Spallation analysis with a closed trans-scale formulation damage evolution

A closed, trans-scale formulation of damage evolution based on the statistical microdamage mechanics is summarized in this paper. The dynamic function of damage bridges the mesoscopic and macroscopic evolution of damage. The spallation in an aluminium plate is studied with this formulation. It is found that the damage evolution is governed by several dimensionless parameters, i.e., imposed Deborah numbers De* and De, Mach number M and damage number S. In particular, the most critical mode of the macroscopic damage evolution, i.e., the damage localization, is deter-mined by Deborah number De+. Deborah number De* reflects the coupling and competition between the macroscopic loading and the microdamage growth. Therefore, our results reveal the multi-scale nature of spallation. In fact, the damage localization results from the nonlinearity of the microdamage growth. In addition, the dependence of the damage rate on imposed Deborah numbers De* and De, Mach number M and damage number S is discussed.

Microdamage Evolution, Energy Dissipation and Their Trans-Scale Effects on Macroscopic Failure

The process of damage evolution concerns various scales, from micro- to macroscopic. How to characterize the trans-scale nature of the process is on the challenging frontiers of solid mechanics. In this paper, a closed trans-scale formulation of damage evolution based on statistical microdamage mechanics is presented. As a case study, the damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that the following dimensionless numbers: reduced Mach number M, damage number S, stress wave Fourier number P, intrinsic Deborah number D*, and the imposed Deborah number De*, govern the whole process of deformation and damage evolution. The evaluation of P and the estimation of temperature increase show that the energy equation can be ignored as the first approximation in the case of spallation. Hence, apart from the two conventional macroscopic parameters: the reduced Mach number M and damage number S, the damage evolution in spallation is mainly governed by two microdamage-relevant parameters: the Deborah numbers D* and De*. Higher nucleation and growth rates of microdamage accelerate damage evolution, and result in higher damage in the target plate. In addition, the mere variation in nucleation rate does not change the spatial distribution of damage or form localized rupture, while the increase of microdamage growth rate localizes the damage distribution in the target plate, which can be characterized by the imposed Deborah number De*.

Critical Sensitivity and Trans-Scale Fluctuations in Catastrophic Rupture

Rupture in the heterogeneous crust appears to be a catastrophe transition. Catastrophic rupture sensitively depends on the details of heterogeneity and stress transfer on multiple scales. These are difficult to identify and deal with. As a result, the threshold of earthquake-like rupture presents uncertainty. This may be the root of the difficulty of earthquake prediction. Based on a coupled pattern mapping model, we represent critical sensitivity and trans-scale fluctuations associated with catastrophic rupture. Critical sensitivity means that a system may become significantly sensitive near catastrophe transition. Trans-scale fluctuations mean that the level of stress fluctuations increases strongly and the spatial scale of stress and damage fluctuations evolves from the mesoscopic heterogeneity scale to the macroscopic scale as the catastrophe regime is approached. The underlying mechanism behind critical sensitivity and trans-scale fluctuations is the coupling effect between heterogeneity and dynamical nonlinearity. Such features may provide clues for prediction of catastrophic rupture, like material failure and great earthquakes. Critical sensitivity may be the physical mechanism underlying a promising earthquake forecasting method, the load-unload response ratio (LURR).

Trans-Scale Mechanics: Looking For The Missing Links Between Continuum And Micro/Nanoscopic Reality

Problems involving coupled multiple space and time scales offer a real challenge for conventional frameworks of either particle or continuum mechanics. In this paper, four cases studies (shear band formation in bulk metallic glasses, spallation resulting from stress wave, interaction between a probe tip and sample, the simulation of nanoindentation with molecular statistical thermodynamics) are provided to illustrate the three levels of trans-scale problems (problems due to various physical mechanisms at macro-level, problems due to micro-structural evolution at macro/micro-level, problems due to the coupling of atoms/molecules and a finite size body at micro/nano-level) and their formulations. Accordingly, non-equilibrium statistical mechanics, coupled trans-scale equations and simultaneous solutions, and trans-scale algorithms based on atomic/molecular interaction are suggested as the three possible modes of trans-scale mechanics.

Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena. (C) 1997 Published by Elsevier Science B.V.

Habitat degradation and conservation status assessment of gallinaceous birds in the Trans-Himalayas, China

The greatest concentration of Chinese Galliformes occurs in the Trans-Himalayas. We selected 4 northwestern Yunnan counties (Lijiang, Shangri-la, Deqin, and Weixi) in the Trans-Himalayas to assess the conservation status of 9 gallinaceous forest birds. We

A standard CMOS compatible monolithic photo-detector and trans-impedance amplifier

A 1GHz monolithic photo-detector (PD) and trans-impedance amplifier (TIA) is designed with the standard 0.35 mu m CMOS technique. The design of the photo-detector is analyzed and the CMOS trans-impedance amplifier is also analyzed in the paper. The integrating method is described too. The die photograph is also showed in the paper.

Temperature sensitivity of soil respiration is affected by prevailing climatic conditions and soil organic carbon content: A trans-China based case study

National Natural Science Foundation of China [30590381]; Knowledge Innovation Program of the Chinese Academy of Sciences [KZCX2YW-432]; International Partnership Project

Thiophene-NPN Ligand Supported Rare-Earth Metal Bis(alkyl) Complexes. Synthesis and Catalysis toward Highly trans-1,4 Selective Polymerization of Butadiene

A series of new rare-earth metal bis(alkyl) complexes [L(1-3)Ln(CH2SiMe3)(2)(THF)(n)] (L-1 = MeC4H2SCH2NC6H4(Ph)(2)P=NC6H2Me3-2,4,6: Ln = Sc, n = 1 (1a); Ln = Lu, n = 1 (1b); L-2 = MeC4H2SCH2NC6H4(Ph)(2)P=NC6H3Et2-2,6: Ln = Sc, n = 1 (2a); Ln = Lu, n = 1 (2b); Ln = Y, n = 1 (2c); L-3 = MeC4H2SCH2NC6H4(Ph)(2)P=(NC6H3Pr2)-Pr-i-2,6: Ln = Sc, n = 0 (3a)) and (LSc)-Sc-4(CH2SiMe3)(2()THF) (4a) (L-4 = C6H5CH2NC6H4(Ph)(2)P=NC6H3Et2-2,6) have been prepared by reaction of rare-earth metal tris(alkyl)s with the corresponding HL1-4 ligands via alkane elimination.