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Multiresoultion Molecular Mechanics: Accuracy, Stability, and Convergence Analysis

Albert To (University of Pittsburgh), Qingcheng Yang (University of Pittsburgh), Emre Biyikli (University of Pittsburgh)

From Atomistics to Reality: Spanning Scales in Simulations and Experiments Symposium A

Tue 2:40 - 4:00

CIT 165

This work presents a new concurrent atomistic-continuum coupling method called the multiresolution molecular mechanics (MMM) method [1]. By introducing a novel energy sampling framework, MMM aims at accurately and efficiently approximating the atomic energy of the system at different resolutions without the cumbersome interfacial treatment in existing methods. The key features of the MMM method are: (1) consistency with the atomistics framework, (2) consistency with the order of shape functions introduced, and (3) flexibility in energy approximation with respect to accuracy and efficiency. Under the energy sampling framework, several sampling schemes have been devised and tested for interface compatibility in statics settings, and compared to existing methods. Sources of errors in the different approximations have been identified. The proposed method demonstrates very good accuracy in solving crack propagation, surface relaxation, and nanoindentation problems when compared to full atomistic simulations in statics, dynamics and finite temperature settings. Convergence and stability of the proposed method through numerical analysis will also be discussed. [1] Q. Yang, E. Biyikli, and A. C. To, “Multiresolution molecular mechanics: statics,” Computer Methods in Applied Mechanics and Engineering, 258, 26-38, 2013.