Showing papers on "Continuum mechanics published in 1999"

Viscoelastic Acoustic Response of Layered Polymer Films at Fluid-Solid Interfaces: Continuum Mechanics Approach

Abstract: We have derived the general solution of a wave equation describing the dynamics of two-layer viscoelastic polymer materials of arbitrary thickness deposited on solid (quartz) surfaces in a fluid environment. Within the Voight model of viscoelastic element, we calculate the acoustic response of the system to an applied shear stress, i.e. we find the shift of the quartz generator resonance frequency and of the dissipation factor, and show that it strongly depends on the viscous loading of the adsorbed layers and on the shear storage and loss moduli of the overlayers. These results can readily be applied to quartz crystal acoustical measurements of the viscoelasticity of polymers which conserve their shape under the shear deformations and do not flow, and layered structures such as protein films adsorbed from solution onto the surface of self-assembled monolayers.

An adaptive finite element approach to atomic-scale mechanics—the quasicontinuum method

Abstract: Mixed atomistic and continuum methods offer the possibility of carrying out simulations of material properties at both larger length scales and longer times than direct atomistic calculations. The quasicontinuum method links atomistic and continuum models through the device of the finite element method which permits a reduction of the full set of atomistic degrees of freedom. The present paper gives a full description of the quasicontinuum method, with special reference to the ways in which the method may be used to model crystals with more than a single grain. The formulation is validated in terms of a series of calculations on grain boundary structure and energetics. The method is then illustrated in terms of the motion of a stepped twin boundary where a critical stress for the boundary motion is calculated and nanoindentation into a solid containing a subsurface grain boundary to study the interaction of dislocations with grain boundaries.

Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics

Abstract: The force on a dislocation or point defect, as understood in solid-state physics, and the crack extension force of fracture mechanics are examples of quantities which measure the rate at which the total energy of a physical system varies as some kind of departure from uniformity within it changes its configuration One may define similarly a force acting on each element of a mobile interface (a phase boundary or martensitic interface, for example)

Atomistic Finite Deformation Simulations: A Discussion on Length Scale Effects in Relation to Mechanical Stresses

Abstract: In this study, atomistic finite deformation calculations employing the Embedded Atom Method show three items of interest related to continuum field theory. First, a spatial size scale effect on the yield stress is found. In these calculations, mechanical yield point occurred from dislocation initiation at the edge of the numerical specimens. The spatial size scale continued to affect the plastic response up to strains of 30 percent in simple shear for nickel oriented at . The second point is related to the continuum mechanics observation about oscillating global shear stress under simple shear conditions is shown to dampen as the spatial size scale increases. As the spatial length scale increases, the continuum rotational effect coupled with the increase in dislocation population reduces the oscillatory behavior. This confirms the notion proposed by Bammann and Aifantis (1987) in that when more dislocations are initiated with different orientations of the Burger's vectors then the oscillations decrease. Finally, a length scale bridging idea is proposed by relating a continuum single degree offreedom loss coefficient, which relates the plastic energy to the total strain energy, to varying sizes of blocks of atoms. This study illustrates the usefulness of employing the Embedded Atom Method to study mechanisms related to continuum mechanics quantities.

Model for a stationary dense granular flow along an inclined wall

Abstract: The stationary dense granular flow along an inclined plane has been studied in the present work. Several experimental results of the velocity profile published previously can not be described using conventional constitutive laws of continuum mechanics. Considering recent results revealing the diphasic behavior of granular medium under stress, we propose a new constitutive law relating the stress tensor to non-local functions of the velocity field and structural parameters of the material.

Strain-rate-sensitive constitutive law for concrete

Abstract: Concrete strength is highly sensitive to loading procedure, especially in the range of high strain rates On the basis of experimental results, it is demonstrated that the full loading history must be included in a dynamic constitutive model, not just consideration of the current strain rate The rate effect is mainly attributed to internal inertia forces during microdamage evolution A strain-history-dependent constitutive model is proposed based on this retarded activation of microdamage A simplified version allows identification of material parameters for practical application It is shown how this dynamic approach fits into the general framework of continuum damage mechanics

Volumetric Deformation Analysis Using Mechanics-Based Data Fusion: Applications in Cardiac Motion Recovery

Abstract: Non-rigid motion estimation from image sequences is essential in analyzing and understanding the dynamic behavior of physical objects. One important example is the dense field motion analysis of the cardiac wall, which could potentially help to better understand the physiological processes associated with heart disease and to provide improvement in patient diagnosis and treatment. In this paper, we present a new method of estimating volumetric deformation by integrating intrinsic instantaneous velocity data with geometrical token displacement information, based upon continuum mechanics principles. This object-dependent approach allows the incorporation of physically meaningful constraints into the ill-posed motion recovery problem, and the integration of the two disparate but complementary data sources overcomes some of the limitations of the single-image-source-based motion estimation approaches.

Microstructural Stress Tensor of Granular Assemblies With Volume Forces

Abstract: This paper focuses on the discrete expression of stress tensors of assemblies containing discrete particles with volumetric loads acting on them in addition to boundary forces. Instead of the concept of continuum point, a domain containing a finite number of grains is considered. This domain is replaced by a suitably chosen equivalent continuum whose average stress is expressed-assuming that the grains are in equilibrium-in terms of contact forces and properly defined branch vectors. Symmetry of the stress tensor is also analyzed.

A power–flow analysis based on continuum dynamics

Abstract: Based on the governing equations of continuum mechanics, a power-flow analysis is presented. In developing the mathematical model, the concept of energy-flow density vector is introduced, which uniquely defines the energy transmission between one part of a material body/system and another. This approach allows the energy-flow line, the energy-flow potential and the equipotential surface to be defined. From this model, the local equation of energy-flow balance, the equation of energy exchange between two or many subsystems' and the time-average equations are derived to describe the characteristics of energy flow and energy exchange within the continuum. To demonstrate the applicability of the proposed mathematical model, the energy-flow relation between two simple oscillators is discussed and the concept generalized to sequential and non-sequential multiple systems. Such multiple systems are examined and for non-sequential systems, which are analogous to statically indeterminate structural systems, an approach is developed for the solution of their power flow and energy exchange. It is further shown that the governing equation of energy flow is a first-order partial differential equation which does not directly correspond to the equation describing the flow of thermal energy in a heat-conduction problem.

Micromechanical modeling for behavior of cementitious granular materials

Abstract: Crack damage is commonly observed in cementitious granular materials. Previous analytical models based on continuum mechanics have limitations in analyzing localized damages at a microscale level. In this paper, a micromechanics approach is adopted that considers a contract law for the interparticle behavior of two particles connected by a binder. The model is based on the premises that the interparticle binder initially contains microcracks. As a result of external loading, these microcracks propagate and grow. Thus, binders are weakened and fail. Theory of fracture mechanics is employed to model the propagation and growth of the microcracks. The contact law is then incorporated in the analysis for the overall damage behavior of material using a discrete element method. Using this model, the stress-strain behaviors under uniaxial and biaxial conditions were simulated. A reasonable agreement is found between the predictions and experimental results.

A continuum approach to electrorheology

Abstract: An equilibrium thermodynamic approach is employed to derive a continuum-level expression for the electric field-induced stress in uniaxial anisotropic materials. Although this model is developed specifically to describe electrorheological and electrostrictive behavior of suspensions, it also applies to other uniaxial materials such as nonpolar nematic liquid crystals, biaxially oriented polymer films, and paper. This model introduces new electrostriction coefficients, which are material parameters that describe the strain dependence of the dielectric tensor as well as the field-induced stresses. An experimental technique for measuring the electrostriction parameters is outlined. An idealized microscopic model is presented to illustrate the relationships between microscopic parameters and the macroscopic electrostriction coefficients. The model is used to determine the stresses in common applications; predictions from the continuum approach agree with direct calculations from a microscopic approach of the ...

Compaction waves in granular HMX

Abstract: Piston driven compaction waves in granular HMX are simulated with a two-dimensional continuum mechanics code in which individual grains are resolved. The constitutive properties of the grains are modeled with a hydrostatic pressure and a simple elastic-plastic model for the shear stress. Parameters are chosen to correspond to inert HMX. For a tightly packed random grain distribution (with initial porosity of 19%) we varied the piston velocity to obtain weak partly compacted waves and stronger fully compacted waves. The average stress and wave speed are compatible with the porous Hugoniot locus for uni- axial strain. However, the heterogeneities give rise to stress concentrations, which lead to localized plastic flow. For weak waves, plastic deformation is the dominant dissipative mechanism and leads to dispersed waves that spread out in time. In addition to dispersion, the granular heterogeneities give rise to subgrain spatial variation in the thermodynamic variables. The peaks in the temperature fluctuations, known as hot spots, are in the range such that they are the critical factor for initiation sensitivity.

Rheology and diffusion in simple and complex fluids

Abstract: Diffusion and rheology in a mixture of two simple or one simple and one complex fluids are studied systematically in the framework of GENERIC modeling. The main result is a set of intrinsically consistent equations governing the time evolution of the overall mass density, overall momentum density (this equation involves explicit formulae for the scalar hydrodynamic pressure and the extra stress tensor), relative concentration of one fluid, diffusion flux, and the microstructure of the complex fluid. In the process of solving these equations we recover well-known results concerning the influence of stresses on diffusion and obtain new results concerning the influence of diffusion on stresses.

Studies of Elastic-Plastic Instabilities

Abstract: Analyses of plastic instabilities are reviewed, with focus on results in structural mechanics as well as continuum mechanics. First the basic theories for bifurcation and post-bifurcation behavior are briefly presented. Then, localization of plastic flow is discussed, including shear band formation in solids, localized necking in biaxially stretched metal sheets, and the analogous phenomenon of buckling localization in structures. Also some recent results for cavitation instabilities in elastic-plastic solids are reviewed.

Constitutive Relations for Monatomic Gases¶Based on a¶Generalized Rational Approximation¶to the Sum of the Chapman-Enskog Expansion

Abstract: The classical Chapman-Enskog expansions for the pressure deviator P and heat flux q provide a natural bridge between the kinetic description of gas dynamics as given by the Boltzmann equation and continuum mechanics as given by the balance laws of mass, momentum, and energy supplemented by the expansions for P and q. Truncation of these expansions beyond first (Navier-Stokes) order yields instability of the rest state and is inconsistent with thermodynamics. This paper shows how an approximate sum of the Chapman-Enskog expansion via generalized rational approximation eliminates the instability paradox and yields gas dynamics consistent with a generalized Clausius-Duhem inequality.

On the stability of global non-radial pulsations of neutron stars

Abstract: A neutron star is the cosmic nuclear object in which the energy of gravitational pull is brought to equilibrium by elastic energy stored in the neutron Fermi-continuum. Evidence for the viscoelastic behaviour of a stellar nuclear matter provides a seismological model of pulsar glitches interpreted as a sudden release of the elastic energy. In laboratory nuclear physics, the signatures of viscoelasticity of nuclear matter are found in the current investigations on the collective nuclear dynamics, in which a heavy nucleus is modelled by a spherical piece of viscoelastic Fermi-continuum compressed to the normal nuclear density. It is plausible to expect, therefore, that the motions of self-gravitating nuclear matter constituting the interior of neutron stars should be governed by the equations of an elastic solid, rather than by hydrodynamic equations describing the behaviour of gaseous plasma inside the main sequence stars. In this paper, we present arguments that elastodynamic equations, originally introduced in the context of nuclear collective dynamics, can provide a proper account of elasticity in the large scale motions of neutron matter under its own gravity. Emphasis is placed on mathematical physics underlying the constructive description of the continuum mechanics and the rheology of macroscopic nuclear matter. The capability of the elastodynamic approach is examined by analysis of oscillatory dynamics of a neutron star in the standard homogenous model, operating with a spherical mass of self-gravitating degenerate neutron matter whose viscoelastic behaviour is described in terms of the spheroidal and torsional gravitational-elastic eigenmodes, inherenly related to viscoelasticy. The energy variational principle is utilized to compute the frequencies of viscoelastic gravitational pulsations and their relaxation time. The method is demonstrated for both the idealized homogeneous model and the neutron star models constructed on realistic equations of state. Finally, we derive analytic conditions for the stability of a neutron star to linear elastic deformations accompanying the non-radial pulsations, and discuss the fingerprints of these pulsations in the electromagnetic activity of radiopulsars.

A Model for Predicting Grain Boundary Cracking in Polycrystalline Viscoplastic Materials Including Scale Effects

Abstract: A model is developed herein for predicting the mechanical response of inelastic crystalline solids. Particular emphasis is given to the development of microstructural damage along grain boundaries, and the interaction of this damage with intragranular inelasticity caused by dislocation dissipation mechanisms. The model is developed within the concepts of continuum mechanics, with special emphasis on the development of internal boundaries in the continuum by utilizing a cohesive zone model based on fracture mechanics. In addition, the crystalline grains are assumed to be characterized by nonlinear viscoplastic mechanical material behavior in order to account for dislocation generation and migration. Due to the nonlinearities introduced by the crack growth and viscoplastic constitution, a numerical algorithm is utilized to solve representative problems. Implementation of the model to a finite element computational algorithm is therefore briefly described. Finally, sample calculations are presented for a polycrystalline titanium alloy with particular focus on effects of scale on the predicted response.

The Equations of Motion

Abstract: In this chapter, we introduce, with particular reference to the incompressible case, the general system of Navier-Stokes equations. They are capable of describing most phenomena observed in fluid mechanics, including turbulence which is the major issue of this book. However, this system of equations is an approximation which is produced on the basis of more fundamental assumptions of continuum mechanics, namely that any material, fluid or solid, consists of continuous matter which has a definite density, velocity, and internal energy at every point. This matter cannot be destroyed nor created. It obeys Newton’s classical law of mechanics and also certain thermodynamical laws. Moreover, contiguous regions of the medium are assumed to exert forces on each other across their common boundary.

Solutions for combined saturated and unsaturated flow

Abstract: This chapter considers the processes of water flow in variably saturated soils. It begins with the presentation of the currently accepted forms of governing differential equations used to represent variably saturated flow in porous media. The numerical methods for solving the equations of continuum mechanics in the many areas of engineering also have been adopted to the solution of the equations for flow in variably saturated porous media. These methods include classical finite difference methods, integrated finite difference methods, finite element methods, and boundary element methods. Of these methods, the classical finite difference method and the finite element methods have received most of the attention for applications in modeling flows through agricultural soils as well as in other applications related to modeling flows in subsurface hydrology. The chapter considers representative applications of the various numerical methods to the solution of the variably saturated flow equations.

Study on the viscosity of the liquid flowing in microgeometry

Abstract: While micro-fabrication technologies are under extensive exploitation to fully realize the applications of micromachines etc, until the present time the basic mechanisms governing the underlying fundamental principles of these micro- and nano-scale systems have not been fully understood. As the characteristic dimensions of these devices approach micro- and nano-scales, attempts to understand the working phenomena pose great challenges. Under such situations, the commonly applied theories in continuum mechanics often become limiting cases or even completely unsuitable. For example, one of the commonly used properties, viscosity, seems to play an important role in characterizing the behavior of these micro- or nano-scale devices. In this paper, a theoretical study, employing a molecular theory to investigate the effects of the geometrical dimensions on the viscosity and flow characteristics for polar and non-polar liquids will be presented. The results indicate that the effects of the geometrical dimensions on the viscosity of liquids become significant as the dimensions approach the micro- or nano-scale, and these effects are more significant in polar than in non-polar fluids.

Evaluation and visualization of geometrically necessary dislocations in metal microstructures by means of continuum mechanics analysis

Abstract: A numencal technique is shown for the evaluation of dislocation accumulation and their visualization. Plastic slip deformation of modeled metal microstructures are analyzed by a finite element method and developments of distortion density distribution are evaluated in conjunction with gradients of plastic shear strain on crystal slip systems. The technique is applied to simplified geometries ot inclusion - matrix microstructures and a three dimensional scenano of dislocation accumulation around the inclusion is discussed.

Two-dimensional dynamic simulation of fracture and fragmentation of solids

Abstract: We present a two-dimensional discrete model of solids that allows us to follow the behavior of the solid body and of the fragments well beyond the formation of simple cracks. The model, consisting of polygonal cells connected via beams, is an extension of discrete models used to study granular flows. This modeling is particularly suited for the simulation of fracture and fragmentation processes. After calculating the macroscopic elastic moduli from the cell and beam parameters, we present a detailed study of an uniaxial compression test of a rectangular block, and of the dynamic fragmentation processes of solids in various experimental situations. The model proved to be successful in reproducing the experimentally observed subtleties of fragmenting solids. o handle numerically due to the creation and continuous motion of new surfaces. Commonly used numerical methods solve partial differential equations of continuum mechanics. With classical numerical methods such as Finite Elements (FE), Finite Differences (FD) or Boundary Elements (BE) a small number of discontinuities may be considered but these methods cannot encompass the entire fracturing process. The alternative approach is the Discrete Element Method (DEM) in which the elastic medium is considered to be fully discontinuous, i.e. the elastic solid is assembled of discrete elements. The microscopic interaction of the elements is defined such that the model accounts for the macroscopic elastic behavior of materials. The time evolution of the model is followed by solving numerically the equation of motion of the individual elements (Molecular Dynamics (MD)). This model construction results in a “simulated solid” and the modeling of a specific process of a material is referred to as simulation. The inter-element contacts can be considered as grain boundaries which define the � Corresponding author