Coupling the finite element method and molecular dynamics in the framework of the heterogeneous multiscale method for quasi-static isothermal problems |
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| Institution: | 1. Materials Department, University of California, Santa Barbara, Engineering II, Santa Barbara, CA, 93106, USA;2. Department of Mechanical Engineering, University of California, Santa Barbara, Engineering II, Santa Barbara, CA, 93106, USA;3. NASA Glenn Research Center (GRC), 21000 Brookpark Road, Cleveland, OH, 44135, USA;4. Department of Materials Science and Engineering, University of Michigan, 2300 Hayward St, Ann Arbor, MI, 48109, USA;1. Civil Engineering Department, COPPE, Universidade Federal do Rio de Janeiro, 21941-972, Rio de Janeiro RJ, Brazil;2. RDP, ENS Lyon, 46 allée d''Italie, 69007 Lyon, France;3. Laboratoire de Physique Statistique, Ecole Normale Supérieure, UPMC Paris 6, Université Paris Diderot, CNRS - 24 rue Lhomond, 75005 Paris, France;1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, PR China;2. The State Key Laboratory of Mechanical Transmission, Chongqing University, 400044, PR China;3. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China;1. Department of Civil-Environmental Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/A, I 43124 Parma, Italy;2. Department of Industrial Engineering, University of Parma, Parco Area delle Scienze 181/A, I 43124 Parma, Italy;3. Construction Technologies Institute - Italian National Research Council (ITC-CNR), Via Lombardia 49, I 20098 San Giuliano Milanese, Milano, Italy |
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| Abstract: | Multiscale models are designed to handle problems with different length scales and time scales in a suitable and efficient manner. Such problems include inelastic deformation or failure of materials. In particular, hierarchical multiscale methods are computationally powerful as no direct coupling between the scales is given. This paper proposes a hierarchical two-scale setting appropriate for isothermal quasi-static problems: a macroscale treated by continuum mechanics and the finite element method and a microscale modelled by a canonical ensemble of statistical mechanics solved with molecular dynamics. This model will be implemented into the framework of the heterogeneous multiscale method. The focus is laid on an efficient coupling of the macro- and micro-solvers. An iterative solution algorithm presents the macroscopic solver, which invokes for each iteration an atomistic computation. As the microscopic computation is considered to be very time consuming, two optimisation strategies are proposed. Firstly, the macroscopic solver is chosen to reduce the number of required iterations to a minimum. Secondly, the number of time steps used for the time average on the microscale will be increased with each iteration. As a result, the molecular dynamics cell will be allowed to reach its state of thermodynamic equilibrium only in the last macroscopic iteration step. In the preceding iteration steps, the molecular dynamics cell will reach a state close to equilibrium by using considerably fewer microscopic time steps. This adapted number of microsteps will result in an accelerated algorithm (aFE-MD-HMM) obtaining the same accuracy of results at significantly reduced computational cost. Numerical examples demonstrate the performance of the proposed scheme. |
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| Keywords: | Heterogeneous multiscale method HMM Seamless HMM Atomistic-to-continuum coupling Homogenisation Finite element method Molecular dynamics |
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