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Stress Wave Propagation in a Gradient Elastic Medium

Chinese Physics Letters 2002年第7期19卷 950-952页

作者：赵亚薄赵涵等 statekeylaboratoryofnon-linearmechanics InstituteofMechanicsChineseAcademyofSciencesBeijing100080 UniversityofPierreandMarieCurie LaboratoiredeMecaniqueetTechnologie-Cachan61A

The gradient elastic constitutive equation incorporating the second gradient of the strains is used to determine the monochromatic elastic plane wave propagation in a gradient infinite medium and thin rod. The equation of motion, together with the internal material length, has been derived. Various dispersion relations have been determined. We present explicit expressions for the relationship between various wave speeds, wavenumber and internal material length.

关键词： Equations of motion

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CHARACTERISTIC DIMENSIONLESS NUMBERS IN MULTI—SCALE AND RATE—DEPENDENT PROCESSES

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China Particuology 2003年第1期1卷 7-12页

作者： YilongBai MengfenXia HaiyingWang FuiiuKe Authortowhomcorrespondenceshouldbeaddressed. statekeylaboratoryofnon-linearmechanics InstituteofMechanicsChineseAcademyofSciencesBeiiing100080P.R.China

Multi-scale modeling of materials properties and chemical processes has drawn great attention from sci-ence and engineering. For these multi-scale and rate-dependent processes, how to characterize their trans-scale for-mulation is a key point. Three questions should be addressed:How do multi-sizes affect the problems?How are length scales coupled with time scales?How to identify emergence of new structure in process and its effect?For this sake, the macroscopic equations of mechanics and the kinetic equations of the microstructural transforma-tions should form a unified set that be solved *** a case study of coupling length and time scales, the trans-scale formulation of wave-induced damage evolution due to mesoscopic nucleation and growth is discussed. In this problem, the trans-scaling could be reduced to two inde-pendent dimensionless numbers: the imposed Deborah number De=(ac)/(LV) and the intrinsic Deborah num-ber D = (nNc5)/V* ,where a. L, c, V and nN are wave speed, sample size, microcrack size, the rate of micro-crack grovvth and the rate of microcrack nucleation density, respectively. Clearly, the dimensionless number De=(ac)l(LV) includes length and time scales on both meso- and macro- Ievels and governs the progressive process. Whereas, the intrinsic Deborah number D' indicates the characteristic transition of microdamage to macroscopic rup-ture since D is related to the criterion of damage localization, which is a precursor of macroscopic rupture. This case study may highlight the scaling in multi-scale and rate-dependent ***, more generally, we compare some historical examples to see how trans-scale formulations were achieved and what are stili open now. The comparison of various mechanisms governing the enhancement of meso-size effects re-minds us of the importance of analyzing multi-scale and rate-dependent processes case by *** multi-scale and rate-dependent processes with chemical reactions and diffusions, there seems to

关键词： multi-scale rate-dependent Deborah number

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