The Safety Factor of an Elastic-Plastic Body in Plane Strain

1951 ◽  
Vol 18 (4) ◽  
pp. 371-378 ◽  
Author(s):  
D. C. Drucker ◽  
H. J. Greenberg ◽  
W. Prager
Keyword(s):  
Plane Strain ◽  
Safety Factor ◽  
The Other ◽  
Plastic Body ◽  
Elastic Plastic

Abstract Extremum principles are established for the safety factor of an elastic-plastic body made of a Prandtl-Reuss material and subjected to given surface tractions under conditions of plane strain. Since one of these principles establishes a maximum and the other a minimum property of the safety factor, it is possible to establish bounds for the safety factor by the joint use of these principles.

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

Electrical interactions between the giant axons of a polychaete worm (Sabella penicillus L.)

1980 ◽  
Vol 84 (1) ◽  
pp. 119-136
Author(s):  
D. Mellon ◽  
J. E. Treherne ◽  
N. J. Lane ◽  
J. B. Harrison ◽  
C. K. Langley
Keyword(s):  
Safety Factor ◽  
Nerve Cord ◽  
Action Potentials ◽  
Divalent Cations ◽  
Muscular Contraction ◽  
The Body ◽  
The Other ◽  
Intracellular Recordings ◽  
Giant Axons ◽  
Other Hand

Intracellular recordings demonstrated a transfer of impulses between the paired giant axons of Sabella, apparently along narrow axonal processes contained within the paired commissures which link the nerve cords in each segment of the body. This transfer appears not to be achieved by chemical transmission, as has been previously supposed. This is indicated by the spread of depolarizing and hyperpolarizing voltage changes between the giant axons, the lack of effects of changes in the concentrations of external divalent cations on impulse transmission and by the effects of hyperpolarization in reducing the amplitude of the depolarizing potential which precedes the action potentials in the follower axon. The ten-to-one attenuation of electronic potentials between the giant axons argues against the possibility of an exclusively passive spread of potential along the axonal processes which link the axons. Observation of impulse traffic within the nerve cord commissures indicates, on the other hand, that transmission is achieved by conduction of action potentials along the axonal processes which link the giant axons. At least four pairs of intact commissures are necessary for inter-axonal transmission, the overall density of current injected at multiple sites on the follower axon being, it is presumed, sufficient to overcome the reduction in safety factor imposed by the geometry of the system in the region where axonal processes join the giant axons. The segmental transmission between the giant axons ensures effective synchronization of impulse traffic initiated in any region of the body and, thus, co-ordination of muscular contraction, during rapid withdrawal responses of the worm.

Ductile Crack Propagation Simulation of a Cylinder With a Through-Wall Circumferential Flaw Under Excessive Cyclic Torsion Loading

2014 ◽  
Author(s):  
Kiminobu Hojo ◽  
Daigo Watanabe ◽  
Shinichi Kawabata ◽  
Yasufumi Ametani
Keyword(s):  
Cyclic Loading ◽  
Crack Growth ◽  
Rotation Angle ◽  
Fe Analysis ◽  
The Other ◽  
J Integral ◽  
Ductile Crack ◽  
Elastic Plastic ◽  
Cyclic Torsion ◽  
Ductile Crack Growth

A lot of applications of elastic plastic FE analysis to flawed structural fracture behaviors of mode I have been investigated. On the other hand the analysis method has not been established for the case of the excessive cyclic torsion loading with mode II or III fracture. The authors tried simulating the fracture behavior of a cylinder-shaped specimen with a through-walled circumferential flaw subjected to excessive monotonic or cyclic loading by using elastic plastic FE analysis. Chaboche constitutive equation of the used FE code Abaqus was applied to estimate the elastic plastic cyclic behavior. As a result in the case of monotonic loading without crack extension, the relation of torque-rotation angle of the experiment was estimated well by the simulation. Also J-integral by the Abaqus’ function agreed with a simplified J-equation using the calculated torque-rotation angle relation. On the other hand under load controlled cyclic loading associated with ductile crack growth, the calculated torque-rotation angle relation did not agree with the experimental one because of high sensitivity of the used stress-strain curve. J-integral from Abaqus code did not increase regardless of the accumulated crack growth and plastic zone. Several simplified ΔJ calculations tried to explain the experimental ductile crack growth and it seemed that da/dN-ΔJ relation follows the Paris’ law. From these examinations an estimation procedure of the structures under excessive cyclic loading was proposed.

A Compressible Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (2) ◽  
pp. 239-242
Author(s):  
D. R. Bland ◽  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
The State ◽  
Hardening Material ◽  
Included Angle ◽  
Elastic Plastic ◽  
Numerical Example ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract This paper is concerned with a compressible elastic-plastic wedge of an included angle β < π/2 in the state of plane strain. The solution, deduced for an isotropic nonwork-hardening material, employs Tresca’s yield criterion and the associated flow rules. By means of a numerical example the solution is compared with that of an incompressible elastic-plastic wedge in one case (β = π/4) for various positions of the elastic-plastic boundary.

Stresses and Displacements in an Elastic-Plastic Wedge

1957 ◽  
Vol 24 (1) ◽  
pp. 98-104
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Isotropic Material ◽  
Complete Solution ◽  
Normal Pressure ◽  
Stress Strain ◽  
Included Angle ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic

Abstract An elastic, perfectly plastic wedge of an incompressible isotropic material in the state of plane strain is considered, where the stress-strain relations of Prandtl-Reuss are employed in the plastic domain. For a wedge (with an included angle β) subjected to a uniform normal pressure on one boundary, the complete solution is obtained which is valid in the range 0 < β < π/2; this latter limitation is due to the character of the initial yield which depends on the magnitude of β. Numerical results for stresses and displacements are given in one case (β = π/4) for various positions of the elastic-plastic boundary.

Sign in / Sign up

Export Citation Format

Share Document