×

zbMATH — the first resource for mathematics

Mathematical analysis of a bonded joint with a soft thin adhesive. (English) Zbl 1001.74591
Summary: This paper considers the problem of two adherents joined by a soft thin adhesive along their common surface. Using the asymptotic expansion method, the authors obtain a simplified model in which the adhesive is treated as a material surface and is replaced by returning springs. The authors show weak and strong convergence of the exact solution toward the solution of the limit problem. The singularities of the limit problem are analyzed, and it is shown that typically they are logarithmic. Furthermore, the authors investigate the phenomenon of boundary layer by studying the correctors, the extra terms, which must be added to the classical asymptotic expansion to verify the boundary conditions. The correctors show that, contrary to the adherents, in the adhesive there are power-type singularities, which are at the base of the failure of the assemblage.

MSC:
74K30 Junctions
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Goland, M., J. Appl. Mech., ASME 11 (1944)
[2] Adams, R. D., Structural Adhesive Joints in Engineering (1997)
[3] Klarbring, A., Int. J. Eng. Sci. 29 pp 493– (1991) · Zbl 0762.73069
[4] Destuynder, P., Int. J. Num. Methods Eng. 35 pp 1237– (1992) · Zbl 0775.73229
[5] Edlund, U., Comput. Meth. Appl. Mech. Eng. 78 pp 19– (1990) · Zbl 0729.73214
[6] Geymonat, G., Math. Models Methods Appl. Sci. 8 pp 1387– (1998) · Zbl 0940.74060
[7] Suquet, P., Non-Smooth Mechanics and Applications pp 280– (1988)
[8] Ganghoffer, J. E., Eur J. Mech., A/Solids 16 pp 255– (1997)
[9] Geymonat, G., Partial Differential Equations and Applications (1996)
[10] Licht, C., C. R. Acad. Sci. Paris, I 322 pp 295– (1996)
[11] Brezis, H., Ann. Mat. Pur Appl. 4 (123) pp 219– (1980) · Zbl 0434.35079
[12] Acerbi, E., Ann. Inst. Poincarg, Analyse non lingare 3 pp 273– (1986) · Zbl 0607.73018
[13] Acerbi, E., Arch. Rat. Mech. Anal. 92 pp 355– (1986) · Zbl 0624.73021
[14] Lene, F., Int. J. Solids Struct. 18 pp 443– (1982) · Zbl 0488.73065
[15] Lions, J. L., Lecture Notes in Mathematics (1973)
[16] Ciarlet, P G., Plates and Junctions in Elastic Multi-Structures. An Asymptotic Analysis (1990) · Zbl 0706.73046
[17] Ciarlet, P G., Three-Dimensional Elasticity (1988) · Zbl 0648.73014
[18] Grisvard, P., Elliptic Problems in Nonsmooth Domains (1985) · Zbl 0695.35060
[19] Lebon, F., Proceedings of the 8th Congres National Mecama4
[20] Caillerie, D., Math. Meth. Appl. Sci. 2 pp 251– (1980) · Zbl 0446.73014
[21] Lemrabet, K., C. R. Acad. Sci. Paris, I 304 pp 151– (1987)
[22] Leguillon, D., Computation of Singular Solutions in Elliptic Problems and Elasticity, (1987) · Zbl 0647.73010
[23] Grisvard, PR: Singularities in Boundary Wilue Problems (1992)
[24] Grisvard, P., Arch. Rat. Mech. Anal. 107 pp 157– (1989) · Zbl 0706.73013
[25] Nazarov, S. A., Elliptic Problems in Domains with Piecewise Smooth Boundaries (1994) · Zbl 0806.35001
[26] Williams, M. L., J. App. Mech., ASME 19 pp 526– (1952)
[27] Bui, H. D., C. R. Acad. Sci. Paris, II 309 pp 1527– (1989)
[28] Deperrois, A., C. R. Acad. Sci. Paris, II 311 pp 1285– (1990)
[29] Destuynder, P., C. R. Acad. Sci. Paris, I 310 pp 161– (1990)
[30] Timoshenko, S., Theory of Elasticity (1951) · Zbl 0045.26402
[31] Bogy, D. B., J. App. Mech., ASME 38 pp 377– (1971)
[32] Rice, J. R., J. AppL. Mech., ASME 33 pp 418– (1965)
[33] Rice, J. R., J. Appl. Mech., ASME 55 pp 98– (1988)
[34] Adams, R. D., Int. J. Adhesion Adhesives 7 pp 69– (1987)
[35] Hutchinson, J. W., J. Appl. Mech., ASME 54 pp 828– (1987)
[36] Yang, M., Eng. Fract. Mech. 44 pp 155– (1993)
[37] Leguillon, D., C. R. Acad. Sci. Paris, II 319 pp 161– (1994)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.