Summary
In this paper, the strain energy function given by Knowles-Sternberg in 1973 is used, and the contact problem of a rubber notch with a rigid wedge is analyzed. The basic equations of the deformation field near the notch corner are derived and solved. An analytical solution is obtained for the expanding sector while the numerical solution is given for two shrinking sectors. A special interesting case is that a half rubber-like plane contacts with a rigid wedge, for which the completely analytical solutions are obtained for both expanding sector and shrinking sectors. The analysis of this paper is also valid for the contact problem of a rubber wedge with a rigid wedge. To verify the analytical results, a finite element program of nonlinear elasticity is made with which the same problem is calculated, and the results are consistent with the analytical results very well.
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References
Knowles, J., Sternberg, E.: An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack. J. Elasticity3, 67–107 (1973).
Knowles, J., Sternberg, E.: Finite-deformation analysis of the elastostatic field near the tip of a crack: reconsideration and higher-order results. J. Elasticity4, 201–233 (1974).
Knowles, J., Sternberg, E.: Large deformation near a tip of an interface-crack between two Neo-Hookean sheets. J. Elasticity13, 257–293 (1983).
Gao, Y. C.: Elastostatic crack tip behavior for a rubber-like material. Theor. Appl. Fract. Mech.14, 219–231 (1990).
Gao, Y. C.: Large deformation field near a crack tip in a rubber-like material. Theor. Appl. Fract. Mech.26, 155–162 (1997).
Wong, F. S., Shield, R. T.: Large plane deformation of thin elastic sheets of Neo-Hookean material. Z. angew. Math. Phys.20, 176–199 (1969).
Ravichandran, G., Knauss, W. G.: A finite elastostatic analysis of bimaterial interface cracks. Int. J. Fract.39, 235–253 (1989).
Quigley, C. J., Parks, D. M.: The finite deformation field surrounding a mode I plane strain crack in a hyperelastic incompressible material under small-scale nonlinearity. Int. J. Fract.65, 75–96 (1994).
Pidaparti, R. M. V., Yang, T. Y., Soedel, W.: A plane stress finite element method for the prediction of a rubber fracture. Int. J. Fract.39, 255–268 (1989).
Pidaparti, R. M. V., Pontula, G.: Three-dimensional analysis of interface cracks in rubber materials. Int. J. Fract.68, 315–332 (1995).
Hermann, J. M.: An asymptotic analysis of finite deformation near the tip of an interface-crack. J. Elasticity21, 227–269 (1989).
Herrmann, J. M.: An asymptotic analysis of finite deformation near the tip of an interface-crack: part. II. J. Elasticity29, 203–241 (1992).
Ru, C. Q.: Finite strain singular field near the tip of a crack terminating at a material interface. Math. Mech. Solids2, 49–73 (1997).
Le, K. C., Stumpf, H.: The singular elastostatic field due to a crack in rubber-like materials. J. Elasticity32, 183–222 (1993).
Lund, R. A., Westmann, R. A.: Finite element analysis of hyperelastic large deformation crack tip fields. Int. J. Fract.43, 257–270 (1990).
Gao, T. S., Gao, Y. C.: A rubber wedge under the tension of a line load. C. R. Acad. Sci. Paris, t.318, 1–6 (1994).
Gao, Y. C., Liu, B.: A rubber cone under the tension of a concentrated force. Int. J. Solids Struct.32, 1485–1493 (1995).
Chen, S. H., Zhou, Z., Gao, Y. C.: Large strain analysis and FE calculation of a rubber wedge tensioned by a line load. Acta Mech. Sinica32, 117–125 (2000) (in Chinese).
Gao, Y. C.: Large strain analysis of a rubber wedge compressed by a line load at its tip. Int. J. Engng. Sci.36, 831–842 (1998).
Duva, J. M.: The singularity at the apex of a rigid wedge embedded in a nonlinear material. ASME J. Appl. Mech.55, 361–364 (1988).
Duva, J. M.: The singularity at the apex of a rigid wedge after partial seperation. ASME J. Appl. Mech.56, 977–979 (1989).
Fleck, N. A., Durban, D.: Steady penetration of a rigid cone with a rough wall into a powerlaw viscous solid. ASME J. Appl. Mech.58, 872–880 (1991).
Durban, D., Rand, O.: Singular fields in plane-strain penetration. ASME J. Appl. Mech.58, 910–915 (1991).
Hertz, H.: Journal für Mathematik (Crelle)92, 156 (1881).
Gao, Y. C.: Large deformation contact of a rubber notch with a rigid wedge. Int. J. Solids Struct. (forthcoming).
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Chen, S.H., Gao, Y.C. Asymptotic analysis and finite element calculation of a rubber notch contacting with a rigid wedge. Acta Mechanica 147, 111–124 (2001). https://doi.org/10.1007/BF01182356
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DOI: https://doi.org/10.1007/BF01182356