Asymptotic Analysis of a Mode I Crack Propagating Steadily in a Deformation Theory Material

1987 ◽  
Vol 54 (1) ◽  
pp. 79-86 ◽  
Author(s):  
P. Ponte Castan˜eda
Keyword(s):  
Strain Hardening ◽  
Deformation Theory ◽  
Plastic Material ◽  
Mode I ◽  
Algebraic Equations ◽  
Nonlinear Algebraic Equations ◽  
Stress Functions ◽  
Elastic Plastic Material ◽  
Stress And Deformation ◽  
Distribution Of Stress

The near-tip asymptotic stress and deformation fields of a crack propagating steadily and quasi-statically into an elastic-plastic material are presented. The material is characterised by J2-deformation theory, suitably modified to account for unloading and reloading, together with linear strain-hardening. The cases of plane strain and plane stress Mode I are considered. The governing equations are integrated analytically with the assistance of Muskhelishvili’s complex variable formulation. The boundary and continuity conditions then lead to a set of nonlinear algebraic equations in the coefficients of the stress functions to be solved numerically. Explicit results are given for the strength of the singularity, and for the distribution of stress in the plastic loading, elastic unloading, and plastic reloading regions, as functions of the strain-hardening parameter.

scholarly journals Relationship Between Rockwell C Hardness and Inelastic Material Constants

2002 ◽  
Vol 124 (2) ◽  
pp. 179-184 ◽  
Author(s):  
Akihiko Hirano ◽  
Masao Sakane ◽  
Naomi Hamada
Keyword(s):  
Finite Element ◽  
Friction Coefficient ◽  
Strain Hardening ◽  
Yield Stress ◽  
Plastic Material ◽  
Stress And Strain ◽  
Material Constants ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Hardening Coefficient

This paper describes the relationship between Rockwell C hardness and elastic-plastic material constants by using finite element analyses. Finite element Rockwell C hardness analyses were carried out to study the effects of friction coefficient and elastic-plastic material constants on the hardness. The friction coefficient and Young’s modulus had no influence on the hardness but the inelastic materials constants, yield stress, and strain hardening coefficient and exponent, had a significant influence on the hardness. A new equation for predicting the hardness was proposed as a function of yield stress and strain hardening coefficient and exponent. The equation evaluated the hardness within a ±5% difference for all the finite element and experimental results. The critical thickness of specimen and critical distance from specimen edge in the hardness testing was also discussed in connection with JIS and ISO standards.

An Adaptive Pressbrake Control for Strain-Hardening Materials

1986 ◽  
Vol 108 (2) ◽  
pp. 127-132 ◽  
Author(s):  
K. A. Stelson
Keyword(s):  
Strain Hardening ◽  
Material Property ◽  
Plastic Material ◽  
Material Model ◽  
Punch Force ◽  
Elastic Plastic ◽  
The Press ◽  
Elastic Plastic Material ◽  
Thickness Variations ◽  
Force Displacement

An improved adaptive pressbrake control algorithm is described. The problem is to control the punch reversal position of the press so that the final unloaded angle of the bend remains unchanged in the presence of material property and thickness variations of the sheets or plates being bent. Pressbrake control algorithms that use punch force-displacement data to identify thickness and material property variations have shown promise. However, since previous controllers have been based on an elastic-plastic material model, the parts have been overbent. In this paper, a controller based on an elastic, power-law strain-hardening model is proposed. Experiments have shown that the model eliminates the tendency to overbend the parts that is present in the elastic-plastic algorithm.

The Non-Newtonian Fluid in the Collision

2014 ◽  
Vol 538 ◽  
pp. 72-75
Author(s):  
Lei Hou ◽  
Jun Jie Zhao ◽  
Lin Qiu
Keyword(s):  
High Performance ◽  
Plastic Material ◽  
Three Dimensional ◽  
Strain Curve ◽  
Step Length ◽  
Stress And Strain ◽  
Equation Analysis ◽  
Elastic Plastic Material ◽  
Discrete Finite Element ◽  
Distribution Of Stress

This paper studies elastic-plastic material deformation in terms of Cauchy and PTT. It gives certain convergence to the equation analysis in the discrete finite element method; it reaches o (h2+Δt) under the certain step length. Then we carry on Three-dimensional numerical simulation by the high performance software LS-DYNA and the distribution of stress and strain curve is observed.

Elasto-Plastic Analysis of Thick Cylinders Subjected to Internal Electro-Magnetic Loading

2012 ◽  
Vol 28 (3) ◽  
pp. 423-430 ◽  
Author(s):  
H. Rajabi ◽  
A. Darvizeh
Keyword(s):  
Differential Equations ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Plastic Material ◽  
Displacement Vector ◽  
Time Integration ◽  
Shear Deformation Theory ◽  
Elastic Plastic Material ◽  
Electro Magnetic ◽  
Von Mises

AbstractA study of elasto-plastic deformation of circular cylindrical shells subjected to internal electromagnetic forces is presented in this paper. The five governing equations in terms of resultant forces and resultant moments with respect to basic displacement vector components u, v and w are used. Theoretical formulations, based on the first-order shear deformation theory (FSDT), take into consideration transverse shear deformation and rotary inertia. The deformation theory of plasticity is employed for constitutive equations. The cylinders are composed of an elastic-plastic material with the von Mises yield criteria and non-linear plastic behaviour. Galerkin method is employed to convert the partial differential equations (PDEs) to ordinary differential equations (ODEs). The Newmark family of methods is used to numerically time integration of system of coupled second order ODEs. In order to prove the validity of the presented method and the solving process, the results obtained with the present analysis are compared with a set of available data. Good agreement observed between the results of the two approaches. Certainly, the aim of this paper is to create a more reliable and precise mathematical model of hollow-cylinders to avoid performing several experiments.

scholarly journals Plastic Buckling of Initially Imperfect Stiffened Cylinders in Axial Compression

1983 ◽  
Vol 50 (1) ◽  
pp. 88-94
Author(s):  
G. A. Duffett ◽  
B. D. Reddy
Keyword(s):  
Deformation Theory ◽  
Virtual Work ◽  
Compressive Load ◽  
Initial Imperfection ◽  
Complete Information ◽  
Equilibrium Path ◽  
Algebraic Equations ◽  
Buckling Mode ◽  
Nonlinear Algebraic Equations ◽  
Path Bifurcation

The behavior in the plastic range of axially compressed stringer-stiffened cylinders is investigated. The shell under consideration is assumed to have an initial imperfection in the form of sinusoidal deviation both axially and circumferentially. The constitutive relation employed here is J2 deformation theory of plasticity. This relation, as well as kinematic assumptions regarding the behavior of the panels and stiffeners that constitute the stiffened shell, is used in the principle of virtual work to obtain a set of nonlinear algebraic equations whose solution provides complete information about the prebuckling equilibrium path. Bifurcation from the primary path is examined by making use of a functional whose first variation is zero when two solutions to the problem are possible. This leads to an eigenvalue problem, the eigenvalue being the critical compressive load and the eigenfunction being the corresponding buckling mode. Results are presented for shells of different geometries and material properties, and a comparison of results is made with results obtained by others. The imperfect shells analyzed all exhibit stable behavior, with sufficiently large imperfections having a beneficial effect. Results for bifurcation from these paths are also discussed.

An Analysis of Wrinkling in the Swift Cup Test

1980 ◽  
Vol 102 (3) ◽  
pp. 241-248 ◽  
Author(s):  
N. Triantafyllidis ◽  
A. Needleman
Keyword(s):  
Deformation Theory ◽  
Annular Plate ◽  
Plastic Material ◽  
Beam Model ◽  
Linear Elastic ◽  
Theory Of Plasticity ◽  
Flange Wrinkling ◽  
Elastic Plastic Material ◽  
Elastic Spring ◽  
Flow Theory Of Plasticity

The onset of flange wrinkling in the Swift cup test is analyzed as a plastic bifurcation problem. The flange is modelled as an annular plate made of an orthotropic elastic-plastic material that is isotropic in the plane of the plate. The critical drawing stress and displacement obtained employing a deformation theory of plasticity and a flow theory of plasticity are compared. The effects of flange geometry and material properties on wrinkling are investigated. Employing a simple linear elastic spring model of the blankholder, the effect of blankholder stiffness on wrinkling is studied. The present results for the critical stress at the onset of wrinkling and for the number of wrinkles are compared with those obtained previously employing a beam model of the flange.

Spatial free plastic forming of slender parts—numerical approaches for strain-hardening material

2004 ◽  
Vol 218 (6) ◽  
pp. 641-650 ◽  
Author(s):  
M Thalmair ◽  
H Lippmann
Keyword(s):  
Strain Hardening ◽  
Metal Forming ◽  
Plastic Material ◽  
Forming Process ◽  
Hardening Material ◽  
Final Shape ◽  
Metal Forming Process ◽  
Plastic Forming ◽  
Elastic Plastic Material ◽  
Numerical Approaches

A new metal forming process is described in which a slender part may be brought to a prescribed final shape by means of an appropriate, pre-calculated motion of its free ends only. Corresponding calculation schemes are presented for elastic/plastic material with strain hardening, and these are illustrated by practical examples.

scholarly journals Frequency–Amplitude Relationship of a Nonlinear Symmetric Panel Absorber Mounted on a Flexible Wall

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1188
Author(s):  
Yiu-Yin Lee
Keyword(s):  
Elliptic Integral ◽  
Algebraic Equations ◽  
Cavity Depth ◽  
Nonlinear Algebraic Equations ◽  
Flexible Panel ◽  
Flexible Wall ◽  
Elliptic Integral Method ◽  
Flexible Panels ◽  
Relationship Of ◽  
Panel Absorber

This study addresses the frequency–amplitude relationship of a nonlinear symmetric panel absorber mounted on a flexible wall. In many structural–acoustic works, only one flexible panel is considered in their models with symmetric configuration. There are very limited research investigations that focus on two flexible panels coupled with a cavity, particularly for nonlinear structural–acoustic problems. In practice, panel absorbers with symmetric configurations are common and usually mounted on a flexible wall. Thus, it should not be assumed that the wall is rigid. This study is the first work employing the weighted residual elliptic integral method for solving this problem, which involves the nonlinear multi-mode governing equations of two flexible panels coupled with a cavity. The reason for adopting the proposed solution method is that fewer nonlinear algebraic equations are generated. The results obtained from the proposed method and finite element method agree reasonably well with each other. The effects of some parameters such as vibration amplitude, cavity depth and thickness ratio, etc. are also investigated.

scholarly journals A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
E. H. Doha ◽  
D. Baleanu ◽  
A. H. Bhrawy ◽  
R. M. Hafez
Keyword(s):  
Numerical Solutions ◽  
Rational Functions ◽  
Absolute Error ◽  
Delay Systems ◽  
Infinite Interval ◽  
Algebraic Equations ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Linear And Nonlinear ◽  
Pseudospectral Scheme

A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small.

scholarly journals Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams

2005 ◽  
Vol 12 (6) ◽  
pp. 425-434 ◽  
Author(s):  
Menglin Lou ◽  
Qiuhua Duan ◽  
Genda Chen
Keyword(s):  
Perturbation Method ◽  
Dynamic Characteristics ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Solution Process ◽  
Equation Of Motion ◽  
Timoshenko Beams ◽  
Algebraic Equations ◽  
Nonlinear Algebraic Equations ◽  
Shear Distortion

Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are discussed in detail.

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