Showing papers on "Constitutive equation published in 1973"
TL;DR: In this article, a new mechanism for superplastic deformation is described and modelled, which differs fundamentally from Nabarro-Herring and Coble creep in a topological sense: grains switch their neighbors and do not elongate significantly.
1,307 citations
TL;DR: In this article, a general theory of magnetoelasticity is developed for soft ferromagnetic materials of multidomain structure, for which the hysteretic loss and exchange effect may be neglected.
204 citations
TL;DR: In this paper, it was shown that tensile stresses are developed inside a rock with staggered compliant joints, and may be as high as twice the overall shear stresses or the overall compressive stresses.
151 citations
TL;DR: Theoretical results from the field of suspension rheology are studied in the general context of nonlinear continuum mechanics, in order to extract information regarding the formulation of a phenomenological stress relation to model non-Newtonian fluids.
84 citations
TL;DR: In this article, the authors developed a theory of inelastic behavior of crystalline materials subjected to arbitrary deformation, which leads to a simple decomposition rule: the total velocity gradient is the sum of the elastic velocity gradient and the in-elastic velocity gradient.
Abstract: An attempt is made to develop a theory of inelastic behavior of crystalline materials subjected to arbitrary deformation. The introduced concept of elastic motion leads to a simple decomposition rule: the total velocity gradient is the sum of the elastic velocity gradient and the inelastic velocity gradient. The important role of rotations and relevant constitutive relations is discussed and illustrated by an example of a tensile test of a single crystal. The assumption usual in plasticity that plastic deformation does not change the volume of the body follows in the present theory as a consequence of the second law of thermodynamics and material symmetry.
82 citations
TL;DR: In this paper, an entangled network such as a polymer melt or a concentrated solution is described by a set of two simultaneous equations, one of them is a balance of entanglements, the other gives the stress in the classical form of aMaxwell equation.
Abstract: An entangled network such as a polymer melt or a concentrated solution is here described by a set of two simultaneous equations. One of them is a balance of entanglements, the other gives the stress in the classical form of aMaxwell equation.
73 citations
TL;DR: In this article, a new model earthquake process based on the theory of micromorphic continua is introduced, which is described by deformations of microstructure in time.
Abstract: The paper introduces a new model earthquake process based on the theory of micromorphic continua. The processes in a focal region are described by deformations of microstructure in time. It is assumed that the fracturing processes as well as phase transformation of metamorphic phenomena have caused in the past certain non-reversible changes which determine the microstructure of focal region. These internal microstructural elements form the attaching points around which the couple stresses arise. The properties of focal region are determined by the constitutive equations. The micromorphic mechanics considers the existence of body couples as determined by a regional stresses and looks after a response field of stresses, stress moments and strains in the focal region. Further, it is explained how microdislocation field is connected with microdeformations and micromorphic structure. In the considered earthquake structure model a microanisotropy is assumed through the tensor of microinertia. This tensor describes a distribution of microelements. Simple solutions of wave processes in a focal region are presented. The dispersion of waves is discussed.
67 citations
TL;DR: In this paper, the authors present a review of some recent theoretical and experimental developments in the field of nonlinear viscoelastic wave propagation in general materials with memory and discuss the correlation of these theoretical predictions with some recent experimental results obtained for a particular polymeric solid.
61 citations
TL;DR: Using the Rouse-Zimm model of the marcomolecule, the stress constitutive equation of dilute polymer solutions is derived in the form of a functional of temperature and deformation histories as mentioned in this paper.
52 citations
TL;DR: In this paper, a continuum theory of nonlocal electromagnetic elastic solids is proposed and nonlocal and local balance laws and jump conditions are obtained through the use of an extension of Clausius-Duhem inequality, encompassing nonlocal effects.
Abstract: A continuum theory of nonlocal electromagnetic elastic solids is proposed. Nonlocal and local balance laws and jump conditions are obtained. Through the use of an extension of Clausius‐Duhem inequality, encompassing nonlocal effects, E‐M momentum and constitutive equations are derived and restricted.
38 citations
TL;DR: In this article, the simple microfluid theory of Eringen was generalized to include nonlocal effects and the balance laws, jump conditions, and constitutive equations were obtained.
TL;DR: In this paper, the growth of groups of cavities in an isotropic polystyrene-like solid is discussed and a craze formation mechanism is proposed and its stability examined.
Abstract: This paper represents a first attempt to discuss the growth of groups of cavities in an isotropic polystyrene-like solid. Calculations are made on a two-dimensional array of cylindrical voids in a sheet of uniform thickness. Stresses and displacements throughout the solid are obtained by use of the finite element method for both uniaxial and biaxial loading conditions. Elastic perfectly-plastic and strain-softening-hardening material laws are considered. It is shown how groups of voids are much more easily formed than single separate voids. For a strain-softening-hardening constitutive law a craze formation mechanism is proposed and its stability examined.
01 Jan 1973
TL;DR: In the last decade, a rapid development of an understanding of the response of solid materials to high amplitude dynamic loads has led to rapid development in understanding of their response to high frequency dynamic loads.
Abstract: Concentrated research over the last decade has led to rapid development of an understanding of the response of solid materials to high amplitude dynamic loads. Constitutive equations have been developed for such real materials as engineering alloys, fiber composites, porous earth materials, and polymers. Together with the conservation laws, these equations have been incorporated into numerical solution methods which have allowed analysis of such problems as ballistic penetration, high velocity impacts, explosive devices and components, and many others which were intractable only a few years ago. Stress wave codes have also become an indispensable tool in further research on the dynamic behavior of materials.
TL;DR: In this paper, various types of extensional flows and extensional viscosities are defined and methods of measurement discussed, and the role that each extensional flow plays in various polymer fabrication processes is discussed with examples.
Abstract: The various types of extensional flows and extensional viscosities are defined and methods of measurement discussed. The role that each of these extensional viscosities plays in various polymer fabrication processes is discussed with examples. Finally, it is shown how engineering analyses of these complex flow fields are conducted using simplified phenomenological equations for the rheological behavior. This approach is recommended for use until such time as tensorially correct, mathematically tractable constitutive equations that are based on molecular theory are available.
TL;DR: In this paper, a constitutive equation for this ideal material is based on a rate-dependent porecollapse relation obtained previously from a spherical model calculation, which is used to study the propagation of steady waves; closed-form expressions are obtained for the Hugoniots and the differential equation for the steady wave profiles is integrated numerically.
Abstract: A porous material is idealized as a suspension of voids in an incompressible ductile matrix. A constitutive equation for this ideal material is based on a rate‐dependent pore‐collapse relation obtained previously from a spherical model calculation. This theory is used to study the propagation of steady waves; closed‐form expressions are obtained for the Hugoniots and the differential equation for the steady wave profiles is integrated numerically. A feature of the theory is prediction of a finite compaction pressure Pc such that shocking to pressure P* causes partial compaction if P* < Pc and total compaction if P* ≥ Pc. We also discuss a qualitative difference in the behavior of the rate‐dependent energy for these two situations.
TL;DR: In this article, the linear and nonlinear theories of elastic slender curved rods are formulated in a systematic manner and the generalized strains are defined based on the principle of virtual work, and the field equations for finite deformations of curved rods can be simplified in the case of small axial strain and moderately small rotations.
Abstract: The linear and nonlinear theories of elastic slender curved rods are formulated in a systematic manner. Equations of equilibrium for stress resultants and moments are derived. The generalized strains are defined based on the principle of virtual work. Constitutive equations corresponding to small strains are obtained. The field equations for finite deformations of curved rods can be simplified in the case of small axial strain and moderately small rotations. Further simplifications can be made for the case of slightly curved rods. Two examples are presented to illustrate applications of the developed theories.
TL;DR: A relation between the heredity theory with time-invariant nonlinearity and fractional-exponential kernels and the Volterra-Frechet theory for uniaxial tension was established in this article.
Abstract: A relation is established between the heredity theory with time-invariant nonlinearity and fractional-exponential kernels and the Volterra-Frechet theory for uniaxial tension. A constitutive equation is proposed for processes accompanied by decreasing strain. A procedure for determining the necessary material characteristics from creep and recovery data is considered.
TL;DR: In this paper, a set of constitutive equations generalizing the Kelvin-Voigt model has been derived, based upon micropolar theory, and three types of problems, bending, torsion, and wave propagation, are presented.
Abstract: The anisotropic physical properties resembling those of fluids and solids of smectic liquid crystals are discussed. Based upon micropolar theory, a set of constitutive equations generalizing the Kelvin‐Voigt model has been derived. Material moduli are restricted by material symmetry and physical considerations. The concepts of reference state fundamental to smectic liquid crystals are discussed. Three types of problems, bending, torsion, and wave propagation, are presented. Future studies and experiments are suggested with the hope of creating further confidence in the theory.
TL;DR: In this paper, the transformation equations of kinematic, thermodynamic and electromagnetic quantities as well as their spatial and temporal derivatives are derived and their objectivity examined and the restrictions on the form of constitutive equations of continuum physics imposed by the principle of objectivity are studied.
Abstract: In this study we propose a principle of objectivity which is appropriate to the theory of relativity. The transformation equations of kinematic, thermodynamic and electromagnetic quantities as well as their spatial and temporal derivatives are derived and their objectivity examined. Finally the restrictions on the form of constitutive equations of continuum physics imposed by the principle of objectivity are studied.
TL;DR: In this article, the pneumatic tire is treated as a laminated, anisotropic, toroidal shell of revolution possessing bending rigidity, and the plies are constructed of elastic textile cords embedded in an elastic rubber matrix, which are considered homogeneous and orthotropic on a macroscopic scale.
Abstract: The pneumatic tire is treated as a laminated, anisotropic, toroidal shell of revolution possessing bending rigidity. The plies, which are constructed of elastic textile cords embedded in an elastic rubber matrix, are considered homogeneous and orthotropic on a macroscopic scale. The tire shell is considered to deform according to the classical Love hypothesis. The equilibrium, strain‐displacement, and laminate constitutive equations governing the tire shell are reduced to a system of six first order, nonlinear, ordinary differential equations with variable coefficients which are solved numerically by a multi‐segment forward integration technique. The geometrical nonlinearities due to finite displacements are accounted for by an incrementing process using transient coordinates. The theory is illustrated by a numerical calculation which shows good agreement with actual measurements.
TL;DR: In this article, the applicability of linear viscoelasticity theory under repeated or decreasing loadings for these materials is also demonstrated, using a constitutive equation developed by Farris and Fitzgerald which accounts for the maximum strain ever imposed upon a material as well as a weighted average of the strain history.
Abstract: Employing a constitutive equation developed by Farris and Fitzgerald which accounts for the maximum strain ever imposed upon a material as well as a weighted average of the strain history, the family of Pth order Lebesgue norms, the applicability to a sand-asphalt concrete is demonstrated. The inadequacy of linear viscoelasticity theory under repeated or decreasing loadings for these materials is also demonstrated. Practical laboratory determination of the material parameters is described.
01 Jan 1973
TL;DR: In this article, a constitutive equation of differential form is developed which exhibits relaxation from one "instantaneous" non-linear stress-strain relation to a second such relation expressing long time (or low frequency) behaviour.
Abstract: Materials with memory are dispersive, wave propagation speeds being frequency-dependent To illustrate the effects of finite amplitude, a constitutive equation of differential form is developed which exhibits relaxation from one “instantaneous” non-linear stress-strain relation to a second such relation expressing long time (or low frequency) behaviour According to linear theory, the wave produced by a step-function input is diffusive in character, broadening with time, whereas second order theory permits the existence of self-preserving wave forms The evolution of such a wave is studied by matched asymptotic expansion techniques, and criteria found for the development of discontinuities The structure of “strong” shocks is also examined, and in a final section the evolution of such a shock produced by a suddenly-applied strain is studied; at short times the propagation is governed by the instantaneous modulus, and a functional equation describing the evolution to the asymptotic state is derived
TL;DR: In this article, the authors apply the Johnston-Gilman-type constitutive equation to the theory of stress-wave propagation and study the propagation of the stress wave produced in a thin rod by an impact of a long duration.
Abstract: Many theories have been proposed for the propagation of stress waves in metals. They are classified into three types by the constitutive equation; that is, the Karman‐type theory, the Malvern‐type theory, and the Cristescu‐type theory. However, these proposed theories are not sufficient to explain certain facts which are found in the impact test of a thin rod consistently. For example, they fail to explain how the front of the stress wave always travels with the elastic‐wave velocity even in material prestressed into the plastic region, and the plateau of the uniform plastic strain remains in the neighborhood of the impact end. Therefore, in this paper, the authors apply the Johnston‐Gilman‐type constitutive equation to the theory of stress‐wave propagation and study the propagation of the stress wave produced in a thin rod by an impact of a long duration. The results of analysis account for the above‐mentioned two facts consistently, and, moreover, account for other phenomena which occur during the propagation of the stress wave not only in mild steel but also in other metals. From these results, the following conclusions are obtained. It is proper to use the Johnston‐Gilman‐type constitutive equation for the theory of the stress‐wave propagation in mild steel, and it seems that the forms of the constitutive equations of other metals may bear a close resemblance to that of the Johnston‐Gilman‐type constitutive equation. Though the Johnston‐Gilman‐type constitutive equation is based on the microscopic mechanisms of the dislocation theory, the theory of stress‐wave propagation in which it is used is essentially Malvern's theory, which has a noninstantaneous plastic response to an increase of the stress.
TL;DR: In this paper, a systematic procedure developed by Coleman for establishing thermodynamically consistent constitutive equations is used to develop the thermomechanical constitutive equation for the stress and dissipation functions for thermoheologically simple materials.
Abstract: A systematic procedure developed byColeman for establishing thermodynamically consistent constitutive equations is used to develop the thermomechanical constitutive equations for the stress and dissipation functions for thermoheologically simple materials. A comparison is made with similar expressions developed using phenomenological model theory. The influence of thermorheologically simple behavior is illustrated in the solution of the problem of a solid rod undergoing torsional oscillations with temperature dependent properties.
TL;DR: In this article, the basic hypothesis of the constitutive equation can be tested quickly and simply, without introducing any approximations, and in fact without directly determining the relevant memory function.
Abstract: Recently Yamamoto proposed a new procedure to determine the relevant material properties for a widely used viscoelastic fluid constitutive relation. The procedure, based on a hypothetical dependence of the memory function on the rate of deformation, is rather complicated and introduces a few approximations. Also, the procedure was not actually applied to a particular set of experimental data. In this paper it is shown how the basic hypothesis of the constitutive equation can be tested quickly and simply, without introducing any approximations, and in fact without directly determining the relevant memory function. This new procedure is applied to one of the standard model materials; the constitutive relation is revealed to be an inadequate formation for this material.
TL;DR: In this paper, the behavior of elastic-plastic solids under large deformation has been characterized by a class of rate-type constitutive equations, and the relationship between the results obtained in this paper and those of a more familiar form of a theory of elastic solids is indicated.
TL;DR: In this article, general theoretical expressions for the physical parameters of a composite system in relation to those of the constituents are developed by the differential operator representation of constitutive equations for linearly viscoelastic materials.
Abstract: By the differential operator representation of constitutive equations for linearly viscoelastic materials, general theoretical expressions are developed for the physical parameters of a composite system in relation to those of the constituents. The interfacial tension between the dispersed phase and continuous matrix is included in the derivation. The results show that it has effect only on the shear parameter but not on the bulk parameter of the composite system. The general expressions developed in this article represent a unified theory for composite systems. The results are shown to reduce to many special cases obtained by other investigators.
TL;DR: In this article, a non-linear constitutive equation for the heat flux vector is proposed as a more accurate description of heat flow at low temperatures, and two methods for predicting the breakdown of the constant profile wave solution are compared.
Abstract: The equations of thermoelasticity are briefly derived. A non-linear constitutive equation for the heat flux vector is proposed as a more accurate description of heat flow at low temperatures. In the linear theory, it is shown that an exact equation, governing dilatational wave propagation, must be used for certain real materials. The corresponding approximate equation deduced byLord andShulman [1] predicts unstable lower order waves. The strong dilatational shock equations are completed for the extended heat conduction law. Dilatational constant profile waves are studied and used to discuss the shock structure of the dilatational non-heat conducting shock. Two methods for predicting the breakdown of the constant profile wave solution are compared. Both methods coincide in their estimation of the strain that would cause the breakdown. Some conclusions are drawn for real materials.
01 May 1973
TL;DR: In this paper, the condition for stability of a homogeneous state of deformation of an elastic body under dead-loading is derived on the basis of the Hadamard criterion, and the strongellipticity condition then follows as a necessary condition.
Abstract: The condition for stability of a homogeneous state of deformation of an elastic body under dead-loading is derived on the basis of the Hadamard criterion. The strong-ellipticity condition then follows as a necessary condition. The pure homogeneous deformation is then discussed, of a cube of incompressible isotropic neo-Hookean elastic material, under dead-loading by three equal pairs of equal and opposite forces applied to the faces of cube. It is shown that the resulting state of pure homogeneous deformation is not uniquely determined. The implications of this result, with respect to the material stability conditions proposed by Coleman and Noll and by Truesdell and Toupin are discussed. Finally, some explicit restrictions on the strain-energy function are given, which result from the consideration that the velocities of propagation of plane waves in the pure homogeneously deformed material must be real.