Summary
Singular fields and higher order fields near a sharp notch in a power-law material under longitudinal shear are investigated. Using the perturbation method the whole set of eigenvalues is determined. The higher order eigensolutions are constructed by use of the dominant singular solution. Some examples, including the special case of a crack are discussed for different boundary conditions.
Übersicht
Untersucht werden singuläre Felder und Felder höherer, Ordnung an Spitzkerben unter nichtebener Schubbelastung in Materialien mit Potenzgesetz. Die Eigenwerte werden mittels der Störungsrechnung ermittelt. Die Bestimmung der Eigenlösungen höherer Ordnung erfolgt unter Verwendung der dominierenden singulären Lösung. Einige Beispiele, die auch den Spezialfall des Risses einschließen, werden für unterschiedliche Randbedingungen diskutiert.
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References
Hutchinson, J. W.: Singular behaviour at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids 16 (1968) 13–31
Hutchinson, J. W.: Plastic stress and strain fields at a crack tip. J. Mech. Phys. Solids 16 (1968) 337–347
Rice, J. R.;Rosengren, G. F.: Plane strain deformation near a crack tip in a power-law hardening material. J. Mech. Phys. Solids 16 (1968) 1–12
Neuber, H.: Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law. Trans. ASME/E: J. Appl. Mech. 28 (1961) 544–550
Rice, J. R.: Contained plastic deformation near cracks and notches under longitudinals shear. Int. J. Fract. Mech. 2 (1966) 426–447
Rice, J. R.: Stresses due to a sharp notch in a work-hardening, elastic-plastic material loaded by longitudinal shear. Trans. ASME/E: J. Appl. Mech. 34 (1967) 287–298
Amazigo, J. C.: Fully plastic crack in an infinite body under anti-plane shear. Int. J. Solids. Struct. 10 (1974) 1003–1015
Atkinson, C.;Champion, C. R.: Some boundary-value problems for the equation\(\nabla .\left( {\left| {\nabla \phi } \right|^N \nabla \phi } \right) = 0.Q.J.\) Mech. Appl. Math. 37 (1984) 401–419
Durban, D.;Ore, E.: Interface stress singularities at a notch tip in antiplane shear. Trans. ASME/E: J. Appl. Mech. 54 (1987) 470–472
Ore, E.;Durban, D.: Boundary effects at a notch tip in anti-plane shear. Int. J. of Fract. 38 (1988) 15–24
Gross, D.;Yu, S.-W.: The singular field near a sharp notch with mixed boundary conditions for hardening materials under longitudinal shear. Theor. Appl. Fract. Mech. 8 (1987) 199–203
Yu, S.-W.;Gross, D.: The singular field at a rigid flat inclusion in hardening materials under longitudinal shear. Eng. Fract. Mech. 31 (1988) 611–615
Yang, S.;Chao, Y. J.: The singular field at the tip of a wedge-like rigid inclusion in a hardening material under longitudinal shear. Eng. Fract. Mech. 37 (1990) 251–257
Dobrowolski, M.: Nonlinear corner problems and finite element method. ZAMM 64 (1984), T270-T271 (in German)
Dobrowolski, M.: On quasilinear elliptic equations in domains with conical boundary points. J. Reine Angew. Math. 394 (1989) 186–195
Hayashi, K.: Singular stress field at the end of a ribbon-like inclusion in a hardening material under longitudinal shear. Int. J. of Fract. 24 (1984) R121-R125
Anheuser, M.: Singularitäten an den Spitzen von Rissen, Einschlüssen und Kerben in nichtlinearen Materialien. Thesis. Darmstadt: Technical University Darmstadt 1992
Anheuser, M.;Gross, D.: Spannungsfelder an Kerben bei nichtlinearem Materialverhalten. ZAMM 73 (1993) T410-T413
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Dedicated to Prof. Dr.-Ing. F. G. Kollmann on the occasion of his sixtieth Birthday
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Anheuser, M., Gross, D. Higher order fields at crack and notch tips in power-law materials under longitudinal shear. Arch. Appl. Mech. 64, 509–518 (1994). https://doi.org/10.1007/BF00788883
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DOI: https://doi.org/10.1007/BF00788883