Theory of Plastic Bending Waves in a Bar of Strain Rate Material, with Companion Studies on Elastic Bars PDF Download
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Author: H. J. Plass Publisher: ISBN: Category : Elastic rods and wires Languages : en Pages : 0
Book Description
This report contains a theory of bending waves in a rod in which plastic stresses are present. The theory is an extension of that of Malvern for longitudinal waves; it assumes a strain rate law similar to his for both bending stresses and shear stress. It is assumed, as in the Timoshenko equation, that shear deformation and rotatory inertia are important in determining the properties of the waves.
Author: H. J. Plass Publisher: ISBN: Category : Elastic rods and wires Languages : en Pages : 0
Book Description
This report contains a theory of bending waves in a rod in which plastic stresses are present. The theory is an extension of that of Malvern for longitudinal waves; it assumes a strain rate law similar to his for both bending stresses and shear stress. It is assumed, as in the Timoshenko equation, that shear deformation and rotatory inertia are important in determining the properties of the waves.
Author: T X Yu Publisher: World Scientific ISBN: 9814500402 Category : Technology & Engineering Languages : en Pages : 572
Book Description
From the point of view of mechanics, this monograph systematically demonstrates the theory of plastic bending and its engineering applications; most of the contents of the book are based on the authors' research in the past decade. The monograph not only expounds the contributions of the authors to the fundamental theory of plastic bending, but also presents various applications of the theory in sheet metal forming, particularly in the analysis and prediction of springback and wrinkling of strips and plates subjected to bending or stamping. In addition to theoretical modelling, attention has also been paid to the development of related numerical methods; comparisons with experimental results are also presented.
Author: Jacob Lubliner Publisher: ISBN: Category : Metals Languages : en Pages : 16
Book Description
A theory of plastic wave propagation in bars is formulated on the basis of a general quasi linear constitutive equation. It is shown that the ''strain-rate-independent'' and ''strain rate-dependent'' theories are special cases of the generalized theory, and conditions are shown under which one or the other may be valid. (Author).
Author: Stanford University. Department of Applied Mechanics Publisher: ISBN: Category : Languages : en Pages : 94
Book Description
The general case of plane wave propagation for combined stresses is considered in a half-space. The analysis is based on an elastic-plastic theory for an isotropic work-hardening material which satisfies a flow or incremental type law. The stress-strain curve is assumed concave towards the strain axis with possibly a bend at yield. The wave propagation analysis determines the motion to be governed by a system of quasi-linear hyperbolic equations of the first order. Two different types of loading are considered in this study--the coupled double shear loading and the combined pressure and shear. The loading functions are continuous and are assumed to be uniformly distributed over the surface for all t. Two distinct wave speeds are found in the plastic region for both loading types. For general loading plastic flow can propagate with each wave speed which may be as fast as the elastic wave speed. This is contrary to wave for a single stress component. This fact may have an important bearing on the interpretation of experiment, for which, in the past, propagation of plastic waves at elastic wave speed has been considered to indicate rate effects. Solutions of the problems are obtained by numerical integration along the characteristics on a step by step basis. The loading-unloading boundaries are determined in the x - t plane. For a simple case of the double shear problem when the components are in proporation, very good agreement is obtained between the numerical result and the known analytical solution. (Author).
Author: Munirathnam Valathur Publisher: ISBN: Category : Elastic wave propagation Languages : en Pages : 116
Book Description
Lubliner suggested that the uniaxial constitutive equation (1.1) be used in the numerical solution of wave-propagation problems, and that the results approximating those of either hypothesis may be obtained in extreme cases. He further showed on the basis of an extremely simple, piece-wise linear, model of plastic-viscoplastic behavior, that results approaching the viscoplastic hypothesis will be obtained under one or more of the following circumstances: (1) weak impact, (2) long bar, (3) short 'relaxation' time (or natural time of the material); that converse conditions will lead to results approaching the plastic hypothesis; and that intermediate conditions require the use of the general constitutive equation. The purpose of the present study is to test further the validity of Lubliner's suggestions by means of numerical solutions of representative wave-propagation problems in bars whose mechanical behavior is described by the uniaxial constitutive equation, slightly modified to account for loading-unloading behavior.
Author: H. J Plass (Jr) Publisher: ISBN: Category : Languages : en Pages : 136
Book Description
The simplest approximate traveling wave theory is that which describes the longitudinal waves in a long rod resulting from an axial distrubance applied to the end of the rod. The present report covers primarily the theoretical phase of the project, although some experimental results are included for comparison purposes.
Author: H. J. Plass
Author: H. J. Plass
Author: T X Yu
Author: Jacob Lubliner
Author: Giovanni Bianchi
Author: H. J. Plass
Author: Stanford University. Department of Applied Mechanics
Author: Munirathnam Valathur
Author: William H. Hoppmann (II.)
Author: University of Texas. Structural Mechanics Research Laboratory
Author: H. J Plass (Jr)