Cosserat Elastoplastic Finite Elements for Masonry Structures

Abstract:

A Finite Elements formulation previously developed for Cosserat elastic plates, has been extended herein to the elastoplastic framework. Material non-linearities are taken into account through the implementation of a backward-Euler closest-point-projection algorithm, for which the definition of non-smooth yield loci and non-associated plastic potentials and evolution laws is made possible. An existing homogenized elastic constitutive model and a set of yield criteria for the out-of-plane behaviour of block-masonry are implemented in the code and their validity is discussed based on the comparison with Discrete Elements simulations. The comparison is carried out in both the static and the dynamic regime.

• Periodical: Key Engineering Materials (Volume 624)
• Pages: 131-138
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.624.131
• Online since: September 2014
• Authors: Michele Godio*, Ioannis Stefanou, Karam Sab, Jean Sulem
• Keywords: Cosserat Dynamics, Discrete Element, Finite Element, Masonry, Multi-Surface Plasticity

References

[1] G. Salerno and G. de Felice, Continuum modeling of periodic brickwork, Int. J. Solids Struct., vol. 46, no. 5, p.1251–1267, Mar. (2009).

DOI: 10.1016/j.ijsolstr.2008.10.034

[2] A. Pau and P. Trovalusci, Block masonry as equivalent micropolar continua: the role of relative rotations, Acta Mech., vol. 223, no. 7, p.1455–1471, May (2012).

DOI: 10.1007/s00707-012-0662-8

[3] P. Trovalusci and A. Pau, Derivation of microstructured continua from lattice systems via principle of virtual works: the case of masonry-like materials as micropolar, second gradient and classical continua, Acta Mech., vol. 225, no. 1, p.157–177, Aug. (2013).

DOI: 10.1007/s00707-013-0936-9

[4] J. Sulem and H. Mühlhaus, A continuum model for periodic two-dimensional block structures, Mech. Cohesive Frict. Mater., vol. 2, no. March 1996, p.31–46, (1997).

DOI: 10.1002/(sici)1099-1484(199701)2:1<31::aid-cfm24>3.0.co;2-o

[5] I. Stefanou, J. Sulem, and I. Vardoulakis, Three-dimensional Cosserat homogenization of masonry structures: elasticity, Acta Geotech., vol. 3, no. 1, p.71–83, Feb. (2008).

DOI: 10.1007/s11440-007-0051-y

[6] M. Godio, Etude théorique et numérique du comportement dynamique tridimensionnel des structures en maçonnerie, MSc Thesis ENPC, (2012).

[7] J. Simo, J. G. Kennedy, and S. Gonvindjee, Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms, Int. J. Numer. Methods Eng., vol. 26, no. June 1987, p.2161–2185, (1988).

DOI: 10.1002/nme.1620261003

[8] R. de Borst, Simulation of strain localization: a reappraisal of the Cosserat continuum, Eng. Comput., vol. 8, no. 4, p.317–332, (1991).

DOI: 10.1108/eb023842

[9] D. Addessi, A 2D Cosserat finite element based on a damage-plastic model for brittle materials, Comput. Struct., vol. 135, p.20–31, Apr. (2014).

DOI: 10.1016/j.compstruc.2014.01.003

[10] P. Trovalusci and R. Masiani, Material symmetries of micropolar continua equivalent to lattices, Int. J. Solids Struct., (1999).

DOI: 10.1016/s0020-7683(98)00073-0

[11] P. Trovalusci and R. Masiani, Non-linear micropolar and classical continua for anisotropic discontinuous materials, Int. J. Solids Struct., vol. 40, no. 5, p.1281–1297, Mar. (2003).

DOI: 10.1016/s0020-7683(02)00584-x

[12] D. Addessi, E. Sacco, and A. Paolone, Cosserat model for periodic masonry deduced by nonlinear homogenization, Eur. J. Mech. - A/Solids, vol. 29, no. 4, p.724–737, Jul. (2010).

DOI: 10.1016/j.euromechsol.2010.03.001

[13] D. Addessi and E. Sacco, A multi-scale enriched model for the analysis of masonry panels, Int. J. Solids Struct., vol. 49, no. 6, p.865–880, Mar. (2012).

DOI: 10.1016/j.ijsolstr.2011.12.004

[14] D. Baraldi, E. Reccia, A. Cazzani, and A. Cecchi, Comparative Analysis of Numerical Discrete and Finite Element Models: the Case of in-Plane Loaded Periodic Brickwork, Compos. Mech. Comput. Appl. An Int. J., vol. 4, no. 4, p.319–344, (2013).

DOI: 10.1615/compmechcomputapplintj.v4.i4.40

[15] E. Reccia, A. Cazzani, and A. Cecchi, FEM-DEM Modeling for Out-of-plane Loaded Masonry Panels: A Limit Analysis Approach, Open Civ. Eng. J., p.231–238, (2012).

DOI: 10.2174/1874149501206010231

[16] K. Sab, J. Dallot, and A. Cecchi, Determination of the overall yield strength domain of out-of-plane loaded brick masonry, Int. J. Multiscale Comput. Eng., (2007).

DOI: 10.1615/intjmultcompeng.v5.i2.20

[17] Itasca Consulting Group, 3DEC 5. 0., Minneapolis, (2013).

[18] P. Cundall, Formulation of a three-dimensional distinct element model—Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks, Int. J. Rock Mech. Min. …, vol. 25, no. 3, p.107–116, (1988).

DOI: 10.1016/0148-9062(88)92293-0

[19] J. V. Lemos, Discrete Element Modeling of Masonry Structures, Int. J. Archit. Herit., vol. 1, no. 2, p.190–213, May (2007).