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Statistical Mesomechanics of Solid, Linking Coupled Multiple Space and Time Scales

[+] Author and Article Information
Y. L. Bai

State Key Laboratory of Non-linear Mechanics (LMN), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P. R. China

H. Y. Wang

State Key Laboratory of Non-linear Mechanics (LMN), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P. R. China

M. F. Xia

State Key Laboratory of Non-linear Mechanics (LMN), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P. R. China and Department of Physics, Peking University, Beijing 100871, P. R. China

F. J. Ke

State Key Laboratory of Non-linear Mechanics (LMN), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P. R. China and Department of Applied Physics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China

Appl. Mech. Rev 58(6), 372-388 (Nov 01, 2005) (17 pages) doi:10.1115/1.2048654 History:

This review begins with the description of a new challenge in solid mechanics: multiphysics and multiscale coupling, and its current situations. By taking spallation as an example, it is illustrated that the fundamental difficulty in these multiscale nonequilibrium problems is due to the hierarchy and evolution of microstructures with various physics and rates at various length levels in solids. Then, some distinctive thoughts to pinpoint the obstacles and outcome are outlined. Section 3 highlights some paradigms of statistical averaging and new thoughts to deal with the problems involving multiple space and time scales, in particular the nonequilibrium damage evolution to macroscopic failure. In Sec. 4, several frameworks of mesomechanics linking multiple space and time scales, like dislocation theory, physical mesomechanics, Weibull theory, and stochastic theory, are briefly reviewed and the mechanisms underlying the trans-scale coupling are elucidated. Then we turn to the frameworks mainly concerning damage evolution in Sec. 5, namely, statistical microdamage mechanics and its trans-scale approximation. Based on various trans-scale frameworks, some possible mechanisms governing the trans-scale coupling are reviewed and compared in Sec. 6. Since the insight into the very catastrophic transition at failure is closely related to strong trans-scale coupling, some new concepts on nonequilibrium and strong interaction are discussed in Sec. 7. Finally, this review is concluded with a short summary and some suggestions. “This review article cites 130 references.”

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Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Damage mechanics in the perspective of the expansion of human knowledge (3)

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Figure 2

Schematic illustration of the microscopic, mesoscopic, and macroscopic length scales in a polycrystal (59)

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Figure 3

Microscopic and macroscopic scales in traditional statistical physics

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Figure 4

The solution region of microdamage number density n0(t,C,C0). The shaded indicates where nonzero solution locates. C=Cf(C0,t) or C0=C0f(C,t) are the microdamage fronts moving upward (114).

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Figure 5

Effects of De* on damage localization trans-scale sensitivity (116)

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Figure 6

(a) Quasi-Fibonacci series (1,2,3,5,8,13,20,…) of breaking is a sensitive microstructure for cascading, In (b), the cascading will stop at a stable status (71).

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Figure 7

Critical sensitivity of cluster mean field (CMF) model (N=10,000, β=2) (125)

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