Numerical Simulations of Topologically Interlocked Materials Coupling DEM Methods and FEM Calculations: Comparison with
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1188-LL05-05
Numerical Simulations of Topologically Interlocked Materials Coupling DEM Methods and FEM Calculations: Comparison with Indentation Experiments Charles Brugger1,2, Marc C. Fivel1 and Yves Brechet1 1 SIMaP-GPM2, INP Grenoble/CNRS, 101 Rue de la Physique, BP46, 38402 St Martin d’Hères cedex, France 2 Present address: Institute of mechanics, materials and civil engineering (iMMC), Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
ABSTRACT Planar assemblies of interlocked cubic blocs have been tested in indentation. Experiments are performed on blocs made of plaster. Influence of key parameters such as the surface roughness, the compression stress and the number of blocs are investigated. A numerical modeling is then proposed based on discrete element method. Each bloc is represented by its centre coordinates. Constitutive equations obtained by finite element simulations are introduced to model the contact between the blocs. The numerical tool is then applied to the case of indentation loading. It is found that the model reproduces all the experimental tendencies. INTRODUCTION Interlocked materials are architectured materials from their very definition. Inspired from civil engineering, they are formed of blocs of a variety of geometries: tetrahedrons, cubes, osteomorphic pieces, etc. The interlocking property is obtained by the topology of the contacts and the application of compression loading conditions at the periphery of the assembly [1-2]. z
3
4 5
2 1
6
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Figure 1: Example of an assembly of cubic elements. A typical assembly of cubic shape elements is given in figure 1. Each cube is maintained by six neighbors. The vertical displacement along z < 0 of the central bloc is prohibited by cubes 1, 3 and 5. Similarly, the vertical displacement toward z > 0 direction is inhibited by the contacts
with blocs 2, 4 and 6. Compression stress in the medium plane is needed in order to insure the contacts between all the blocs. As shown by Dyskin et al. [3-4] for cubic blocs and by Autruffe et al. for osteomorphic blocs [5-6], the mechanical response in indentation is very sensitive to the quality of the contact between the blocs. Thus special attention should be paid in the contact laws when building up a numerical model devoted to such assemblies. In this paper we have first realized assemblies of cubic blocs made of plaster. The effects of the surface roughness and the cube size have been investigated. Then, a discrete element model in which the interaction laws between two blocs are obtained by finite element simulations has been developed. Applications are then performed in the case of indentation loading and comparisons are made with the experimental observations. INDENTATION EXPERIMENTS A 270 x 280 mm assembly made of 30mm large plaster cubes has been realized and tested in indentation (see figure 2a). The number of cubes is 68. Each cube was mould in a dedicated frame which imposes five out of the six dimensions of the bloc. This induces uncertainties on one dimension of the cub
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