Contact Transform for the Biharmonic Equation Applicable to Plane Stress Elastoplastic Elliptical Hole Problems

An analytical technique is developed that reduces the unknown elastic-plastic boundary of a linear elastic-perfectly plastic material containing an elliptical hole under tensile plane stress loading conditions into an equivalent mathematical problem with known boundaries. This mathematical transform...

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Veröffentlicht in:Journal of elasticity Jg. 117; H. 2; S. 139 - 161
1. Verfasser: Unger, David J.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Netherlands 01.12.2014
Springer Nature B.V
Schlagworte:
Automotive Engineering
Boundaries
Classical Mechanics
Contact
Equivalence
Mathematical analysis
Mathematical models
Perturbation methods
Physics
Physics and Astronomy
Plane stress
Transformations (mathematics)
Tresca yield condition
74C05
74A45
Perfectly plastic
Mode I crack
37J55
Linear elastic
ISSN:0374-3535, 1573-2681
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Abstract An analytical technique is developed that reduces the unknown elastic-plastic boundary of a linear elastic-perfectly plastic material containing an elliptical hole under tensile plane stress loading conditions into an equivalent mathematical problem with known boundaries. This mathematical transformation may facilitate this problem’s solution by either analytical or numerical means. Yield is assumed to occur in this analysis under the Tresca yield criterion. An example elastic-plastic problem illustrating this method is drawn from existing literature in the form of a perturbation solution for an elliptical hole derived by a series expansion about a circular boundary.
AbstractList An analytical technique is developed that reduces the unknown elastic-plastic boundary of a linear elastic-perfectly plastic material containing an elliptical hole under tensile plane stress loading conditions into an equivalent mathematical problem with known boundaries. This mathematical transformation may facilitate this problem’s solution by either analytical or numerical means. Yield is assumed to occur in this analysis under the Tresca yield criterion. An example elastic-plastic problem illustrating this method is drawn from existing literature in the form of a perturbation solution for an elliptical hole derived by a series expansion about a circular boundary.
An analytical technique is developed that reduces the unknown elastic-plastic boundary of a linear elastic-perfectly plastic material containing an elliptical hole under tensile plane stress loading conditions into an equivalent mathematical problem with known boundaries. This mathematical transformation may facilitate this problem's solution by either analytical or numerical means. Yield is assumed to occur in this analysis under the Tresca yield criterion. An example elastic-plastic problem illustrating this method is drawn from existing literature in the form of a perturbation solution for an elliptical hole derived by a series expansion about a circular boundary.[PUBLICATION ABSTRACT]
Author Unger, David J.
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CitedBy_id crossref_primary_10_1016_j_compgeo_2021_104589
Cites_doi 10.1007/s10659-009-9235-z
10.1007/BF00183821
10.1007/s10659-008-9159-z
10.1098/rsta.1921.0006
10.1016/j.tafmec.2005.05.007
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Keywords Tresca yield condition
74C05
74A45
Perfectly plastic
Mode I crack
37J55
Linear elastic
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J.R. Rice (9468_CR13) 1968
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References_xml – reference: GriffithA.A.The phenomena of rupture and flow in solidsTrans. R. Soc. Lond. A192022116319810.1098/rsta.1921.00061921RSPTA.221..163G
– reference: UngerD.J.Analytical Fracture Mechanics2011MineolaDover
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– reference: UngerD.J.Path independent integral for an elliptical hole in a plate under tension for plane stress deformation theoryJ. Elast.200892217226242568210.1007/s10659-008-9159-z1163.74008
– reference: CourantR.HilbertD.Methods of Mathematical Physics1962New YorkWiley0099.29504
– reference: LiebersteinH.M.Theory of Partial Differential Equations1972New YorkAcademic Press12170245.35001
– reference: IvlevD.D.ErshovL.V.Perturbation Method in the Theory of an Elastic-Plastic Body1978Moscow“Nauka,” Glav. red. fiziko-matematicheskoi lit-ry160170(in Russian)
– reference: RiceJ.R.Contained plastic deformation near cracks and notches under longitudinal shearInt. J. Fract. Mech.19662426447
– reference: SokolovskiiV.V.Theory of Plasticity19693MoscowVyssh. shkola391392(in Russian)
– reference: CherepanovG.P.Mechanics of Brittle Fracture1979New YorkMcGraw-Hill0442.73100
– reference: UngerD.J.Large plastic deformations accompanying the growth of an elliptical hole in a thin plateJ. Elast.201099117130260208610.1007/s10659-009-9235-z05730978
– reference: De BruijnN.G.Asymptotic Methods in Analysis1981New YorkDover10110556.41021
– reference: InglisC.E.Stresses in a plate due to the presence of cracks and sharp cornersTrans. Inst. Nav. Archit.191355219241
– reference: LawrenceJ.D.A Catalog of Special Plane Curves1972MineolaDover42430257.50002
– reference: RiceJ.R.LiebowitzH.Mathematical analysis in the mechanics of fractureFracture: An Advanced Treatise1968New YorkAcademic Press191311
– reference: KachanovL.M.Fundamentals of the Theory of Plasticity2004MineolaDover
– reference: MalvernL.E.Introduction to the Mechanics of a Continuous Medium1969Englewood CliftPrentice-Hall
– reference: UngerD.J.Perfectly plastic caustics for the opening mode of fractureTheor. Appl. Fract. Mech.200544829410.1016/j.tafmec.2005.05.007
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  volume-title: Fracture: An Advanced Treatise
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  volume-title: Theory of Partial Differential Equations
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Snippet An analytical technique is developed that reduces the unknown elastic-plastic boundary of a linear elastic-perfectly plastic material containing an elliptical...
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SubjectTerms Automotive Engineering
Boundaries
Classical Mechanics
Contact
Equivalence
Mathematical analysis
Mathematical models
Perturbation methods
Physics
Physics and Astronomy
Plane stress
Transformations (mathematics)
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Title Contact Transform for the Biharmonic Equation Applicable to Plane Stress Elastoplastic Elliptical Hole Problems
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Volume 117
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