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Practical Time Averaging of Nonlinear Dynamics with Application to Plasticity from Discrete Dislocation Dynamics
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Practical Time Averaging of Nonlinear Dynamics with Application to Plasticity from Discrete Dislocation Dynamics. |
| 개인저자 | Chatterjee, Sabyasachi. |
| 단체저자명 | Carnegie Mellon University. Civil and Environmental Engineering. |
| 발행사항 | [S.l.]: Carnegie Mellon University., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 177 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04B. Dissertation Abstract International |
| ISBN | 9781687991720 |
| 학위논문주기 | Thesis (Ph.D.)--Carnegie Mellon University, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Advisor: Acharya, Amit. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | A novel approach to meso/macroscale plasticity is proposed that does not involve postulating constitutive assumptions beyond those embodied in Discrete Dislocation Dynamics (DD) methodology and macroscopic elastic response. It involves forefront ideas in the mechanics of solids (e.g. continuum mechanics of defects) and applied mathematics, e.g. Young measure theory of averaging for nonlinear Ordinary Differential Equation (ode) systems and their approximation by numerical techniques. This is achieved by a carefully designed coupling of an exact, non-closed Partial Differential Equation (pde) based theory (Mesoscale Field Dislocation Mechanics, MFDM) representing the evolution of averaged dislocation dynamics with DD simulations, MFDM utilizes inputs obtained from space-time averaged response of fast, local DD simulations. The rationale behind using this coupled pde-ode based approach instead of a completely DD based approach is the vast separation in time scales between plasticity applications that operate at quasi-static loading rate (ranging between $10. |
| 요약 | {-6}~s. |
| 요약 | {-1}$ to $1 ~ s. |
| 요약 | {-1}$), and the fundamental time scale of dislocation motion as embodied in DD on the order of nanoseconds. Thus, it is impractical to use conventional DD to reach appreciable strain rates using \\emph{realistic} loading rates. We discuss the method behind generating the required constitutive inputs for MFDM from DD simulations using a rigorous mathematical theory of averaging ode response, and its essential adaptation for practical implementation that we have called Practical Time Averaging (PTA). In the final part, we derive statements for the evolution of coarse variables that represent an averaged behavior of microscopic dislocation dynamics. We show that the exact averaged evolution equations are extremely cumbersome and non-closed and, more often than not, an infinite hierarchy, and therefore it is more reasonable to close it at a low level using inputs obtained from averaged, stress-coupled, interaction dynamics of dislocations. This acts as a further justification for our coupled MFMD-DD approach. |
| 일반주제명 | Mechanics. Materials science. |
| 언어 | 영어 |
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: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
