Showing papers on "Continuum mechanics published in 1969"

Introduction to the mechanics of a continuous medium

Abstract: 1. Vectors and Tensors. 2. Strain and Deformation. 3. General Principles. 4. Constitutive Equations. 5. Fluid Mechanics. 6. Linearized Theory of Elasticity. Appendix I: Tensors. Appendix II: Orthogonal Curvilinear.

A mixture of viscous elastic materials with different constituent temperatures

Abstract: : Constitutive equations are discussed for a mixture of any number of materials with elastic and viscous properties in which the constituents may have different temperatures.

On Dual Approximation Principles and Optimization in Continuum Mechanics

Abstract: A unified expression of some of the boundary value problems of continuum mechanics is developed. A central role is given to the notion of a Legendre dual transformation in displaying the simple analytical structure of each problem considered. A systematic method of deriving reciprocal variational principles is described. General boundary value problems governed by inequalities as well as equations are then considered. Convexity of the dual functions related by the Legendre transformation is shown to be the basis of uniqueness theorems and extremum principles. Attention is drawn to the relevance of the literature on mathematical programming theory. M any examples are given, involving new or recent results in elasticity, plasticity, fluid mechanics and diffusion theory.

A micromorphic approach to dislocation theory and its relation to several existing theories.

Abstract: : Two separate continuum dislocation theories are presented; one dealing with static incompatible, micropolar dislocations and disclinations, as encountered in initial stress problems, and the other with a dynamical theory of micromorphic solids containing continuous distributions of dislocations Relationships between several continuum dislocation theories and micromorphic mechanics are established by providing extensions and new interpretations of the micromorphic theory First both micromorphic and micropolar theories of elastic solids are summarized, and then the theories of Kroner, Fox, and Berdichevskii and Sedov are discussed in some detail within this framework In the last section, by use of micromorphic kinematics, dislocation density, strain, and microstrain tensors are introduced and constitutive equations are constructed Together with the balance laws this constitutes a complete dynamical theory The theory is intended for predictions of motions and micromotions of a solid containing dislocations undergoing elastic deformations From the micromotion, the dislocation density and first stress moments can be calculated (Author)

Incremental analysis of large deformations in mechanics of solids with applications to axisymmetric shells of revolution

Abstract: Incremental analysis of large deformations in continuum mechanics with applications to axisymmetric shells of revolution

Space-time structure in high energy interactions

Abstract: The preceding two talks were motivated by the courageous faith that our present ideas of the continuum and the gravita-tional field extend into the range of elementary particle sizes and far below. Equally interesting to high-energy physicists is the possibilitv that these ideas of saace and time are already at the very edge of their domain and are wrong for shorter distances and times, and that high-energy experiments are a probe through which departure from the classical continuum can be discovered. The present talk is devoted to this alternative. The difficulty is that all our present theoretical work is based on a microscopic continuum and one is faced by the rather formidable problem of redoing all physics in a continuum-free manner. Yet I think those who cope with the conceptual problems of quantum field theory for enough years eventually get sick of the ambiguities and divergencies that seem to derive from the continuum and are driven to seek some way out of this intellectual impasse. I would like to describe a program of this kind that I have been led into after vainly trying to extract some information,; about the small from extremely non-linear field theories. The starting point here also is Riemann, who explicitly poses the question of whether the world is a continuous or a discrete manifold in his famous inaugural lecture. He points out certain philosophical advantages of the discrete manifold, in fact argues for it more strongly than for the continuous. and set devotes his life to the continuous. m Y

The formulation of theories in generalized continuum mechanics and their physical significance

Abstract: This chapter discusses a model that is a composite structure consisting, in the undeformed state, of identical rectangular cells arranged in a lattice structure and bonded together on their adjacent surfaces. It is assumed that the material of each cell is a continuum of the type in which the deformation is completely described by the ordinary displacement field. The displacement field in each cell is expanded as a Taylor series about the particle that is initially at the center of mass. The coefficients in this series, together with the vector position of this particle, may then be considered as generalized coordinates describing the deformation of the cell. These coordinates are associated with the particle initially at the center of mass of the cell. The kinetic energy and rate at which work is done by the external forces is presented in a manner similar to that employed in the previous case.

Continuum mechanics of media with internal structure

Abstract: This chapter focuses on systems with internal structure—for example, systems that consist of particles that can translate and rotate about their center of gravity like a rigid body or that have a magnetic moment According to modern physics, such a system can be treated as a part of a collection of similar systems, called an ensemble In the theory of the ensemble, the actual behavior of the system is represented by the average behavior of the ensemble However, because of mathematical difficulties, it is impossible to treat actual problems by the methods of ensemble theory, and one has to content with the basic equations of continuum mechanics that, in fact, are conservation equations They provide consistent and rigorous information but avoid the need of deriving constitutive equations The introduction of the theory of the Cosserat Continuum provides the opportunity for extending the classical formalism by defining some kinematical quantities that describe physical phenomena characterized by internal degrees of freedom In the continuum theory, these quantities never refer to the particular properties of individual molecules but to the average of many molecules in an element Continuum echanics is a coarse-grained theory

Finite element formulation for linear thermoviscoelastic materials

Abstract: Report presents the finite difference equations in time and finite element matrix equations in space for general linear thermovisoelastic problems. The equations are derived for a general three-dimensional body but are applicable to one- and two-dimensional configurations with minor changes.

A continuum theory for an elastic solid with elastic micro-inclusions

Abstract: Elastic particulate composite solid with microinclusions, deriving dispersion relations governing plane longitudinal wave propagation modes by analogy with continuum theory

On dislocations, plasticity and micromorphic mechanics.

Abstract: : Within the framework of micromorphic mechanics a continuum theory of dislocations is formulated for solids undergoing elastic deformations. The micromotion gradients and spin degrees of freedom of the micromorphic theory together with the concept of the Burgers circuit provide the kinematic variables, strain measures and dislocation tensors fundamental to the theory. The balances of momentum, first stress moments and energy are basic to the present theory. Together with a set of constitutive equations for the stress and stress moments, the field equations are complete. Thermodynamical restrictions and the uniqueness of static and dynamic solutions are discussed. The plane wave solution of the linear theory is discussed in detail. The dispersive branch obtained in the velocity dispersion is similar to the experimental findings of others and should provide reasonable support for the theory. The micropolar initial stress-couple stress problem containing distributions of dislocations and disclinations is formulated. Relations between the present work and existing theories are discussed. (Author)

Some aspects of linear irreversible thermodynamics and continuum mechanics in the presence of electromagnetic fields

Abstract: Irreversible thermodynamics, conservation principles, andMaxwell relations are used to obtain the constitutive equations for a homogeneous fluid and aKelvin-Voigt viscoelastic solid in a electromagnetic field. Heat conduction equations for aVan der Waals gas and the viscoelastic media are obtained in a natural way and the effects of the electromagnetic fields are investigated.