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Author: Stanford University. Division of Engineering Mechanics Publisher: ISBN: Category : Languages : en Pages : 14
Book Description
The problem of moving boundaries separating elastic regions from plastic regions in one dimensional plastic wave propagation was considered by several investigators. These boundaries are called unloading waves if the material at a section changes from a plastic state to an elastic state as the wave passes the section. If the material changes from an elastic state to a plastic state, the moving boundary is called a loading wave. It was shown by other authors that the speed of an unloading wave or a loading wave must satisfy certain conditions if the time derivatives of the stress sigma sub t, on both sides of the elastic-plastic boundary are not zero. The purpose of the note is to clarify the situation in which sigma sub t and its higher derivatives are zero on both sides of the elastic-plastic boundary. (Author).
Author: Stanford University. Division of Engineering Mechanics Publisher: ISBN: Category : Languages : en Pages : 14
Book Description
The problem of moving boundaries separating elastic regions from plastic regions in one dimensional plastic wave propagation was considered by several investigators. These boundaries are called unloading waves if the material at a section changes from a plastic state to an elastic state as the wave passes the section. If the material changes from an elastic state to a plastic state, the moving boundary is called a loading wave. It was shown by other authors that the speed of an unloading wave or a loading wave must satisfy certain conditions if the time derivatives of the stress sigma sub t, on both sides of the elastic-plastic boundary are not zero. The purpose of the note is to clarify the situation in which sigma sub t and its higher derivatives are zero on both sides of the elastic-plastic boundary. (Author).
Author: T. C. T. Ting Publisher: ISBN: Category : Languages : en Pages : 23
Book Description
In one dimensional wave propagation such as longitudinal waves in a rod, an elastic-plastic boundary may start at the end x = 0 of the rod depending on the stresses prescribed at x = 0. The initial slope of the elastic-plastic boundary at x = 0 can be determined easily if the time derivative sigma sub t of the stress sigma on both sides of the elastic-plastic boundary are not zero. In this paper, the initial slope of the elastic-plastic boundary (or boundaries) is determined analytically when sigma sub t at x = 0 is continuous and vanishes at time t = t sub 0 while the second derivative sigma sub tt at t sub 0 may or may not be continuous. It is seen that an elastic region can be generated near the end of the rod even though the stress state at the end is continuously plastic. (Author).
Author: W. K. Nowacki Publisher: Elsevier ISBN: 1483153932 Category : Science Languages : en Pages : 259
Book Description
Stress Waves in Non-Elastic Solids is a comprehensive presentation of the principles underlying the propagation of stress waves in non-elastic solids, with emphasis on wave problems in the theory of plasticity. This book exposes wave propagation problems for a range of material responses and justifies the hypotheses introduced in specialized theories and the simplifications made in the analysis of particular problems. Both analytical and numerical methods of solving problems are described, and a large number of solutions to specific problems of wave propagation in inelastic solids are given. This book is comprised of six chapters and begins with an overview of the fundamental equations of the dynamics of inelastic media. The dynamical properties of metals and soils are discussed, offering an account of the most representative theories of plasticity and viscoplasticity. The next chapter considers the basic definitions of discontinuity surfaces and the conditions that must to be satisfied across these surfaces. Certain mathematical fundamentals are given, referring to systems of differential equations, quasi-linear and semi-linear, of the first order. Initial and boundary value problems for hyperbolic equations are also formulated. The remaining chapters focus on methods of solving stress wave propagation problems, including one-dimensional plane waves and longitudinal-transverse waves. Wave propagation problems for elastic-plastic and elastic/viscoplastic media are treated in detail, along with the most important problem of shock waves in metals and soils. The last chapter deals with thermal wave propagation problems. This monograph will be a valuable resource for students and practitioners of engineering, physics, and mathematics.
Author: A. Bedford Publisher: ISBN: Category : Science Languages : en Pages : 320
Book Description
This volume outlines the basic concepts and methods of the theory of wave propagation in elastic materials. The linear theory of elasticity is covered, culminating in the displacement equations of motion. One-dimensional waves are analyzed through the D'Alembert solution.
Author: Peter A. Tuschak Publisher: ISBN: Category : Languages : en Pages : 33
Book Description
For several types of excitation of one-dimensional elastic-plastic stress waves in a rod, unloading waves propagate which interact with the loading waves. The moving boundary at which this interaction occurs is the unloading boundary. A knowledge of the location of this boundary and the behavior exhibited on it is necessary for the solution of wave propagation problems of this kind. A technique is presented to obtain an arbitrary number of terms in series expressions describing the response in semi-infinite rods. Several examples, including finite mass impact of the rod, are given to illustrate the use of the technique. The technique will determine the initial portion of the boundary in a finite length rod. (Author).
Author: Stanford University. Department of Applied Mechanics Publisher: ISBN: Category : Languages : en Pages : 58
Book Description
The analysis of the propagation of plastic waves for one-dimensional stress and one-dimensional strain are compared and contrasted. The former pertains to waves along a thin rod or wire, the latter to waves through a slab. The influence of finite strain is studied in some detail. The theory of the propagation of plastic waves of combined stresses is reviewed with particular emphasis on the waves propagated in one space dimension due to the application of perpendicular, independent, uniform shear tractions on the surface of a half-space. Solutions obtained numerically from characteristic theory are discussed, and some unexpected features of the coupling between stress components are remarked upon. Simple wave solutions are also reviewed, and aspects pertinent to tests for dynamic plastic material characteristics are mentioned. Some recent work clarifying aspects of the determination of elastic-plastic boundaries is also described. (Author).
Author: George C. Sih Publisher: Springer Science & Business Media ISBN: 9400918666 Category : Science Languages : en Pages : 222
Book Description
More than six years ago, several of Rabotnov's close friends and colleagues from the USSR and USA decided to contribute a volume on Plasticity and Failure of Solids in honor of his 70th birthday. The celebration was interrupted unexpectedly by his death on May 13, 1985 at which time another decision was made still to publish the work, but as a memorial volume. As in any field of scientific endeavor, research confronts the scientists with anomalies; our chosen area is no exception. The ways in which failure criteria and plasticity theory are combined can differ widely among the researchers; they will never yield quite the same results. Each of the invited contributors has, therefore, been encouraged to express his views and to expound on his personal opinion. The contributors are free of enumeration from the authority and/or consensus of any scientific society or community. What impedes scientific process is the esoteric tradition of accepting ideas and theories by consensus among members of societies and communities. The absence of such a trend is refreshing; the collaboration between the authors from the USSR and the USA had to be one of the contributing factors. Finally, the editors wish to acknowledge the authors who have made the publication of this volume possible. a. c. Sib S. T. Mileiko AJ. Ishlinsky xi The late Professor Yuriy Nickolaevich Rabotnov (February 24, 1914 - May 13, 1985) xii Scientific biography of the late academician Yu. N.
Author: F. McCarthy Publisher: Elsevier ISBN: 1483290662 Category : Technology & Engineering Languages : en Pages : 663
Book Description
This volume contains a timely collection of research papers on the latest developments in the ever-increasing use of elastic waves in a variety of contexts. There are reports on wave-propagation in various types of media: in both isotropic and anisotropic bodies; in homogeneous and inhomogeneous media; in media with cracks or inclusions in random media; and in layered composites.The bulk of the papers are concerned with propagation in elastic media, but also included are viscoelastic, thermoelastic and magneto-electroelastic wave propagation, as well as waves in porous and piezo-electric bodies. Consideration is given to propagation in bodies as diverse as stretched elastic strings to surfaces such as thin walled cylinders, and thin films under stress. Applications considered include the determination of the depth of cracks; analysis of ground motions generated by a finite fault in seismology; surface wave spreading on piezo-electric solids; and dynamical stress intensity factors. Most of the papers are theoretical in nature, and many are complemented by numerical studies. Also included are a general survey on experimental techniques, and reports on experimental work.The volume will be of interest to those who do theoretical studies of elastic wave propagation and to those who apply elastic waves whether in seismology, non-destructive testing, the fabrication of devices or underwater acoustics, etc.
Author: D. T. Liu Publisher: ISBN: Category : Languages : en Pages : 75
Book Description
This report is concerned mainly with plane-wave propagation of large amplitude stresses in a medium where motion transverse to the direction of wave propagation is presented. Both the partial differential equations governing the stress-wave propagation and the jump conditions across a shock discontinuity are developed using the basic principles of the conservation of mass, momentum, and energy. The criterion for a stable shock front is discussed, and the wave structure arising, when the criterion is no longer satisfied, is described, The constitutive law is discussed in some detail with particular emphasis on the elastic-plastic behavior of ductile solids. The finite difference method is developed for solving onedimensional shock wave propagation problems with initial and boundary conditions prescribed in terms of pressure or velocity; i.e., arbitrary pressure pulse input, free surface, or an interface between two different media. The operational FORTRAN computer program is described in some detail. Capabilities include predicting the shock wave response, possible bond separation, and spallation failure in a multilayered medium composed of up to four different materials. Sample calculations which serve to illustrate the difference between the hydrodynamic and elastic-plastic behavior of solids under shock compression are also included. (Author).
Author: Stanford University. Division of Engineering Mechanics
Author: Stanford University. Division of Engineering Mechanics
Author: T. C. T. Ting
Author: W. K. Nowacki
Author: James Chen Mao
Author: A. Bedford
Author: Peter A. Tuschak
Author: Stanford University. Department of Applied Mechanics
Author: George C. Sih
Author: F. McCarthy
Author: D. T. Liu