Multiresolution molecular mechanics: adaptive analysis. (English) Zbl 1425.74026

Summary: The concurrent atomistic/continuum coupling method Multiresolution Molecular Mechanics (MMM) has been presented for statics [Q. Yang et al., ibid. 258, 26–38 (2013; Zbl 1296.74006)] and dynamics [E. Biyikli et al., ibid. 274, 42–55 (2014; Zbl 1296.74005)], its convergence and error structure has been analyzed [Q. Yang et al., ibid. 269, 20–45 (2014; Zbl 1296.74132)], and a unified and consistent framework for general finite element shape functions has been introduced [Q. Yang and A. C. To, ibid. 283, 384–418 (2015; Zbl 1423.74038)]. The current work presents the adaptivity analysis of the MMM method. To start, the rationale and formulation of the MMM method are briefly introduced. Later, two main features of the adaptivity scheme, refinement and coarsening, are discussed and described in detail and step-by-step procedures are outlined. The adaptivity is tested using three numerical examples: (i) 1-D wave propagation, (ii) 2-D dislocation, and (iii) 3-D nanoindentation. The results of numerical examples agree well with those of full atomistic simulations. Furthermore, control parameters of adaptivity schemes offer much flexibility to adjust between accuracy and efficiency. The introduced adaptivity schemes are simple, effective, and accurate owing to the consistency and robustness of MMM.


74A25 Molecular, statistical, and kinetic theories in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics


Full Text: DOI


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