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A computational model for analysis of rate-dependent interface damage which leads to interface crack initiation and propagation in multi-domain structures exposed to shear type cyclic loading is presented. Modelling of interface damage, accounting generally for various stress vs. separation relations of common cohesive zone models in this type of models, is restricted here to one with an exponential relation. The model also includes viscosity and internal parameters for the interface damage to observe a fatigue- like behaviour where a crack appears for smaller magnitudes of periodical loadings in comparison to pure uploading.
The computational approach, physically based on evolution of stored and dissipated energies, behind the model results in a kind of variational formulation. Moreover, solving the problem for variables characterising the elastic state of the structure, the multi-domain symmetric Galerkin boundary element method is advantageously used. Finally, the variational character of the solution requires implementation of (sequential) quadratic programing solvers into the computer code which is fully implemented in MATLAB.
The presented numerical results for a rather academic structure demonstrate the properties of the described model and enable to extend its applicability to more general problems of engineering practice.
cohesive interface, fatigue life, interface damage, quadratic programming, quasistatic delamination, symmetric Galerkin boundary element method
[1] Roe, K. & Siegmund,T., An irreversible cohesive zone model for interface fatigue crack growth simulation. Engineering Fracture Mechanics, 70(2), pp. 209–232, 2003.
[2] Bouvard, J., Chaboche, J., Feyel, F. & Gallerneau, F., A cohesive zone model for fatigue and creep–fatigue crack growth in single crystal super alloys. International Journal of Fatigue, 31(5), pp. 868–879, 2009.
[3] Roth, S., Hütter, G. & Kuna, M., Simulation of fatigue crack growth with a cyclic cohesive zonemodel. International Journal of Fracture, 188(1), pp. 23–45, 2014.
[4] Raous, M., Cangemi, L. & Cocu, M., A consistent model coupling adhesion, friction andunilateral contact. Computer Methods in Applied Mechanics and Engineering, 177(6), pp. 383–399, 1999.
[5] Roubíček, T., Souček, O. & Vodička, R., A model of rupturing lithospheric faults with reoccurring earthquakes. SIAM Journal on Applied Mathematics, 73(4), pp. 1460–1488, 2013.
[6] Vodička, R. & Krajníková, K., A quasi-static delamination model with rate-dependent interface damage exposed to cyclic loading. Key Engineering Materials, 774, pp. 84–89, 2018.
[7] Vodička, R., Aquasi-staticinterfacedamagemodelwithcohesivecracks:SQP–SGBEM implementation. Eng Anal Bound Elem, 62, pp. 123–140, 2016.
[8] Vodička, R. & Mantič, V., An energy based formulation of a quasi-static interface damage model with a multi linear cohesive law. Discrete & Continuous Dynamical Systems-S, 10(6), pp. 1539–1561, 2017.
[9] Vodička, R. & Krajníková, K., A numerical approach to an interface damage model under cyclic loading. Lecture Notes in Civil Engineering, ed. M. Wahab, Springer, Vol. 20, pp. 54–66, 2019.
[10] Roubíček, T., Panagiotopoulos, C. & Mantič, V., Quasistatic adhesive contact of viscoelastic bodies and its numerical treatment for very small viscosity. Zeitschrift angew Math Mech, 93, pp. 823–840, 2013.
[11] Roubíček, T., Panagiotopoulos,C. & Mantič,V., Local-solution approach to quasistatic rate-independent mixed-mode delamination. Mathematical Models and Methods in Applied Sciences, 25(7), pp. 1337–1364, 2015.
[12] Vodička, R., Mantič, V. & Roubíček, T., Energetic versus maximally-dissipative local solutions of a quasi-static rate-independent mixed-mode delamination model. Meccanica, 49(12), pp. 2933–296, 2014.
[13] Dostál, Z., An optimal algorithm for bound and equality constrained quadratic programming problems with bounded spectrum. Computing, 78(4), pp. 311–328, 2006.
[14] Dostál, Z., Optimal Quadratic Programming Algorithms, volume 23 of Springer Optimization and Its Applications. Springer: Berlin, 2009.
[15] Nocedal, J. & Wright, S., Numerical Optimization. Springer, 2006.
[16] Bonnet, M., Maier, G. & Polizzotto, C., Symmetric Galerkin boundary element method. Applied Mechanics Reviews, 51(11), pp. 669–704, 1998.
[17] Sutradhar, A., Paulino, G. & Gray, L., The symmetric Galerkin Boundary Element Method. Springer-Verlag: Berlin, 2008.
[18] Vodička, R., Mantič, V. & París, F., Symmetric variational formulation of BIE for domain decomposition problems in elasticity–an SGBEM approach for non conforming discretizations of curved interfaces. CMES— Computer Modeling in Engineering & Sciences, 17(3), pp. 173–203, 2007.
[19] Vodička, R., Mantič, V. & Roubíček,T., Quasistatic normal-compliance contact problem of visco-elastic bodies with Coulomb friction implemented by QP and SGBEM. Journal of Computational and Applied Mathematics, 315, pp. 249–272, 2017.
[20] Vodička, R., Mantič, V. & París, F., Two variational formulations for elastic domain decomposition problems solved by SGBEM enforcing coupling conditions in a weak form. Engineering Analysis with Boundary Elements, 35(1), pp. 148–155, 2011.
[21] Hertzbeg, R., Vinci, R. & Hertzberg, J., Deformation and Fracture Mechanics of Engineering Materials, 5th edn., John Wiley & Sons: New York, 2012.
[22] París, P. & Erdogan, F., A critical analysis of crack propagation laws. ASME Journal of Basic Engineering, 85(4), pp. 528–533, 1963.