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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: 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: 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: Lili Wang Publisher: Elsevier ISBN: 0080470971 Category : Technology & Engineering Languages : en Pages : 549
Book Description
The primary objective of Foundations of Stress Waves is to give the reader an understanding of stress wave behaviour while taking into account the dynamic constitutive equations of elastic-plastic solids. The author has combined a 'materials characteristics' approach with a 'singularity surface' approach in this work, which readers will find to be a novel and unique route to solving their problems. Helps engineers understand the effects and behavior of stress waves in various materials Aids in the process of engineering design, testing, and evaluation
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: Joel Lipkin Publisher: ISBN: Category : Languages : en Pages : 84
Book Description
Experiments are reported in which annealed aluminum tubes are subjected to a static plastic torque followed by a longitudinal compressive impact. Measurements are made of both longitudinal and shear strain-time profiles at stations along the specimen. Qualitatively, the strain response at the gages corresponds to the arrival of a fast wave for which shear strain decreases while longitudinal strain increases followed by a slow wave for which both shear and longitudinal strains increase. A rate independent theory of combined longitudinal and torsional plastic wave propagation for workhardening materials is found to be adequate for predicting many features of the observed strain-time response in the specimens. For the particular case of an isotropic workhardening, elastic-plastic material, numerical solutions of the governing equations are compared with the results of the experiments. The same assumed material behavior is used for comparing observed behavior at unloading waves with theoretical predictions. Discrepancies are shown to be explainable in terms of the inadequacy of the assumption of strain-rate independent behavior. (Author).
Author: T. C. T. Ting Publisher: ISBN: Category : Languages : en Pages : 20
Book Description
A general study is given of plane and cylindrical wave propagation of combined stresses in an elastic-plastic medium. The coefficients of the governing differential equations, when written in matrix notation, are symmetric matrices and can be divided into sub-matrices each of which has a special form. The relations between the stresses on both sides of an elastic-plastic boundary are derived. Also presented are the restrictions on the speed of an elastic-plastic boundary. (Author).
Author: T. X. Yu Publisher: John Wiley & Sons ISBN: 1118929845 Category : Science Languages : en Pages : 292
Book Description
Fundamental guidance—including concepts, models, and methodology—for better understanding the dynamic behavior of materials and for designing for objects and structures under impact or intensive dynamic loading This book introduces readers to the dynamic response of structures with important emphasis on the material behavior under dynamic loadings. It utilizes theoretical modelling and analytical methods in order to provide readers with insight into the various phenomena. The content of the book is an introduction to the fundamental aspects, which underpin many important industrial areas. These areas include the safety of various transportation systems and a range of different structures when subjected to various impact and dynamic loadings, including terrorist attacks. Presented in three parts—Stress Waves in Solids, Dynamic Behaviors of Materials Under High Strain Rate, and Dynamic Response of Structures to Impact and Pulse Loading—Introduction to Impact Dynamics covers elastic waves, rate dependent behaviors of materials, effects of tensile force, inertial effects, and more. The book also features numerous case studies to aid in facilitating learning. The strength of the book is its clarity, balanced coverage, and practical examples, which allow students to learn the overall knowledge of impact dynamics in a limited time whilst directing them to explore more advanced technical knowledge and skills. Considers both the dynamic behavior of materials and stress waves, and the dynamic structural response and energy absorption, emphasizing the interaction between material behavior and the structural response Provides a comprehensive description of the phenomenon of impact of structures, containing both fundamental issues of wave propagation and constitutive relation of materials, and the dynamic response of structures under impact loads Based on the authors’ research and teaching experience as well as updated developments in the field Introduction to Impact Dynamics is the perfect textbook for graduate and postgraduate students, and will work as a reference for engineers in the fields of solid mechanics, automotive design, aerospace, mechanical, nuclear, marine, and defense.
Author: Stanford University. Department of Applied Mechanics
Author: Stanford University. Department of Applied Mechanics
Author: Ning Nan
Author: Stanford University. Department of Applied Mechanics
Author: Ram Parkash Goel
Author: Lili Wang
Author: W. K. Nowacki
Author: Joel Lipkin
Author: T. C. T. Ting
Author: T. X. Yu
Author: Ram Parkash Goel