| Summary: | 博士 === 國立清華大學 === 動力機械工程學系 === 93 === A novel clustered atomistic-continuum mechanics (CACM) method, based on the finite element theory, has been proposed to simulate the mechanical characteristics of the nano-scaled structures. To accomplish the nano-scaled mechanical numerical simulation via CACM, the specific atomic groups are modeled as the clustered elements and the chemical bonding energies between the said clustered groups are described. Hence, the mechanical characteristics of the nano-scaled structure could be represented by the numerical model of CACM. The transient mechanical response of the nano-scaled molecules and the interested chemical bonds could be analyzed by the proposed method. Comparing the proposed method with the conventional molecule dynamic (MD) method, the CACM could efficiently extend total atom numbers from thousands atoms to million atoms, the total simulated time from nano seconds to seconds and the time step from femto second to micron second. Moreover, the CACM could simulate the structure with several different kinds of the chemical binding energies.
The dsDNA molecule is treated as the test vehicle of the proposed CACM method. Through dsDNA CACM model, the mechanics of dsDNA could be represented visually. Moreover, the numerical simulations exhibit good agreements with the experimental results which are obtained by the single molecule manipulation technique. Additionally, the response of the chemical bonds in dsDNA while applying the external loading would be then elucidated, including the stacking energy bonds and hydrogen bonds. Moreover, the mechanical characteristic of the dsDNA with different sequence would be then understood.
Since the analyzed domain of the dsDNA related problem is the nano-scale, both the micro-scaled mechanics (quantum mechanics) and the macro-scaled mechanics (continuum mechanics) should be considered. Therefore, the nano-scaled modeling should consider the size effect, the complementary of the classical and quantum mechanics and the experimental oriented modeling method. In order to implement the said modeling theory, the proposed CACM is based on the continuum mechanics, and it is deduced form the micro-macro numerical analysis technique of the finite element method. Moreover, the CACM comprises both the clustered atomistic and atomistic-continuum methods. The clustered atomistic method treats the covalent bond atom groups as clustered elements with effective characteristic properties. The atomistic-continuum method transfers from the stacking energy and hydrogen bond energy into the different types of virtual elements. Therefore, the freely-untwisting dsDNA model could be numerically represented by the CACM, and the simulation result could be obtained by the transient finite element solver. Good agreement was achieved between the numerical simulation and single molecular experimental results, with the mechanical behavior of stretching dsDNA being revealed.
Furthermore, the predictive capability of the dsDNA model based on the CACM would be then investigated. The numerical models of the stretching both-strand-fixed dsDNA and that of the unzipping the dsDNA were established, respectively. Good agreements between these two models and experimental results were achieved. Moreover, the simulation results of the both-strand-fixed dsDNA under tensile loading clarified the mechanical behavior of dsDNA stretching. Additionally, the sequence-dependent mechanical response of the unzipping dsDNA would be reveal by the simulation results of the dsDNA CACM, and the molecular biological phenomenon, such as the replication and transcription, could be then understood.
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