Nonuniqueness in Contained Plastic Deformation

1980 ◽  
Vol 47 (2) ◽  
pp. 273-277 ◽  
Author(s):  
P. G. Hodge ◽  
D. L. White
Keyword(s):  
Plastic Deformation ◽  
Boundary Value Problem ◽  
Yield Point ◽  
Displacement Field ◽  
Point Load ◽  
Point Of View ◽  
Computational Point ◽  
Plastic Structure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

It is well known that in a well-defined load-controlled boundary-value problem for an elastic/perfectly-plastic structure the displacements are unique if the structure is everywhere elastic, and they are not unique at the yield-point load when the structure becomes a mechanism. The present paper is concerned with the range of contained plastic deformation between these two extremes. Several examples are given in which more than one displacement field exists for loads less than the yield-point load. The significance of this phenomenon is commented on from a physical, mathematical, and computational point of view.

Crushing of an Elastic-Perfectly Plastic Ring or Tube Between Two Planes

1987 ◽  
Vol 54 (1) ◽  
pp. 159-164 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Plastic Deformation ◽  
Numerical Integration ◽  
Mathematical Problem ◽  
Plastic Ring ◽  
Perfectly Plastic ◽  
Analytical Approximations ◽  
Original Shape ◽  
Thin Ring ◽  
Elastic Perfectly Plastic

A thin ring is crushed between two rigid planes. Due to plastic deformation the ring does not recover its original shape when the compression is removed. For an elastic-perfectly plastic flexural material, the ring undergoes two to five different stages. The mathematical problem is formulated and solved by exact numerical integration and accurate analytical approximations.

The Elastic-Softening Failure of Floating Beams

1988 ◽  
Vol 32 (01) ◽  
pp. 37-43
Author(s):  
Paul C. Xirouchakis
Keyword(s):  
Carrying Capacity ◽  
Maximum Load ◽  
Point Load ◽  
Negative Stiffness ◽  
Load Carrying Capacity ◽  
Perfectly Plastic ◽  
Load Carrying ◽  
Elastic Perfectly Plastic ◽  
The Moment ◽  
Elastic Softening

The solution is presented for an infinite elastic-softening floating beam under a point load. The response depends on two nondimensional parameters: the negative stiffness coefficient that characterizes the descending part of the moment-curvature curve, and the nondimensional softening region half-length. The solution exhibits two important features that the elastic-perfectly plastic solution does not show. First, in certain ranges of parameters, the elastic-softening beam has a clearly defined maximum load carrying capacity. Second, in some other ranges of parameters, the elastic-softening beam has a minimum load or residual strength. The beam stiffens up upon further deformation due to the reactions of the water foundation. Critical softening parameters are calculated that separate stable from unstable behavior.

Numerical Investigation of the Plastic Contact Deformation between Hemispheres: Variation of Radii Ratio and Normal Loads

2015 ◽  
Vol 1123 ◽  
pp. 16-19
Author(s):  
Rifky Ismail ◽  
T. Prasojo ◽  
Mohammad Tauviqirrahman ◽  
J. Jamari ◽  
D.J. Schipper
Keyword(s):  
Plastic Deformation ◽  
Normal Load ◽  
Asperity Contact ◽  
Frictionless Contact ◽  
Finite Element Software ◽  
Total Displacement ◽  
Perfectly Plastic ◽  
Deformation Ratio ◽  
Elastic Perfectly Plastic ◽  
Local Plastic Deformation

Investigation of local plastic deformation between rough surfaces in mechanical components such as gears, camshaft and bearings is very important. Contact between real surfaces occurs at the summits of the highest asperities which vary in height and radius. The plastic deformation of the contact between two asperities was studied in this paper. Asperity contact was modelled as a contact between hemispheres. The commercial finite element software, ABAQUS, was employed to perform the numerical contact analysis of the elastic perfectly-plastic deforming hemispheres with the ratios of radii (R2/R1) from 1 to 7. Normal loads of 5000 N, 8000 N and 11000 N were applied to the frictionless contact of the hemispheres. It was shown that the plastic deformation ratio (ωp1/ωp2) decreases as the radii ratio increases. The higher normal load showed a lower plastic deformation ratio for high radii ratio. The results indicate that the radii ratio contributes to the severity of the plastic deformation and the total displacement of the contacting asperities.

An Upper Bound on the Small Displacements of Elastic, Perfectly Plastic Structures

1972 ◽  
Vol 39 (4) ◽  
pp. 959-963 ◽  
Author(s):  
A. R. S. Ponter
Keyword(s):  
Upper Bound ◽  
Limit State ◽  
Upper Bounds ◽  
Variable Loading ◽  
Plastic Structure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Additional Calculation

An inequality is described which allows the evaluation of upper bounds to the displacement of an elastic/perfectly plastic structure subject to variable loading. Simple examples indicate that although the bound may not be very accurate, it may well provide a useful additional calculation to the limit state and shakedown solutions.

scholarly journals Use of shakedown maps to assess plastic flow in railway curves

2019 ◽  
Vol 234 (4) ◽  
pp. 417-425
Author(s):  
SJ Hawksbee ◽  
GJ Tucker ◽  
M Burstow
Keyword(s):  
Finite Element Analysis ◽  
Plastic Deformation ◽  
Finite Element ◽  
Plastic Flow ◽  
Material Model ◽  
Element Analysis ◽  
Contact Conditions ◽  
Effective Measure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Plastic deformation of rails can occur on tight curves, which can significantly reduce the rail life. This paper investigated the phenomena of gross plastic deformation, or plastic flow, using multibody vehicle–track interaction and simplified finite element analysis. The focus is on understanding the contact conditions on the low rail of curves and how these differ from those in shakedown maps. To this end, two trial sites are simulated using multibody vehicle–track software. The contact conditions are then compared against several criteria assumed in the derivation of the shakedown maps. A further assumption implicit in the shakedown maps is also investigated by a non-linear finite element analysis. In this case, a more realistic Chaboche material model is used as opposed to the simple linear elastic–perfectly plastic model in the shakedown theory. The results of the finite element analysis are combined with a bespoke indicator of plastic flow to assess the influence of distance to shakedown limits on the likely plastic flow. Finally, a simple interpolation scheme is used to map the finite element results back to the trial sites. The interpolated results for the sites are used to evaluate the influence of running speed and different levels of wheel profile wear. Results suggest that the bespoke indicator defined in this work can be used as an effective measure of plastic flow; this measure is then used to quantify the influence of cant excess on the rates of plastic flow.

Causes and Consequences of Nonuniqueness in an Elastic/Perfectly-Plastic Truss

1986 ◽  
Vol 53 (2) ◽  
pp. 235-241 ◽  
Author(s):  
P. G. Hodge ◽  
K.-J. Bathe ◽  
E. N. Dvorkin
Keyword(s):  
Plastic Deformation ◽  
Plastic Material ◽  
Complete Solution ◽  
Physical Modelling ◽  
Equilibrium Equations ◽  
First Order ◽  
Perfectly Plastic ◽  
Points Of View ◽  
Elastic Perfectly Plastic

A complete solution to collapse is given for a three-bar symmetric truss made of an elastic/perfectly-plastic material, using linear statics and kinematics, and the solution is found to be partially nonunique in the range of contained plastic deformation. The introduction of a first-order deviation from symmetry and/or the inclusion of first-order nonlinear terms in the equilibrium equations is found to restore uniqueness. The significance of these effects is analyzed and discussed from mathematical, physical, modelling, computational, and engineering points of view.

Mechanical and Thermodynamic Considerations of an Assemblage of Homogeneous Elastic-Plastic States

1968 ◽  
Vol 35 (3) ◽  
pp. 596-603 ◽  
Author(s):  
David Rubin
Keyword(s):  
Plastic Deformation ◽  
Mechanical Behavior ◽  
Strain Energy ◽  
Material Behavior ◽  
Free State ◽  
Elastic Plastic ◽  
Elastic Range ◽  
Perfectly Plastic ◽  
Stress Free State ◽  
Elastic Perfectly Plastic

The mechanics and the thermodynamics of plastic deformation are considered in terms of a general assemblage or continuum of elastic, perfectly plastic elements or states. Such models not only match the external mechanical behavior of real materials structures and continua, but they also afford a simple thermodynamic definability. A consideration of the internal behavior shows that the stress-free state has the maximum elastic range. Hardening in the sense of an increasing macroscopic elastic range is accompanied by a release of stored strain energy; the stress-free state always is restorable. This behavior is appropriate for real structures and continua. However, it is precisely these continuum characteristics which make the assemblages inappropriate models of material behavior. Barriers to continuing plastic deformation are required which do exist on the microscale, but lie outside of the scope of the most complex of these thermodynamically well-defined assemblages.

scholarly journals Theoretical extension of elastic-perfectly plastic deformation length in roll forming of a channel section

2013 ◽  
Vol 47 (1/2/3/4) ◽  
pp. 33
Author(s):  
Roohollah Azizi Tafti ◽  
Hassan Moslemi Naeini ◽  
Mehdi Salmani Tehrani ◽  
Bernard F. Rolfe ◽  
Matthias Weiss
Keyword(s):  
Plastic Deformation ◽  
Roll Forming ◽  
Channel Section ◽  
Perfectly Plastic ◽  
Deformation Length ◽  
Elastic Perfectly Plastic

scholarly journals Plasticity Detection and Quantification in Monopile Support Structures Due to Axial Impact Loading

2018 ◽  
Vol 148 ◽  
pp. 15003 ◽  
Author(s):  
P.C. Meijers ◽  
A. Tsouvalas ◽  
A.V. Metrikine
Keyword(s):  
Plastic Deformation ◽  
Impact Load ◽  
Offshore Wind ◽  
Pile Head ◽  
Offshore Wind Turbines ◽  
Perfectly Plastic ◽  
Rod Model ◽  
Recent Developments ◽  
Elastic Perfectly Plastic ◽  
Detection And Quantification

Recent developments in the construction of offshore wind turbines have created the need for a method to detect whether a monopile foundation is plastically deformed during the installation procedure. Since measurements at the pile head are difficult to perform, a method based on measurements at a certain distance below the pile head is proposed in this work for quantification of the amount of plasticity. By considering a onedimensional rod model with an elastic-perfectly plastic constitutive relation, it is shown that the occurrence of plastic deformation caused by an impact load can be detected from these measurements. Furthermore, this plastic deformation can be quantified by the same measurement with the help of an energy balance. The effectiveness of the proposed method is demonstrated via a numerical example.

General Properties of Yield-Point Load Surfaces

1968 ◽  
Vol 35 (1) ◽  
pp. 107-110 ◽  
Author(s):  
P. G. Hodge ◽  
Chang-Kuei Sun
Keyword(s):  
Strain Rate ◽  
Yield Point ◽  
Yield Surface ◽  
Plastic Material ◽  
Point Load ◽  
Perfectly Plastic ◽  
Plastic Mechanism ◽  
Rate Vector ◽  
Strain Rate Vector ◽  
Interaction Surface

A structure made of a rigid perfectly plastic material and subjected to more than one independent load is considered. A mode vector is defined for any plastic mechanism and shown to have the same properties relative to the yield-point load interaction surface that the strain-rate vector has to the material yield surface. An application to a circular plate under two independent loads leads to close bounds on the interaction curve.

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