Multiscale-Method based on Atomistic/Continuum Coupling for Tribological Problems at Nanoscale.
Final Report Abstract
The progress of the project can be summarized in three parts: • preliminary investigation of the influence of surface texture on friction by full MD simulations; • development of the FE-MD coupling algorithm for dynamic problems; • the improvement of various implementations. The main challenges originally planned for a second phase of the project are the thermal-mechanical coupling of the FE-MD model and the development of more general constitutive relations for the FE model that can be used not just for perfect crystals. We have developed the selective damping algorithm, which can orthogonally decompose the kinetic energy of the MD model into a mechanical part that can be passed into the FE model and a high-frequency part that is proposed to be transferred to the FE model as thermal energy. Such idea is based on the similarity we found between our selective damping formulation and equations of motion for thermostated MD models. The similarity also suggests a connection between the damping power applied to the high-frequency motion of the MD model and the internal heat source of the FE model. More detailed studies will be conducted in this direction, especially the study of the background theories on temperature-controlled MD simulations. To establish the thermo-mechanical coupling of the MD model and the FE model, we also need corresponding constitutive relations for the FE model. The elastic part can be estimated using the Cauchy-Born rule. For the thermal part and the thermal-mechanical coupling part, we need to establish links between the Hamiltonian equations of the MD model and the thermal-mechanical equations of the continuum mechanics model. We have found Li’s work [8] as an excellent guidance for this task. So far we do not have any clear idea for how to develop the plastic constitutive relation for the FE model based on underlying MD model, but since our focus of this project is tribological problems instead of large deformation or indentation problems, the plastic deformation is expected to be concentrated near the surface, which can be always converted into the MD model by using the adaptivity algorithm we have developed before. These implementation will be kept in a hybrid style, where core algorithms, such as coupling routine and solvers, will be coded in C++ and the routines for the pre-, post-process and visualization in MATLAB.
Publications
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Molecular dynamics simulation of lubricated contact between textured surfaces, Proc. Appl. Math. Mech. 12: 517 - 518, 2012
Khromov, O., Shan, W. and Nackenhorst, U.
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Selective damping method for weakly coupled FE-MD models, Proc. Appl. Math. Mech. 12: 439 - 440, 2012
Shan, W. and Nackenhorst, U.
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Selective damping for the weak Arlequin coupling of molecular dynamics and Finite Element Method. Int. J. Numer. Meth. Engng. 2013;96: 176-202
Shan, W. and Nackenhorst U.
