models of the interatomic interactions. This viewpoint has become extremely popular with the quasicontinuum method. The application of these ideas to carbon nanotubes presents a peculiarity with respect to usual crystalline materials: their structure relies on a two-dimensional curved lattice. This renders the cornerstone of crystal elasticity, the Cauchy–Born rule, insufficient to describe the effect of curvature. We discuss the application of a theory which corrects this deficiency to the mechanics of carbon nanotubes (CNTs). We review recent developments of this theory, which include the study of the convergence characteristics of the proposed continuum models to the parent atomistic models, as well as large scale simulations based on this theory. The latter have unveiled the complex nonlinear elastic response of thick multiwalled carbon nanotubes (MWCNTs), with an anomalous elastic regime following an almost absent harmonic range.

A unified formulation for continuum mechanics applied to fluid-structure interaction in flexible tubes

Abstract: This paper outlines the development of a new procedure for analysing continuum mechanics problems with a particular focus on fluid-structure interaction in flexible tubes. A review of current methods of fluid-structure coupling highlights common limitations of high computational cost and solution instability. It is proposed that these limitations can be overcome by an alternative approach in which both fluid and solid components are solved within a single discretized continuum domain. A single system of momentum and continuity equations is therefore derived that governs both fluids and solids and which are solved with a single mesh using finite volume discretization schemes. The method is validated first by simulating dynamic oscillation of a clamped elastic beam. It is then applied to study the case of interest-wave propagation in highly flexible tubes-in which a predicted wave speed of 8.58m/s falls within 2% of an approximate analytical solution. The method shows further good agreement with analytical solutions for tubes of increasing rigidity, covering a range of wave speeds from those found in arteries to that in the undisturbed fluid.

Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics

Abstract: In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have recently been proposed. They aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We provide here a theoretical ground for such a coupling in a one-dimensional setting. We briefly study the general case of a convex energy, and next concentrate on a specific example of a nonconvex energy, the Lennard-Jones case. In the latter situation, we prove that the discretization needs to account in an adequate way for the coexistence of a discrete model and a continuous one. Otherwise, spurious discretization effects may appear. We provide a numerical analysis of the approach.

A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues I: A General Formulation

Abstract: In this paper a theoretical framework for the study of residual stresses in growing tissues is presented using the theory of mixtures. Such a formulation must necessarily be a solid-multiphase mode...

Derivation of Higher Order Gradient Continuum Models from Atomistic Models for Crystalline Solids

Abstract: We propose a new upscaling scheme for the passage from atomistic to continuum mechanical models for crystalline solids. It is based on a Taylor expansion of the deformation function and allows us to capture the microscopic properties and the discreteness effects of the underlying atomistic system up to an arbitrary order. The resulting continuum mechanical model involves higher order terms and gives a description of the specimen within the quasi-continuum regime. Furthermore, the convexity of theatomistic potential is retained, which leads to well-posed evolution equations. We numerically compare our technique to other common upscaling schemes for the example of an atomic chain. Then we apply our approach to a physically more realistic many-body potential of crystalline silicon. Here the above-mentioned advantages of our technique hold for the newly obtained macroscopic model as well.

Non‐local damage model based on displacement averaging

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.

Atomistic Simulations of Materials Fracture and the Link between Atomic and Continuum Length Scales

Abstract: The macroscopic fracture response of real materials originates from the competition and interplay of several atomic-scale mechanisms of decohesion and shear, such as interplanar cleavage and dislocation nucleation and motion. These phenomena involve processes over a wide range of length scales, from the atomic to the macroscopic. The authors briefly review the attempts to span these length scales in dislocation and fracture modeling by (1) fully atomistic large-scale simulations of millions of atoms or more, approaching the continuum limit from the bottom-up; (2) directly coupling atomic-scale simulations and continuum mechanics, in a top-down approach; and (3) by defining a set of variables common to atomistic simulations and continuum mechanics and feeding the results of atomistic simulations into continuum-mechanics models in the form of constitutive relations. For this latter approach, the authors discuss in detail the issues crucial to ensuring the consistency of the atomistic results and continuum mechanics. A case study of the constitutive-relation approach is presented for the problem of dislocation nucleation from a crack tip in a crystal under stress; a comparison of the results of atomistic simulations to the Peierls-Nabarro continuum model is made.

Modelling dislocation–obstacle interactions in metals exposed to an irradiation environment

Abstract: Irradiation of metals with high-energy atomic particles creates obstacles to glide, such as voids, dislocation loops, stacking-fault tetrahedra and irradiation-induced precipitates through which dislocations have to move during plastic flow. Approximations based on the elasticity theory of defects offer the simplest treatment of strengthening, but are deficient in many respects. It is now widely recognised that a multiscale modelling approach should be used, wherein the mechanisms and strength parameters of interaction are derived by simulation of the atomic level to feed higher-level treatments based on continuum mechanics. Atomic-scale simulation has been developed to provide quantitative information on the influence of stress, strain rate and temperature. Recent results of modelling dislocations gliding under stress against obstacles in a variety of metals across a range of temperature are considered. The effects observed include cutting, absorbing and dragging obstacles. Simulations of 0 K provide for direct comparison with results from continuum mechanics, and although some processes can be represented within the continuum treatment of dislocations, others cannot.

Numerical modelling of landslide runout. A continuum mechanics approach

Abstract: Increasing population density and development of mountainous terrains bring human settlements within reach of landslide hazards. Perhaps the most serious threat arises from small, high frequency landslides such as debris flows and debris avalanches. On the other hand, large and relatively rare rock avalanches also constitute a significant hazard, due to their prodigious capacity for destruction. Such landslides involve the spontaneous failure of entire mountain slopes, involving volumes measured in tens or hundreds million m3 and travel distances of several kilometres. Flow-like movements of rocks can be identified among the most dangerous and damaging of all landslide phenomena. Since it often proves impossible to mitigate their destructive potential by stabilising the area of origin, risk analyses, including predictions of runout, have to be performed. With these predictions losses can be reduced, as they provide means to define the hazardous areas, estimate the intensity of the hazard, and work out the parameters for the identification of appropriate protective measures. At the same time, reliable predictions of runout can help to avoid exceedingly conservative decisions regarding the development of hazardous areas. Risk evaluation of these events requires the comprehension of two fundamental problems: the initiation and the runout. Even though the specification of the initial conditions is also a primarily problem, which is not yet resolved, the runout, that is the flowing and stopping phases of the mass, is here analysed. Numerical simulation should provide a useful tool for investigating, within realistic geological contexts, the dynamics of these flows and of their arrest phase. In the 1970's the most widely used and perhaps earliest model proposed for the analysis of rockslides and similar phenomena was that of a rigid block on an inclined plane. In recent years, new and more sophisticated models based on a continuum mechanics approach have emerged. Together with continuum mechanics models, a noteworthy type of modelling is that based on a discontinuum mechanics approach, in which the run out mass is modelled as an assembly of particles moving down along a surface. It is probably fair to state that Savage and Hutter in 1989 developed the first continuum mechanical theory capable of describing the evolving geometry of a finite mass of a granular material and the associated velocity distribution as an avalanche slides down inclined surfaces. Their model provided a more complete analysis of such flows than previous models had done, and its extension as well as comparison with laboratory experiments demonstrated it to be largely successful. A continuum mechanics approach assumes that during an avalanche, the characteristic length in the flowing direction is generally much larger than the vertical one, e.g. the avalanche thickness. Such a long-wave scaling argument has been widely used in derivation of continuum flow models. This leads to depth-averaged models governed by generalized Saint Venant equations. Nowadays, these models provide a fruitful tool for investigating the dynamics and extent of avalanches. Anyway, whatever the applied analytical model, results of a numerical simulation depend on the value assigned to the constitutive parameter of the assumed rheology. The aim of the dissertation is the development and validation of a three dimensional numerical model able to run analyses of propagation on a complex topography and the setting of a procedure direct to define some reference values for characteristic parameters of an assumed rheology. Case histories having a different runout path and material type are analysed and compared, the obtained values could be considered useful guidelines to study a potential landslide. The choice of a certain approach rather than another is the result of a careful analysis of advantages and disadvantages of each existing method. All choices are made never forgetting to remain focused on real problems and real behaviour of a mass. By consequence, each problem tackled and solved is directed to guarantee more realistic results. Whatever the chosen numerical approach, it is fundamental to know in detail the type of phenomenon that will be studied. In this sense, it is important to learn from past events and to always have on mind that each analysed problem is not abstract but it is linked to a real site. In the present work, a continuum mechanics approach has been followed. The original version (SHWCIN) of the implemented three dimensional code was developed at the Institut de Physique du Globe de Paris but before using it to run analysis of propagation on a complex topography many fundamental changes are necessary. Trying to reduce the uncertainty range of values to be assigned in prediction to rheological parameters, the numerical code DAN (Hungr, 1995) is applied to back analyse a set of case histories of landslides selected from literature. For prediction, the main limitation of DAN is due to the fact that it reduces a complex and heterogeneous 3D problem into an extremely simple formulation and the width of propagation is a part of the input data. But, when a back analysis is run, the geometry of propagation is already known. Therefore, the limits of DAN in some way disappear. Also, cases for which a DEM (Digital Elevation Model) is not available can be analysed. Moreover, advantages in using this code are mainly due to its simplicity, it makes possible an immediate and rapid numerical simulation of many real cases. The methodology here proposed consists in using DAN to run back analyses of as many case histories as possible and the new three dimensional code to predict propagation of a mass on a complex topography. It is important to underline that when values obtained from back analyses are used to simulate a potential landslide, only cases having similar characteristics (e.g. run out area shape, material type) can be compared. To guarantee correctness of this approach it is necessary to verify that DAN results, if used as input data in a three dimensional numerical code, give approximately the same solution. Cases for which a DEM pre-collapse is available are analysed with both DAN and the new code. After a critic overview of landslide classifications and a detailed description of those phenomena known as rock avalanches (Ch. 2), a description of existing propagation methods has been done, underlining advantages and disadvantages of each considered approach (Ch. 3). On the basis of possibility of application on analysis of real cases a continuum mechanics approach has then been followed, two numerical codes have been analysed: SHWCIN and DAN (Ch. 4). The SHWCIN code was originally used to carry out simple numerical simulations of a mass released from a gate or from a hemi-spherical cap on an inclined plane and results were analysed considering the centre line section. To simulate the movement on a complex three dimensional topography, the code has been numerically implemented allowing to: reduce mesh-dependency effects on results of propagation by using an irregular mesh, change gravity components as a function of the considered topography, change earth pressure coefficients in a condition of anisotropy of normal stresses, take into account both different constitutive laws and pore water effects. Each of these changes has been carefully validated. Once the final version of the code was obtained it has been tested through numerical analysis of laboratory tests and back analysis of case histories obtained from literature (Ch. 5). In order to create a database of well described phenomena and rheological parameters, that can be useful guidelines when prediction is the aim of an analysis, case histories have been analysed with DAN following a procedure that gives the possibility of calibrating the model in order to obtain the best value for each of the parameters required by the assumed rheology (Ch. 6).

Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Finite Element Method and Absolute Nodal Coordinate Formulation

Abstract: Three formulations for a flexible spatial beam element for dynamic analysis are compared: a finite element method (FEM) formulation, an absolute nodal coordinate (ANC) formulation with a continuum mechanics approach and an ANC formulation with an elastic line concept where the shear locking of the asymmetric bending mode is suppressed by the application of the Hellinger–Reissner principle. The comparison is made by means of an eigenfrequency analysis on two stylized problems. It is shown that the ANC continuum approach yields too large torsional and flexural rigidity and that shear locking suppresses the asymmetric bending mode. The presented ANC formulation with the elastic line concept resolves most of these problems.Copyright © 2005 by ASME