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Keywords: discrete approach, homogenized approach, ballast, granular materials, coupling, multiscale.

Summary

The aim of this paper is to present a formulation for coupling between a discrete approach at the microscopic scale and a homogenized approach deduced from the discrete approach at the macroscopic scale. This approach is proposed for more applications in civil engineering problems. It can be used to simulate the ballast grains under the railways of a high-speed train.

A brief study on the different coupled approach [1], is presented in the introduction. We have concluded that in all proposed approaches, these efforts confirm that the issue of how to partition energy within an atomistic-continuum overlap region needs to be adressed properly in order to maintain the integrity of the two views of material deformation, atomistic and continuum, and to obtain accurate solutions.

In what follows we have studied an undimensionnal model. This model consists of a beam resting on grains of ballast modelled by springs with elastic behavior as the supports of the beam on which we apply a load. We developed a discrete approach and a homogenized approach for the static calculation. We concluded on the existence of several cases where the homogenized approach cannot replace the discrete approach.

Due to this difference, we proposed an approach which consists of a homogenized approach with the elements of large size compared to the discrete one. Using a criterion of coupling, the size of the elements will be refined when necessary.

In conclusion we can summarize the efficiency of this coupled approach from two points of view. Firstly, we observe the good match between the discrete and the coupled behavior and secondly, a reduction in the number of elements which implies a reduction in the computation time compared to that needed in the discrete approach.

References

1: W.A. Curtin, R.A. Miller, "Atomistic/continuum coupling in computational materials science", Modelling and Simulation in Materials Science and Engineering, 11, R33-R68, 2003. doi:10.1088/0965-0393/11/3/201

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 89 PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: M. Papadrakakis and B.H.V. Topping Paper 39 Coupled Discrete and Continuum Approach to the Behaviour of Ballast M. Hammoud, D. Duhamel, K. Sab and F. Legoll University Paris-Est, Navier Institute, LAMI, Ecole des Ponts, Marne-la-Vallée, France doi:10.4203/ccp.89.39 purchase the full-text of this paper Full Bibliographic Reference for this paper M. Hammoud, D. Duhamel, K. Sab, F. Legoll, "Coupled Discrete and Continuum Approach to the Behaviour of Ballast", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 39, 2008. doi:10.4203/ccp.89.39 Keywords: discrete approach, homogenized approach, ballast, granular materials, coupling, multiscale. Summary The aim of this paper is to present a formulation for coupling between a discrete approach at the microscopic scale and a homogenized approach deduced from the discrete approach at the macroscopic scale. This approach is proposed for more applications in civil engineering problems. It can be used to simulate the ballast grains under the railways of a high-speed train. A brief study on the different coupled approach [1], is presented in the introduction. We have concluded that in all proposed approaches, these efforts confirm that the issue of how to partition energy within an atomistic-continuum overlap region needs to be adressed properly in order to maintain the integrity of the two views of material deformation, atomistic and continuum, and to obtain accurate solutions. In what follows we have studied an undimensionnal model. This model consists of a beam resting on grains of ballast modelled by springs with elastic behavior as the supports of the beam on which we apply a load. We developed a discrete approach and a homogenized approach for the static calculation. We concluded on the existence of several cases where the homogenized approach cannot replace the discrete approach. Due to this difference, we proposed an approach which consists of a homogenized approach with the elements of large size compared to the discrete one. Using a criterion of coupling, the size of the elements will be refined when necessary. In conclusion we can summarize the efficiency of this coupled approach from two points of view. Firstly, we observe the good match between the discrete and the coupled behavior and secondly, a reduction in the number of elements which implies a reduction in the computation time compared to that needed in the discrete approach. References 1 W.A. Curtin, R.A. Miller, "Atomistic/continuum coupling in computational materials science", Modelling and Simulation in Materials Science and Engineering, 11, R33-R68, 2003. doi:10.1088/0965-0393/11/3/201 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 £95 +P&P)
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