年間 6 号発行
ISSN 印刷: 1543-1649
ISSN オンライン: 1940-4352
Indexed in
MICROMORPHIC CONTINUA: APPLICATION TO THE HOMOGENIZATION OF DIATOMIC MASONRY COLUMNS
要約
In the frame of continuum mechanics, the theory of general micromorphic continua is a key element for modeling mechanical systems of discrete building blocks such as masonry structures. This stems from the fact that the kinematics of the particle, in the terminology of Germain (Germain, P., The Method of Virtual Power in Continuum Mechanics, Part 2: Microstructure. SIAM J. Appl. Math., vol. 25, pp. 556-575, 1973), is quite rich to cover the various degrees of freedom of the discrete microstructure. In the present paper, we derive a third-order micromorphic continuum for modeling diatomic masonry columns. Our analysis is extended to the dynamic regime. For linear elastic interfaces, the derived continuum is compared with the discrete model in terms of the dispersion curves. It is shown that the continuum approximates well the discrete structure for wavelengths five to ten times bigger than the size of the elementary cell. Therefore, the presented model may be the base for future engineering applications in the field of cultural heritage assets, because it might be an alternative approach in the mechanical modeling of ancient colonnades, whose study is mostly performed with the discrete element method. As it is well known, continuum models are quite flexible, computationally cheaper, and may give insight to the fundamental properties of the systems at hand.
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Aboudi, J., Mechanics of Composite Materials.
-
Bakhvalov, N. and Panasenko, G., Homogenisation: Averaging Process in Periodic Media.
-
Bazant, Z. P. and Christensen, M., Analogy between micropolar continuum and grid frameworks under initial stress. DOI: 10.1016/0020-7683(72)90093-5
-
Besdo, D., Inelastic behaviour of plane frictionless block-systems described as cosserat media.
-
Eringen, A. C., Microcontinuum Field Theories I: Foundations and Solids.
-
Germain, P., The method of virtual power in continuum mechanics, Part 2: Microstructure. DOI: 10.1137/0125053
-
Kittel, C., Introduction to Solid States Physics.
-
Komodromos, P., Papaloizou, L., and Polycarpou, P., Simulation of the response of ancient columns under harmonic and earthquake excitations. DOI: 10.1016/j.engstruct.2007.11.004
-
Kumar, R. S. and McDowell, D. L., Generalized continuum modelling of 2-D periodic cellular solids. DOI: 10.1016/j.ijsolstr.2004.06.038
-
Mindlin, R. D., Microstructure in linear elasticity. DOI: 10.1007/BF00248490
-
Mindlin, R. D., Second gradient of strain and surface-tension in linear elasticity. DOI: 10.1016/0020-7683(65)90006-5
-
Muhlhaus, H.-B., Sulem, J., and Unterreiner, P., Discrete and continuous models for dry masonry columns. DOI: 10.1061/(ASCE)0733-9399(1997)123:4(399)
-
Papamichos, E., Vardoulakis, I., and Muhlhaus, H.-B., Buckling of layered elastic media: A Cosserat-continuum approach and its validation. DOI: 10.1002/nag.1610140703
-
Pasternak, E. and Muhlhaus, H.-B., Generalized homogenization procedures for granular material. DOI: 10.1007/s10665-004-3950-z
-
Sanchez-Palencia, E. and Zaoui, A., Homogenization Techniques for Composite Media. DOI: 10.1007/3-540-17616-0
-
Stefanou, I., Sulem, J., and Vardoulakis, I., Homogenization of interlocking masonry structures using a generalized differential expansion technique. DOI: 10.1016/j.ijsolstr.2010.02.011
-
Stefanou, I., Psycharis, I., and Georgopoulos, I.-O., Dynamic response of reinforced masonry columns in classical monuments. DOI: 10.1016/j.conbuildmat.2010.12.042
-
Stefanou, I., Vardoulakis, I., and Mavraganis, A., Dynamic motion of a conical frustum over a rough horizontal plane. DOI: 10.1016/j.ijnonlinmec.2010.07.008
-
Sulem, J. and Mühlhaus, H.-B., A continuum model for periodic two-dimensional block structures. DOI: 10.1002/(SICI)1099-1484(199701)2:1<31::AID-CFM24>3.0.CO;2-O
-
Trovalusci, P., Capecchi, D., and Ruta, G., Genesis of the multiscale approach for materials with microstructure. DOI: 10.1007/s00419-008-0269-7
-
Trovalusci, P. and Massiani, R., Non-linear micropolar and classical continua for anisotropic discontinuous materials. DOI: 10.1016/S0020-7683(02)00584-X
-
Baraldi Daniele, Bullo Sandra, Cecchi Antonella, Continuous and discrete strategies for the modal analysis of regular masonry, International Journal of Solids and Structures, 84, 2016. Crossref
-
Godio Michele, Stefanou Ioannis, Sab Karam, Sulem Jean, Sakji Seddik, A limit analysis approach based on Cosserat continuum for the evaluation of the in-plane strength of discrete media: Application to masonry, European Journal of Mechanics - A/Solids, 66, 2017. Crossref