Showing papers on "Continuum mechanics published in 1974"
TL;DR: The integral forms of the balance laws are given for the following quantities: mass, linear momentum, angular momentum, total energy and entropy Starting from these integral balance laws, the jump conditions and the entropy source at the interface are derived as discussed by the authors.
194 citations
TL;DR: In this paper, a set of constitutive equations for nonlocal thermoelastic solids is developed by means of the nonlocal thermodynamics and the axiom of objectivity.
181 citations
TL;DR: It is a widespread belief even today that classical mechanics is a dead subject, that its foundations were made clear long ago, and that all that remains to be done is to solve special problems as mentioned in this paper.
Abstract: It is a widespread belief even today that classical mechanics is a dead subject, that its foundations were made clear long ago, and that all that remains to be done is to solve special problems. This is not so. It is true that the mechanics of systems of a finite number of mass points has been on a sufficiently rigorous basis since Newton. Many textbooks on theoretical mechanics dismiss continuous bodies with the remark that they can be regarded as the limiting case of a particle system with an increasing number of particles. They cannot. The erroneous belief that they can had the unfortunate effect that no serious attempt was made for a long period to put classical continuum mechanics on a rigorous axiomatic basis. Only the recent advances in the theory of materials other than perfect fluids and linearly elastic solids have revived the interest in the foundations of classical mechanics. A clarification of these foundations is of importance also for the following reason. It is known that continuous matter is really made up of elementary particles. The basic laws governing the elementary particles are those of quantum mechanics. The science that provides the link between these basic laws and the laws describing the behavior of gross matter is statistical mechanics.
157 citations
TL;DR: In this article, the authors studied the deformation in ferritic - martensitic and ferritic pearlitic steels with 0.3 vol.% inclusion in a continuous matrix.
122 citations
TL;DR: The theory of polar fluids has been applied to thin lubricating films and to problems involving surface films as discussed by the authors, and it is also applied to real fluids carrying charged particles and subjected to an external electromagnetic field that causes the particles to rotate relative to their neighbors.
Abstract: Publisher Summary The chapter discusses the theory of polar fluids. The focus is on the foundations of the theory and applications of the theory are also discussed. The foundation of the theory of polar fluids is divided into five subsections. The first is concerned with the kinematics of polar-fluid motions, the second with dynamics and thermodynamics, the third with the formulation of constitutive relations for polar fluids, the fourth with the formulation of boundary value problems, and the fifth with the solutions to typical boundary-value problems. The foundations of the theory are described in terms of contemporary studies on the foundations of continuum mechanics and thermodynamics. The applications of the theory of polar fluids have been, for example, to suspensions, to blood flow, and to mean turbulent flow. The theory is also applied to thin lubricating films and to problems involving surface films. Another area of application of the theory of polar fluids is to real fluids carrying charged particles and subjected to an external electromagnetic field that causes the particles to rotate relative to their neighbors. The chapter presents the related theories of fluid behavior. The chapter concludes by describing the relationship of polar-fluid theory to theories of a similar nature.
115 citations
TL;DR: In this article, the authors derived explicit linear constitutive relations for straight isotropic circular rods of non-uniform cross-section, in terms of an approximate specific Gibbs free energy function.
Abstract: Starting with the three-dimensional theory of classical continuum mechanics, some aspects of both the nonlinear and the linear theories of elastic rods are discussed. Detailed attention is given to the derivation of constitutive equations for the linear isothermal theory of elastic rods of an isotropic material and of variable cross-section, deduced by an approximation procedure from the three-dimensional equations. Explicit linear constitutive relations are obtained for straight isotropic circular rods of non-uniform cross-section; the explicit calculation is carried out (in terms of an approximate specific Gibbs free energy function) in four distinct parts, since the complete system of equations involved separate into those appropriate for extensional, torsional and two flexural modes of deformation. A system of displacement differential equations is derived for flexure of a beam of variable circular cross-section; they reduce to those of the Timoshenko beam theory when the radius of the cross-section is constant.
109 citations
TL;DR: A tentative measure of the forces tending to cause crack growth, the apparent crack extension force, is defined within the framework of continuum mechanics as mentioned in this paper, which is specialized to elastic, viscoelastic and elastic-plastic materials.
50 citations
01 Jan 1974
45 citations
Book•
01 Jan 1974
TL;DR: In this paper, the authors consider the problem of crack tip in non-local elasticity in the theory of elasticity and show that cracks in elasticity can be caused by earthquake energy.
Abstract: Aspects of earthquake energy.- Construction of earth models.- The Fe2O theory of planetary cores.- Principles of fracture mechanics.- Fracture problems in a nonhomogeneous medium.- Dynamics, of fracture propagation.- Nonlocal elasticity and waves.- On the problem of crack tip in nonlocal elasticity.- Statistical problems in the theory of elasticity.- Internal stresses in crystals and in the earth.- The elements of non-linear continuum mechanics.- Anisotropic elastic and plastic materials.- Symmetric micromorphic continuum: Wave propagation, point source solutions and some applications to earthquake processes.- Surface deformation in Iceland and crustal stress over a mantle plume.- Fault displacement and ground tilt during small earthquakes.
44 citations
01 May 1974
TL;DR: A general theory of contract impact problems cast in a variational theorem suitable for implementation with the finite element method is presented in this article, where the numerical scheme is described as is the structural analysis computer code in which it is contained.
Abstract: This report presents a general theory of contract-impact problems cast in a variational theorem suitable for implementation with the finite element method. The numerical scheme is described as is the structural analysis computer code in which it is contained.
Book•
01 Jan 1974
TL;DR: In this article, a discussion on a continuum theory with microstructure for wave propagation in laminated composites is presented, and the phase velocity spectrum of the general theory is investigated for one-dimensional wave propagation at various propagation angles with respect to the laminates.
Abstract: : A discussion is presented on a continuum theory with microstructure for wave propagation in laminated composites. Continuum model construction is based upon an asymptotic scheme in which dominant signal wavelengths are assumed large compared to typical composite microdimensions. A hierarchy of models is defined by the order of truncation of the obtained asymptotic sequence. Particular attention is given to the lowest order dispersive theory. The phase velocity spectrum of the general theory is investigated for one-dimensional wave propagation at various propagation angles with respect to the laminates. Retention of all terms in the asymptotic sequence is found to yield the exact elasticity spectrum, while spectral collation of the lowest order dispersive theory with the first three modes of the exact theory gives excellent agrement. (Author, modified-PL)
01 Jan 1974
TL;DR: In this paper, the authors consider the finite deformation of a magnetized and/or polarized elastic body placed in an electro-magnetic field and derive the force distribution of electromagnetic origin and influence of the deformation on the field.
Abstract: In this paper we consider the finite deformation of a magnetized and/or polarized elastic body, placed in an electro-magnetic field We shall be concerned with the general dynamic problem, in which the body may be magnetically saturated or non-saturated, and may conduct currents But we shall confine our considerations to the non-relativistic case, ie we assume the velocities to be small with respect to the velocity of light In our theory we aim at a unification of electro-magnetic theory and continuum mechanics: we shall derive the force distribution of electro-magnetic origin and the influence of the deformation of the body on the field
01 Jan 1974
TL;DR: For the thermomechanics of nematic and cholesteric liquid crystals, the Ericksen-Leslie theory and the theory based upon micropolar continuum mechanics are presented in this paper.
Abstract: For the thermomechanics of nematic and cholesteric liquid crystals, the Ericksen-Leslie theory and the theory based upon micropolar continuum mechanics are presented. The similarities and differences in basic laws of motion and constitutive equations between these two theories are discussed in detail. For illustrative purpose solutions of some special problems are given in order to illustrate special features of these theories.
TL;DR: In this paper, a summary of some recent attempts to relate the results of the kinetic theory of rigid and flexible macromolecules to continuum mechanics results is given. But this summary is limited to the case of a single particle.
Abstract: A summary is given of some recent attempts to relate the results of the kinetic theory of rigid and flexible macromolecules to continuum mechanics results.
TL;DR: In this paper, the authors developed a continuum mechanics of multilayered plates under initial stress to include the case where some or all of the layers are constituted by thinly laminated materials with couple stresses.
TL;DR: In this paper, a new formulation of the mechanics of deformation of continuous filament textile yarns has been carried out which utilizes the concepts of classical continuum mechanics, particularly the stress tensor.
Abstract: A new formulation of the mechanics of deformation of continuous filament textile yarns has been carried out which utilizes the concepts of classical continuum mechanics, particularly the stress tensor. The stresses acting on a fiber are divided into a tensile stress T acting along its axial direction, and compressive stresses Pn and Pb acting in the direction of the normal and binormal vectors of the equivalent space curve. The resulting expressions for the stress distribution in the yarn and the applied tensile force and torque are more general than those derived by earlier researchers.
TL;DR: In this article, a method has been developed to estimate the buckling loads of a beam embedded in an elastic continuum using Mindlin's equations for calculating displacements of the continuum.
Abstract: The problem of buckling of piles driven into soil and of fibers embedded in a matrix can be studied by idealizing the same as a beam in elastic continuum. In case of pile foundations, the beams are of finite length. A method has been developed to estimate the buckling loads of a beam embedded in an elastic continuum using Mindlin's equations for calculating displacements of the continuum. Results are compared with subgrade reaction theories to show that the latter underestimates the buckling loads. Buckling loads calculated for two end conditions, pinned and fixed, are shown to depend on the relative stiffness factor, length to width ratio, and the ratio of the elastic moduli of the beam and the continuum.
TL;DR: In this article, a new technique has been developed where the grain-size effect is incorporated into the rheological analysis and the analysis is subsequently made use of in understanding die-less drawing of superplastic bars.
Abstract: By making use of the empirical relations between stress and strain rate useful expressions concerning the variation of viscosity and activation energies for superplastic deformation are derived. The analyses of superplasticity, based on conventional continuum mechanics, neglect grain size effects. A new technique has been developed where the grain-size effect is incorporated into the rheological analysis. The analysis is subsequently made use of in understanding die-less drawing of superplastic bars. It is shown that the analysis is able to predict stress-strain rate relations, viscosity variation and so forth satisfactorily. It is concluded that the present analysis could be useful in practical situations where the constitutive equations are of great importance.
TL;DR: In this article, the basic equations of the general relatiyistic continuum mechanics are derived in Eulerian coordinates by a variational principle with subsidiary conditions, which are physical requirements for system and processes (reversibility, particle conservation), and consequences of definitions (normalization of velocity).
Abstract: The basic equations of the general relatiyistic continuum mechanics are derived in Eulerian coordinates by a variational principle with subsidiary conditions. For liquids and solids the Einsteinian field equations with the attached energy-momentum tensor and the adequate equations of motion for the mechanical and thermodynamical quantities follow. The subsidiary conditions are on the one hand physical requirements for system and processes (reversibility, particle conservation), on the other hand consequences of definitions (normalization of velocity). Lin's principle of the identity of particles is discussed. It is necessary as a subsidiary condition.
Dissertation•
01 Jan 1974
01 Jan 1974
TL;DR: A nonlinear viscoelastic model has been developed to describe the non-Newtonian viscosities and the primary normal stress differences of high polymers at steady-state shearing flow as discussed by the authors.
Abstract: A nonlinear viscoelastic model has been developed to describe the non-Newtonian viscosities and the primary normal stress differences of high polymers at steady-state shearing flow. It has been demonstrated that the Huang-Shangkuan model gives the best representation of the experimental data for a wide range of shear rates. In the high shear rate region the Huang-Shangkuan model is distinguished among other models by its capability to predict the nonNewtonian viscosities and the primary normal stress differences which the other models fail to predict. Continuum mechanics, Lodge's network theory and Rouse's theory provide specific information in developing our model. The theoretical aspect of this model is also supported by the experimental data, which were taken using the accurate Weissenberg rheogoniometer. APPROVAL OF DISSERTATION A NONLINEAR VISCOELASTIC MODEL
TL;DR: In this article, non-constant forms for the film thickness are constructed for which reduction of the two-dimensional problem to consideration of Laplace's equation is possible via Baecklund-type transformations; the approach is somewhat analogous to one adopted in gasdynamics to obtain canonical forms for systems descriptive of physical situations.
Abstract: In the case of constant film thickness, Reynolds' equation of plane lubrication theory reduces to Laplace's equation for the pressure distribution. In this paper, non-constant forms for the film thickness are constructed for which reduction of the two-dimensional problem to consideration of Laplace's equation is possible. This is achieved via Baecklund-type transformations; the approach is somewhat analogous to one adopted in gasdynamics and recently in other areas of Continuum Mechanics to obtain canonical forms for systems descriptive of physical situations.
01 Jan 1974
TL;DR: In this paper, an introductory account of non-linear continuum mechanics is given, particularly emphasizing those aspects of the subject which may be of potential interest to geophysicists, and a review is given.
Abstract: In this review, I shall give an introductory account of non-linear continuum mechanics, particularly emphasizing those aspects of the subject which may be of potential interest to geophysicists.
TL;DR: In this article, the energy release integral of Rice and Cherepanov type is derived more generally by employing an energy balance equation which is often used in continuum mechanics, and the integral is then applied to the tearing test of a finite viscoelastic material.
Abstract: The energy release integral ofRice andCherepanov type is derived more generally by employing an energy balance equation which is often used in continuum mechanics. Several results are observed from this energy release integral. The integral is then applied to the tearing test of a finite viscoelastic material. An equation is established to relate the energy release rate and the average strain concentration along the notch surface, a more general result than the one obtained previously for the finite elastic materials.