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Sunday, July 26, 2020 | History

2 edition of Spherically symmetric motions of elastic and elastic-plastic materials. found in the catalog.

Spherically symmetric motions of elastic and elastic-plastic materials.

Frank Bent

# Spherically symmetric motions of elastic and elastic-plastic materials.

## by Frank Bent

Written in English

Edition Notes

Thesis (M.Phil.) - University of East Anglia, School of Mathematics and Physics, 1971.

ID Numbers
Open LibraryOL13844939M

The motion of a self-gravitating hyperelastic body is described through a time-dependent mapping from a reference body into physical space, and its material properties are determined by a. Cavitation instabilities in elastic-plastic solids under spherically-symmetric and axisymmetric loadings were investigated using the finite element method. Both quasi-static and dynamic analyses.

We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic. Axially & Spherically Symmetric Solutions for Elastic-Plastic Solids Under Quasi-Static Loading Spherically Symmetric Solution for Large Strain Elasticity Problems Simple Dynamic Solutions for Linear Elastic Solids 5. Analytical Techniques and Solutions for Linear Elastic .

An important problem in quantum mechanics is that of a particle in a spherically symmetric potential, i.e., a potential that depends only on the distance between the particle and a defined center particular, if the particle in question is an electron and the potential is derived from Coulomb's law, then the problem can be used to describe a hydrogen-like (one-electron) atom (or ion). 2 Lagrangian approach for static spherically symmetric vac-uum solutions To begin with, we recall the action for modiﬁed F(R)-theories: S = 1 2κ2 Z d4x √ −gF(R), (4) where g is the determinant of metric tensor gµν and F(R) is a generic function of the Ricci scalar R. We shall look for static spherically symmetric (SSS) solutions of the.

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### Spherically symmetric motions of elastic and elastic-plastic materials by Frank Bent Download PDF EPUB FB2

T he spherically-symmetric motion of interfaces between regions deforming elastically and those deforming plastically is considered.

It has been shown elsewhere (for example, in work by L.W. M orland and A.D. C ox () and M.J. K enning ()) that, during both spherically-symmetric and uniaxial motions in rate-independent materials, six essentially different types of motion can by: 2.

The character of the wave motion produced in an elastic-plastic body of infinite extent by the application of a uniform pressure p (t) to the surface of a spherical cavity is known to depend upon the magnitude of p(0) in relation to the critical pressure p cr = Y(0) (1 − v)/(1 − 2v), where Y (0) is the initial yield stress and v the Poisson's ratio of the by:   A solution is constructed for the wave motion induced by the application of a continuously increasing uniform pressure on the surface of a spherical cavity in an infinite elastic-plastic medium.

The small amplitude linearization in conjunction with parabolic work-hardening leads to constant wave speeds in both elastically and plastically deforming regions, so that linear wave function Cited by: 7. Zelenina A.A., Zubov L.M. () Spherically Symmetric Deformations of Micropolar Elastic Medium with Distributed Dislocations and Disclinations.

In: dell'Isola F., Eremeyev V., Porubov A. (eds) Advances in Mechanics of Microstructured Media and Structures. Advanced Structured Materials, vol Springer, Cham.

First Online 28 February Cited by: 1. Our intention in this paper is to discuss two different equations of state in the static and spherically symmetric context with two different materials. In  the familiar Kirchhoff-St. Venant stored energy functional for hyper-elastic isotropic materials has been extended to the relativistic case.

Recall that this functional is quadratic in theCited by: 6. T wo closed-form radially symmetric elastic-plastic wave solutions, corresponding to spherical cavity loadings, are compared to numerical solutions constructed by a finite difference code.

An infinitesimal strain theory, with plastic incompressibility, a Mises yield condition and either perfectly plastic flow or parabolic work hardening, allows wave function representations in both elastically.

We developed an analytical model for the elastic-plastic response of a compressible material from the uniform expansion of a spherically symmetric cavity. Previous models consider the material as incompressible.

Numerical results from both models showed the effect of compressibility. M.J. Kenning, Existence and uniqueness of spherically-symmetric elastic-plastic interface motions, Journal of the Mechanics and Physics of Solids, /(75).

European Journal of Mechanics A/Solids 25 () – Transient responses of a magneto-electro-elastic hollow sphere for fully coupled spherically symmetric problem H.M. Wang a,∗, H.J. Ding b a Department of Mechanics, Zhejiang University, HangzhouPR China b Department of Civil Engineering, Zhejiang University, HangzhouPR China Received 2 June.

Axially/Spherically Symmetric elasticity; Axially and Spherically Symmetric Solutions for Elastic-Plastic Solids. Assume that the disk is made from an elastic-perfectly plastic material with yield stress Y and density.

We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory.

axially and spherically symmetric solutions to quasi-static elastic-plastic problems spherically symmetric solution to quasi-static large strain elasticity problems simple dynamic solutions for linear elastic materials 5 solutions for linear elastic solids general principles airy function solution to plane stress and strain static linear.

Overview of elastic material models. There are two general types of elastic material. Linear elastic constitutive relations model reversible behavior of a material that is subjected to small strains. Nearly all solid materials can be represented by linear elastic constitutive equations if they are subjected to sufficiently small stresses.

axially and spherically symmetric solutions to quasi-static elastic-plastic problems. spherically symmetric solution to quasi-static large. strain elasticity problems. simple dynamic solutions for linear elastic materials.

5 solutions for linear elastic solids. general principles. airy function solution to plane stress and strain static. @article{osti_, title = {THE RESPONSE OF ELASTIC SPHERICAL SHELLS TO SPHERICALLY SYMMETRIC INTERNAL BLAST LOADING}, author = {Baker, W E and Allen, F J}, abstractNote = {Results are presented from an analytical study of the reaction of an idealized nuclear reactor containment shell to internal transient loading which could be caused by reactor runaway.

To this purpose we first introduce a new definition of homogeneous, spherically symmetric (hyper)elastic body in Euler coordinates, i.e., in terms of matter fields defined on the current physical.

We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The mate-rials considered belong to the class of John elastic materials and reduce to perfect uids when the rigidity parameter is set to zero.

We nd numerical support that such elastic bodies exist with di. Synthetic seismograms for a spherically symmetric, non-rotating, elastic and isotropic Earth model Pablo Gregorian J Abstract A synthetic seismogram is a predicted seismogram, based on an assumed Earth model.

Synthetic seismograms are a valuable tool for investigating the Earth’s interior, because synthetics can be compared with. arXiv:gr-qc/v2 12 Jan STATIC SELF-GRAVITATING ELASTIC BODIES IN EINSTEIN GRAVITY LARS ANDERSSON, ROBERT BEIG, AND BERND G.

In this paper, a class of static spherically symmetric solutions of the general relativistic elasticity equations is discussed. The main point of the discussion is the comparison of two matter models given in terms of their stored energy functionals, i.e., the rule which gives the amount of energy stored in the system when it is deformed.

The response can be elastic, elastic-plastic or completely plastic depending on the structure and bonding type of the material as well as the shape and size of the » In this case, it was found that the idealization of plastic deformation by an expanding cavity concept is a satisfactory one.A void in an infinite elastic-plastic material grows without bound when a cavitation stress limit is reached.

Such unstable void expansion, driven by the elastic energy stored in the surrounding material, has been studied for the relatively simple case of spherically symmetric conditions and also for a spherical void in an axisymmetric remote stress field.axially and spherically symmetric solutions to quasi-static elastic-plastic problems.

spherically symmetric solution to quasi-static large. strain elasticity problems. simple dynamic solutions for linear elastic materials. 5 solutions for linear elastic solids. general principles. airy function solution to plane stress and strain static linear Price: \$