Keywords: discrete element, coupled DEM-FEM, reinforced concrete, impact, transient dynamics.

The general framework of this study deals with prediction of reinforced concrete structure response under severe local dynamic load such as an impact due to an aircraft, a missile or a near-field explosion. A reliable and efficient design of structures under such a loading needs to take into account local discontinuities due to impact as well as the global response of structure that may have an elastic response far from impacted area.

These facts naturally lead to proposing a coupled finite element - discrete element approach. Locally, the DEM is used to analyze discontinuous phenomena such as failures, fragmentation and compaction. The FEM is applied on the remaining structure to reduce both times of computation and modelling. With this coupled method, different structural responses may be predicted such as the missile penetration, damage of the structure and global displacement or first natural frequencies.

In a first part, this paper describes the DEM used. It consists of rigid spheres with a complex interaction law; it has been validated in previous studies by means of simulations of quasi-static and dynamic tests performed on concrete structures [1]. A new identification process of local parameters is proposed improving the reliability and the reproducibility of the model. On concrete samples, quasi-static tests such as compression and tensile tests have been made and the results have been compared with experimental trials [2].

The coupling uses a bridging domain [3] where the coupling relations are introduced by means of Lagrange multipliers. A temporal relaxation method is used to reduce the spurious reflection due to the discontinuity of the size discretisation between the two approaches [4]. The proposed method has been validated by comparison with a full discrete element model [4]. This paper presents the modelling of an impact of a rocky block on a concrete slab. The results of the full discrete element model and the coupled model are quite similar.

The last part describes an adaptation of the coupling method between discrete element and finite element of the shell type. The shell element used is a four node element based on Reissner-Mindlin model [5]. The main idea of this new approach is to define fictitious nodes in order to build a fictitious three-dimensional finite element. With this fictitious nodes, the previously described method is used. Some elastic and static tests are presented. Results begin to validate the model although dynamic tests must be carried out.

1

S. Hentz, L. Daudeville, F.V. Donzé, "Identification and validation of a discrete element model for concrete", ASCE Journal of Engineering Mechanics, 130(6): 709-719, 2004. doi:10.1061/(ASCE)0733-9399(2004)130:6(709)

2

T. Gabet, Y. Malécot, L. Daudeville, "Triaxial behaviour of concrete under high stresses: Influence of the loading path on compaction and limit states", Cem. Concr. Res., 38(3), 403-412, 2008. doi:10.1016/j.cemconres.2007.09.029

3

S.P. Xiao, T. Belytschko, "A bridging domain method for coupling continua with molecular dynamics", Comput. Methods Appl. Mech. Engrg.,193, 1645-1669, 2004. doi:10.1016/j.cma.2003.12.053

4

E. Frangin, P. Marin, L. Daudeville, "On the use of combined finite/discrete element method for impacted concrete structures", Journal of Physics IV, 2006. doi:10.1051/jp4:2006134071

5

E. Reissner, "Linear and nonlinear theory of shells", in Thin Shell Structures, (Fung and Sechler Eds.), Prentice Hall, p. 29-44, 1974.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)