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Multiresolution molecular mechanics : = Theory and applications.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Multiresolution molecular mechanics :/
Reminder of title:	Theory and applications.
Author:	Yang, Qingcheng.
Description:	1 online resource (198 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:	Dissertation Abstracts International78-05B(E).
Subject:	Mechanical engineering. -
Online resource:	click for full text (PQDT)
ISBN:	9781369418965

Multiresolution molecular mechanics : = Theory and applications.
Yang, Qingcheng.

Multiresolution molecular mechanics :Theory and applications. - 1 online resource (198 pages)

Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

A general mathematical framework, Multiresolution Molecular Mechanics (MMM), is proposed to consistently coarse-grain molecular mechanics at different resolutions in order to extend the length scale of nanoscale modeling of crystalline materials. MMM is consistent with molecular mechanics in the sense that the constitutive description such as energy and force calculations is exactly the same as molecular mechanics and no empirical and phenomenological constitutive relationships in continuum mechanics are employed. As such, MMM can converge to full molecular mechanics naturally.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369418965Subjects--Topical Terms:

557493
Mechanical engineering.
Index Terms--Genre/Form:

554714
Electronic books.

Multiresolution molecular mechanics : = Theory and applications.
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099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Yang, Qingcheng. $3 1180410
245 1 0 $a Multiresolution molecular mechanics : $b Theory and applications.
264 0 $c 2016
300 $a 1 online resource (198 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
500 $a Adviser: Albert C. To.
502 $a Thesis (Ph.D.) $c University of Pittsburgh $d 2016.
504 $a Includes bibliographical references
520 $a A general mathematical framework, Multiresolution Molecular Mechanics (MMM), is proposed to consistently coarse-grain molecular mechanics at different resolutions in order to extend the length scale of nanoscale modeling of crystalline materials. MMM is consistent with molecular mechanics in the sense that the constitutive description such as energy and force calculations is exactly the same as molecular mechanics and no empirical and phenomenological constitutive relationships in continuum mechanics are employed. As such, MMM can converge to full molecular mechanics naturally.
520 $a As many coarse-graining approaches, MMM is based on approximating the total potential energy of a full atomistic model. Analogous to quadrature rules employed to evaluate energy integrals in finite element method (FEM), a summation rule is required to evaluate finite energy summations. Most existing summation rules are specifically designed for the linear interpolation shape function and their extensions to high order shape functions are currently not clear. What distinguishes MMM from existing works is that MMM proposes a novel summation rule framework SRMMM that is valid and consistent for general shape functions. The key idea is to analytically derive the energy distribution of the coarse-grained atomistic model and then choose some quadrature-type (sampling) atoms to accurately represent the derived energy distribution for a given shape function. The optimal number, weight and position of sampling atoms are also determined accordingly, similar to the Gauss quadrature in FEM. The governing equations are then derived following the variational principle.
520 $a The proposed SRMMM is verified and validated numerically and compared against many other summation rules such as Gauss-quadrature-like rule. And SRMMM demonstrates better performance in terms of accuracy and computational cost. The convergence property of MMM is also studied numerically and MMM shows FEM-like behavior under certain circumstance. In addition, MMM has been applied to solve problems such as crack propagation, atomic sheet shear, beam bending and surface relaxations by employing high order interpolation shape functions in one (1D), two (2D) and three dimensions (3D) .
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mechanical engineering. $3 557493
655 7 $a Electronic books. $2 local $3 554714
690 $a 0548
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Pittsburgh. $3 1178873
773 0 $t Dissertation Abstracts International $g 78-05B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10298881 $z click for full text (PQDT)