Showing papers on "Continuum mechanics published in 1987"

Nonlocal damage theory

Abstract: In the usual local finite element analysis, strain softening causes spurious mesh sensitivity and incorrect convergence when the element is refined to vanishing size. In a previous continuum formulation, these incorrect features were overcome by the imbricate nonlocal continuum, which, however, introduced some unnecessary computational complications due to the fact that all response was treated as nonlocal. The key idea of the present nonlocal damage theory is to subject to nonlocal treatment only those variables that control strain softening, and to treat the elastic part of the strain as local. The continuum damage mechanics formulation, convenient for separating the nonlocal treatment of damage from the local treatment of elastic behavior, is adopted in the present work. The only required modification is to replace the usual local damage energy release rate with its spatial average over the representative volume of the material whose size is a characteristic of the material. Avoidance of spurious mesh ...

Rheology of the earth

Abstract: Preface. Introduction to the second edition. Introduction to the first edition. Part One: Rheology of Continua. 1. Continuum mechanics and rheology. 2. Stress, deformation and strain. 3. Elasticity. 4. Flow, strain rate and viscosity. 5. Strength, failure and plasticity. Part Two: The Continuum Approach to Earth Rheology. 6. The short timescale: seismological Earth models. 7. Temperature and heat transfer. 8. The long timescale: geodynamics and plate tectonics. Part Three: The Microphysical Approach to Earth Rheology. 9. The atomic basis of deformation. 10. Creep of polycrystals at high temperature and pressure. 11. Deformation maps and isomechanical groups. 12. Earth rheology from microphysics. References. Acknowledgements. Index.

Critical State Soil Mechanics via Finite Elements

Abstract: Initial chapters describe basic theories of continuum mechanics, critical state soil mechanics and finite element techniques Most of the book is devoted to the description of an 8000 line FORTRAN program called CRISP (critical state program) which uses the finite element technique and allows predictions to be made of ground deformations using critical state theories CRISP differs from most programs used in geotechnics in that it is possible to predict the development of deformations with time When used in this way the program enforces continuity of water flow through soil as well as equilibrium of total stresses Advice as to when critical state theories might be expected to give good (or not so good) results is also provided (TRRL)

High velocity flow in porous media

Abstract: Experimental observations have established that the proportionality between pressure head gradient and fluid velocity does not hold for high rates of fluid flow in porous media. Empirical relations such as Forchheimer equation have been proposed to account for nonlinear effects. The purpose of this work is to derive such nonlinear relationships based on fundamental laws of continuum mechanics and to identify the source of nonlinearity in equations.

Erythrocyte membrane elasticity and viscosity.

Abstract: The classical theory of elasticity (35) treats the material of a deformable body as a three-dimensional continuum in which internal stresses occur as the body is deformed by external forces acting over its surface. Although the internal stresses are caused by the displacement of atoms or molecules from an original state of equilibrium, the molecular character of the material is ignored. This means that every volume element within the material must contain enough molecules to guarantee that the thermal fluctuation of anyone molecule does not effect the local state of stress. Since biomembranes in general and red cell membranes in particular are only a few molecules thick, they can form a continuum only in the plane of the membrane. Thus, the methods of classical, three-dimensional continuum mechanics must be compressed into a two-dimensional world in which "stress resultants" or "tensions" (force per unit width of membrane surface) are defined on the surface of the membrane (8, 25, 48). Measurement of the surface stress resultants and the corresponding surface deformations permits the material properties of the membrane surface to be calculated (15, 16, 20). These surface properties represent a summation, over the thickness of the membrane, of the properties of the lamellar, molecular structures that form the membrane.

The Derivation of Constitutive Relations from the Free Energy and the Dissipation Function

Abstract: Publisher Summary This chapter examines the derivation of constitutive relations from the free energy and the dissipation function. Continuum mechanics allows one to establish constitutive relations, deducing them from a single pair of scalar functions characterizing the material. The simplest materials dealt with in continuum mechanics are elastic. More general processes and those taking place in more general materials are irreversible and require more constitutive relations, connecting the dissipative forces with the velocities. The orthogonality condition and the equivalent extremum principles have been established for velocities in the form of vectors or symmetric tensors. It is found that if the deformation of an elastic body is neither isothermal nor adiabatic, the strain tensor has to be supplemented by the additional independent state variable. The connection between stress and elastic strain is given by the generalized Hooke's law and connects the stress with the plastic strain and its time rate. It is found that orthogonality in velocity space, which is essentially responsible for the results, does not necessarily imply orthogonality in force space.

Numerical Methods in Fracture Mechanics

Abstract: After a short introduction sketching the continuum mechanics description, the basic equations of Fracture Mechanics will be evaluated with particular emphasis on the numerical treatment.

A Continuum Theory of Crack Shielding in Ceramics

Abstract: : A phenomenological constitutive model is proposed which aims at describing the overall effect of microfracture in ceramics. Based on this model, the asymptotic stress, strain and displacement fields at the tip of a stationary macroscopic crack are determined in closed form. The near-tip stress-intensity factor is computed and observed to be significantly smaller than the applied stress-intensity factor even for moderate amounts of damage. (Author)

Stress Assisted Diffusion in Elastic and Viscoelastic Materials.

Abstract: T he governing field equations and boundary conditions for stress assisted diffusion are derived from basic principles of continuum mechanics and irreversible thermodynamics Attention is confined to elastic and viscoelastic material response, with emphasis on isotropy and the case of small strains It is shown that both the diffusion process and the saturation levels are stress dependent In viscoelstic materials the time-dependence of the moisture boundary condition causes the saturation level to drift with time In addition, the diffusion process becomes non-linear in stress, in spite of the linearity of the mechanical behavior

Crack layer theory

Abstract: A damage parameter is introduced in addition to conventional parameters of continuum mechanics and consider a crack surrounded by an array of microdefects within the continuum mechanics framework. A system consisting of the main crack and surrounding damage is called crack layer (CL). Crack layer propagation is an irreversible process. The general framework of the thermodynamics of irreversible processes are employed to identify the driving forces (causes) and to derive the constitutive equation of CL propagation, that is, the relationship between the rates of the crack growth and damage dissemination from one side and the conjugated thermodynamic forces from another. The proposed law of CL propagation is in good agreement with the experimental data on fatigue CL propagation in various materials. The theory also elaborates material toughness characterization.

Slow variations in continuum mechanics

Abstract: Publisher Summary This chapter describes the slow variations in continuum mechanics. The hydraulic approximation is a simple and useful idea, which as the quasicylindrical approximation has its counterpart in other branches of mechanics. The key to treating a slow variation is to rescale the coordinates in different directions so that the variation formally becomes normal. This transfers the perturbation parameter from the boundary conditions to the differential equations, which can accordingly be simplified by approximation. It is remarkable that this simplification also renders the approximate solution uniformly valid. The method of slow variations has been applied mostly to thin two-dimensional shapes in the plane, or slender axisymmetric ones in three dimensions.. It is found that axisymmetric problems of slow variation can be treated in exactly the same way as symmetric plane problems, and the results have a similar structure.

The theory of elastic-plastic deformation at finite strain with induced anisotropy modeled as combined isotropic-kinematic hardening

Abstract: A T heory of elastic-plastic deformation with strain induced anisotropy based on finite-deformation-valid continuum mechanics is presented. On the foundation of nonlinear kinematics which provides strict uncoupling of elastic and plastic deformation rate terms according to their physical origins, it introduces a basis for the modified plastic rate of deformation Dp suggested by G.J. Creus, A.G. Groehs and E.T. Onat in a report entitled “Constitutive Equations for Finite Deformations of Elastic-Plastic Solids,” 1984, in which this variable was suggested in order to give an elegant mathematical structure to the theory. Dp is shown to express the resultant rate of deformation in the current configuration of the elastically-plastically deforming material which is envisaged to be generated by the pure plastic flow and the anisotropy-caused spin, both considered to be occurring in the unstressed state. From this basis an elastic-plastic theory is developed in the case where the strain-induced anisotropy takes the form of combined isotropic-kinematic hardening, although the concepts involved also apply to more general anisotropic characteristics. A general evolution equation is adopted for the back stress α, the kinematic-hardening shift of the yield surface, its rate of growth being expressed as a general form-invariant function of α and Dp, including a general term expressing the influence of the spin of α because it is embedded in the deforming material. By providing an expression for the total strain rate as the sum of the strain rate Dp and an elastic term, linear in the Jaumann derivative of Kirchhoff stress, it is shown that (Dp dt) is the residual strain increment following a loading/unloading cycle imposed by a stress increment. By considering materials which obey the normality rule it is also shown that the instantaneous elastic-plastic moduli have the symmetries necessary for generating a rate potential function and hence can be incorporated into Hill's variational principle valid for solving problems involving finite deformation and convenient for finite-element exploitation.

Anisotropic Aspects of Material Damage and Application of Continuum Damage Mechanics

Abstract: The application of continuum mechanics to the anisotropic aspect of material damage is discussed. The microstructual change due to material damage usually depends significantly on the direction of the local stress and local strain, and is intrinsically anisotropic. Thus, the oriented nature observed in various kinds of damage and its effect on mechanical behaviour of the materials are first reviewed. Then, the modeling of the anisotropic damage states of materials in terms of mechanical variables is discussed. Definition of damage variables in terms of effective area reduction, change of elastic constants and microscopic character of cavity configuration are reviewed. Damage models based on scalar, vector, and tensor variables are presented. Finally, application of anisotropic damage theories developed by use of these variables will be discussed with special emphasis on elastic damage, elastic-plastic damage, spall damage, creep damage and the coupling of these kinds of damage.

Nonlinear magnetoacoustic equations

Abstract: The present work sets forth in a rotationally invariant form the basic equations of nonlinear magnetoacoustics. Presented in the quasimagnetostatic approximation, these equations are useful to treat both bulk and surface nonlinear wave‐propagation phenomena in centrosymmetric magnetostrictive materials (such as ferromagnetic polycrystalline materials, which can be used in the conception of electromagnetic‐acoustic transducers, so‐called EMATS). The equations obtained are based on a strict use of nonlinear continuum mechanics and the electrodynamics of continua with magnetomechanical interactions. All equations are given a material (invariant) form that proves to be most convenient in the study of nonlinear problems in anisotropic bodies.

Kinematic Constraints, Constitutive Equations and Failure Rules for Anisotropic Materials

Abstract: It is common in many branches of continuum mechanics to treat material as though it is incompressible. Although no material is truly incompressible, there are many materials in which the ability to resist volume changes greatly exceeds the ability to resist shearing deformations; examples are liquids with low viscosity, like water, and some natural and artificial rubbers. For such materials, the assumption of incompressibility is a good approximation in many circumstances, and often greatly simplifies the solution of specific problems. It should be noted, though, that there are occasions when even a small degree of compressibility may produce a major effect; an example is the propagation of sound waves in water.

Thermodynamic form of the equation of motion for perfect fluids of grade n

Abstract: We propose a thermodynamic form of the equation of motion for perfect fluids of grade n which generalizes the one given by J. Serrin in the case of perfectly compressible fluids ([1], p. 171). First integrals and circulation theorems are deduced and a classification of the flows is given.

Extension of poincare's nonlinear oscillation theory to continuum mechanics (I)—Basic theory and method

Abstract: In this paper we extend Poincare's nonlinear oscillation theory of discrete system to continuum mechanics. First we investigate the existence conditions of periodic solution for linear continuum system in the states of resonance and nonresonance. By applying the results of linear theory, we prove that the main conclusion of Poincare's nonlinear oscillation theory can be extended to continuum mechanics. Besides, in this paper a new method is suggested to calculate the periodic solution in the states of both resonance and nonresonance by means of the direct perturbation of partial differential equation and weighted integration.