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 JAMP  Vol.1 No.6 , November 2013
Development of a Bi-Material Representative Volume Element Using Damaged Homogenisation Approach
Abstract: Most civil engineering structures are formed using a number of materials that are bonded to each other with their surface-to-surface interaction playing key role on the overall response of the structure. Unfortunately these interactions are extremely variable; simplified and extremely detailed models trialed to date prove quite complex. Models that assume perfect interaction, on the other hand, predict unsafe behavior. In this paper a damage mechanics based interaction between two materials of different softening properties is developed using homogenisation approach. This paper describes the process of developing a bi-material representative volume element (RVE) using damaged homogenisation approach. The novelty in this paper is the development of non-local transient damage identification algorithm. Numerical examples prove the stability of the approach for a simplified RVE and encourage application to other shapes of RVEs.
Cite this paper: Jelvehpour, A. and Dhanasekar, M. (2013) Development of a Bi-Material Representative Volume Element Using Damaged Homogenisation Approach. Journal of Applied Mathematics and Physics, 1, 43-47. doi: 10.4236/jamp.2013.16009.
References

[1]   A. Cavicchi and L. Gambarotta, “Collapse Analysis of Masonry Bridges Taking into Account Arch-Fill Interaction,” Engineering Structures, Vol. 27, No. 4, 2005, pp. 605-615. http://dx.doi.org/10.1016/j.engstruct.2004.12.002

[2]   M. Dhanasekar, “Review of Modelling of Masonry Shear,” International Journal of Advanced Engineering Science Applied Mathematics, Vol. 2, No. 3, 2010, pp. 106-118. http://dx.doi.org/10.1007/s12572-011-0022-2

[3]   J. L. Chaboche, “Continuum Damage Mechanics. Present State and Future Trends,” Nuclear Engineering and Design, Vol. 105, No. 1, 1987, pp. 19-33. http://dx.doi.org/10.1016/0029-5493(87)90225-1

[4]   R. H. J. Peerlings, “Enhanced Damage Modelling for Fracture and Fatigue,” Ph.D. Thesis, Technische Universiteit Eindhoven, 1999.

[5]   J. H. P. De Vree, W. A. M. Brekelmans and M. A. J. Van Gils, “Comparison of Nonlocal Approaches in Continuum Damage Mechanics,” Computers and Structures, Vol. 55, No. 4, 1995 pp. 581-588. http://dx.doi.org/10.1016/0045-7949(94)00501-S

[6]   G. Pijaudier-Cabot, Z. P. Ba?ant and M. Tabbara, “Comparison of Various Models for Strain-Softening,” Engineering Computations, Vol. 5, No. 2, 1988, pp. 141-150. http://dx.doi.org/10.1108/eb023732

[7]   R. H. J. Peerlings, R. de Borst, W. A. M. Brekelmans and M. G. D. Geers, “Gradient Enhanced Damage Modelling of Concrete Fracture,” Mechanics of Cohesive-Frictional Material, Vol. 3, No. 4, 1998, pp. 323-342. http://dx.doi.org/10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D

[8]   Z. P. Ba?ant, T. Belytschko and T. Chang, “Continuum Theory for Strain-Softening,” Journal of Engineering Mechanics, Vol. 110, No. 12, 1984, pp. 1666-1692. http://dx.doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1666)

[9]   R. H. J. Peerlings, R. de Borst, W. A. M. Brekelmans and J. H. P. de Vree, “Gradient Enhanced Damage for Quasi-Brittle Materials,” International Journal for Numerical Methods in Engineering, Vol. 39, No. 19, 1996, pp. 3391-3403. http://dx.doi.org/10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D

[10]   M. G. D. Geers, R. de Borst, W. A. M. Brekelmans and R. H. J. Peerlings, “Strain-Based Transient-Gradient Damage Model for Failure Analyses,” Computer Methods in Applied Mechanics and Engineering, Vol. 160, No. 1-2, 1998, pp. 133-153. http://dx.doi.org/10.1016/S0045-7825(98)80011-X

[11]   S. Saroukhani, R. Vafadari and A. Simone, “A Simplified Implementation of a Gradient-Enhanced Damage Model with Transient Length Scale Effects,” Computational Mechanics, Vol. 51, No. 6, 2013, pp. 899-909. http://dx.doi.org/10.1007/s00466-012-0769-8

[12]   A. Anthoine, “Derivation of the In-Plane Elastic Characteristics of Masonry through Homogenization Theory,” International Journal of Solids and Structures, Vol. 32, No. 2, 1995, pp. 137-163. http://dx.doi.org/10.1016/0020-7683(94)00140-R

[13]   T. J. Massart, “Multi-Scale Modelling of Damage in Masonry Structures,” Ph.D. Thesis, Technische Universiteit Eindhoven, 2003.

[14]   M. Dhanasekar, “Comparison of Nonlocal Approaches in Continuum Damage Mechanics,” Ph.D. Thesis, University of Newcastle, 1985.

 
 
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