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A rate-independent approach to the delamination problem. (English) Zbl 1133.74038

Summary: We study delamination processes for elastic bodies glued together by an adhesive as an activated rate-independent process. The adhesive is assumed to absorb a specific amount of energy during the delamination process. A solution is defined by energetic principles of stability and balance of stored and dissipated energies with the work of external loading, realized here through displacement on parts of the boundary. Starting from a time discretization, we construct solutions via a rigorous limiting analysis. Moreover, we provide computer simulations for some model problems using a further finite element spatial discretization.

MSC:

74R20 Anelastic fracture and damage
74G65 Energy minimization in equilibrium problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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[1] Alfano, G., International Journal of Numerical Methods in Engineering 50 pp 1701– (2001) · Zbl 1011.74066 · doi:10.1002/nme.93
[2] Baniotopoulos, C. C., Applications of Mathematics (2002)
[3] Clapeyron, E., ComptesRendusParis pp 208– (1858)
[4] Colli, P., Comm. P. D. E. 15 pp 737– (1990) · Zbl 0707.34053 · doi:10.1080/03605309908820706
[5] Davidson, B. D., Journal of Composite Materials 24 pp 1124– (1990) · doi:10.1177/002199839002401101
[6] Davidson, B. D., Engineering and Fracture Mechanics 55 pp 557– (1996) · doi:10.1016/S0013-7944(96)00037-9
[7] Fleming, D. C., Journal of Composite Materials 30 pp 1977– (1996) · doi:10.1177/002199839603001802
[8] Frémond, M., Comptes Rendus de l’Academie des Sciences, Series II 300 pp 709– (1985)
[9] Frémond, M., Topics in Nonsmooth Mechanics (1988)
[10] Frémond, M., Non-smooth Thermomechanics (2002) · Zbl 0990.80001 · doi:10.1007/978-3-662-04800-9
[11] Fosdick, R., Journal of Elasticity 72 pp 145– (2003) · Zbl 1059.74007 · doi:10.1023/B:ELAS.0000018757.56138.f3
[12] Gill, P. E., SIAM Journal of Optimization 12 pp 979– (2002) · Zbl 1027.90111 · doi:10.1137/S1052623499350013
[13] Guidouche, H., Free Boundary Problems: Applications and Theory IV pp 340– (1985)
[14] Haslinger, J., Finite Element Approximation for Optimal Shaped Design, 1. ed. (1998)
[15] Hörmann, M., Proceedings of the fifth World Congress on Computational Mechanics (WCCM V), July 7-12, 2002, Vienna, Austria
[16] Krejčí, P., Res. Notes Math. 404 pp 47– (1999)
[17] Mainik, A., Calculus of Variations and Partial Differential Equations 22 pp 73– (2004) · Zbl 1161.74387 · doi:10.1007/s00526-004-0267-8
[18] Maugis, D., Contact, Adherence and Rupture of Elastic Solids (1999) · Zbl 0937.74002
[19] Mielke, A., Continuum Mechanics and Thermodynamics 15 pp 351– (2003) · Zbl 1068.74522 · doi:10.1007/s00161-003-0120-x
[20] Mielke, A., Models of Continuum Mechanics in Analysis and Engineering pp 117– (1999)
[21] Mielke, A., Nonlinear Differential Equations and Applications 11 pp 151– (2004)
[22] Mielke, A., Archive for Rational Mechanics and Analysis 162 pp 137– (2002) · Zbl 1012.74054 · doi:10.1007/s002050200194
[23] Ousset, Y., European Journal of Mechanics A/Solids 18 pp 291– (1999) · Zbl 0944.74068 · doi:10.1016/S0997-7538(99)80017-5
[24] Panagiotopoulos, G., Hemivariational Inequalities (1993) · Zbl 0826.73002 · doi:10.1007/978-3-642-51677-1
[25] Point, N., Mathematical Methods in the Applied Sciences 10 pp 367– (1988) · Zbl 0656.73052 · doi:10.1002/mma.1670100403
[26] Point, N., International Journal of Solids and Structures 33 pp 483– (1996) · Zbl 0902.73054 · doi:10.1016/0020-7683(95)00043-A
[27] Point, N., Mathematical and Computer Modelling 28 pp 359– (1998) · Zbl 1126.74359 · doi:10.1016/S0895-7177(98)00127-7
[28] Schreyer, H. L., Computing Methods in Applied Mechanics and Engineering 191 pp 2483– (2002) · Zbl 1054.74070 · doi:10.1016/S0045-7825(01)00409-1
[29] Sprenger, W., Computing Methods in Applied Mechanics and Engineering 185 pp 123– (2000) · Zbl 0966.74069 · doi:10.1016/S0045-7825(99)00255-8
[30] Wells, G. N., International Journal of Numerical Methods in Engineering 54 pp 1333– (2002) · Zbl 1086.74043 · doi:10.1002/nme.462
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