Smeared crack approach: back to the original track

This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh‐size and mesh‐bias spurious dependence when the method is applied ‘straightly’. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd.     

Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry

Experimental results are presented from the extensive program of drained plane strain compression tests on sand carried out in Grenoble over the last two decades. Systematic analysis of photographs of the deforming specimen allowed for measuring deformations and determining strain fields throughout the test, that is: prior to, at, and after the onset of strain localization. The principles, details and accuracy of the procedure are described, as well as its suitability to properly depict the patterns of deformation. Findings concerning the occurrence and progression of strain localization are discussed. The issues of shear band orientation and thickness are addressed, as well as temporary and persistent complex localization patterns, and the volumetric behaviour inside a band after its formation. The influence of such variables as initial state of the sand (effective stress and relative density), specimen size and slenderness, as well as grain size, is discussed. Copyright © 2004 John Wiley & Sons, Ltd     

The second order characteristic condition for plastic flow

In this paper the second order characteristic (discontinuous bifurcation) condition is derived for the granular flow (fully plastic) equations. This second order bifurcation equation is shown to be formally identical to the first order localization requirement during steady elastoplastic deformation provided the elastic compliance tensor is substituted for the product of the plastic multiplier with the flow Hessian. For isotropic yield and flow functions the invariant form of the characteristic condition is given in detail, as well as an alternative expression in adapted co‐ordinates. The characteristic condition can be regarded as defining a hardening function which is maximized to identify the critical angles. When the method is applied to 3D Coulomb flow, Mohr's 3D fracture plane conditions are obtained uniquely. Copyright © 2003 John Wiley & Sons, Ltd.     

资源环境领域的信息化与本土化

本文重点论述了资源环境领域的深层研究问题;同时提出用信息化推动现代化的观点,进而对地球信息科学与数字地球的战略进行了概要地分析。     

Strain localization due to structural in-homogeneities in the Central European Basin System

The large-scale crustal deformations observed in the Central European Basin System (CEBS) are the result of the interplay between several controlling factors, among which lateral rheological heterogeneities play a key role. We present a finite-element integral thin sheet model of stress and strain distribution within the CEBS. Unlike many previous models, this study is based on thermo-mechanical data to quantify the impact of lateral contrasts on the tectonic deformation. Elasto-plastic material behaviour is used for both the mantle and the crust, and the effects of the sedimentary fill are also investigated. The consistency of model results is ensured through comparisons with observed data. The results resemble the present-day dynamics and kinematics when: (1) a weak granite-like lower crust below the Elbe Fault System is modelled in contrast to a stronger lower crust in the area extending north of the Elbe Line throughout the Baltic region; and (2) a transition domain in the upper mantle is considered between the shallow mantle of the Variscan domain and the deep mantle beneath the East European Craton (EEC), extending from the Elbe Line in the south till the Tornquist Zone. The strain localizations observed along these structural contrasts strongly enhance the dominant role played by large structural domains in stiffening the propagation of tectonic deformation and in controlling the basin formation and the evolution in the CEBS.     

An evaluation of residential air radon concentrations and related variables in southeast Michigan,USA

Analysis of 153 residential air radon (Rn-222) screening measurements from southeast Michigan indicates that basements host Rn levels two to three times higher than upper-level rooms. Compared to unfinished basements, finished (e.g., paneled walls, tiled floors) basements apparently reduce indoor air Rn levels while partially finished basements may not. Factor analysis of residence questionnaire data explains 59 percent of the Rn data variance. The volume of pathways (e.g., foundation cracks/holes, uncapped sumps) allowing Rn seepage into the dwelling controls the largest portion, 23 percent, of the explained data variance. The residence water source explains 11 percent of the Rn data variance. Groundwater Rn levels contribute to the air Rn data variability, but the study data cannot quantitatively assess this contribution. Seven percent of the Rn data variance is likely controlled by house depressurization facilitated by residence structural properties. Residences with foundation cracks or poorly sealed joints and low-volume indoor-outdoor air exchange are more prone to this effect. Eighteen percent of the explained Rn data variance correlates with the residence's primary heat source. Evidently, operating combustion sources also induce house depressurization and allow Rn to be drawn into the house through entry paths. Twenty-four percent of the analyses equal or exceed 4 pCi/1 Rn. In residences occupied 5 years by the same individuals, 17 percent of the Rn data are 4 pCi/l; here the arithmetic mean air Rn level is 8.3 pCi/l and the average occupancy period 17.4 years.     

Origin of Gold—Bearing Fluid and Its Initiative Localization Mechanism in Xiadian Gold Deposit,Shandong Province

The composition of quartz inclusions and trace elements in ore indicate that gold-bearing fluid in the Xiadian gold deposit,Shandong Province,stemmed from both mantle and magma,belonging to a composite origin.Based on theoretical analysis and high temperature and high pressure experimental studies,gold-bearing fluid initiative localization mechanism and the forming environment of ore-host rocks are discussed in the present paper.The composite fluid extracted gold from rocks because of its expanding and injecting forces and injecting forces and flew through ore-conducive structures,leading to the breakup of rocks.The generation of ore-host faults and the precipitation of gold-bearing fluid occurred almost simultaneously.This study provides fur-ther information about the relationships between gold ore veins and basic-ultrabasic vein rocks and intermediate vein rocks,the spatial distribution of gold ore veins and the rules governing the migration of ore fluids.     

Reaction localization and softening of texturally hardened mylonites in a reactivated fault zone, central Argentina

The Tres Arboles ductile fault zone in the Eastern Sierras Pampeanas, central Argentina, experienced multiple ductile deformation and faulting events that involved a variety of textural and reaction hardening and softening processes. Much of the fault zone is characterized by a (D2) ultramylonite, composed of fine‐grained biotite + plagioclase, that lacks a well‐defined preferred orientation. The D2 fabric consists of a strong network of intergrown and interlocking grains that show little textural evidence for dislocation or dissolution creep. These ultramylonites contain gneissic rock fragments and porphyroclasts of plagioclase, sillimanite and garnet inherited from the gneissic and migmatitic protolith (D1) of the hangingwall. The assemblage of garnet + sillimanite + biotite suggests that D1‐related fabrics developed under upper amphibolite facies conditions, and the persistence of biotite + garnet + sillimanite + plagioclase suggests that the ultramylonite of D2 developed under middle amphibolite facies conditions. Greenschist facies, mylonitic shear bands (D3) locally overprint D2 ultramylonites. Fine‐grained folia of muscovite + chlorite ± biotite truncate earlier biotite + plagioclase textures, and coarser‐grained muscovite partially replaces relic sillimanite grains. Anorthite content of shear band (D3) plagioclase is c. An30, distinct from D1 and D2 plagioclase (c. An35). The anorthite content of D3 plagioclase is consistent with a pervasive grain boundary fluid that facilitated partial replacement of plagioclase by muscovite. Biotite is partially replaced by muscovite and/or chlorite, particularly in areas of inferred high strain. Quartz precipitated in porphyroclast pressure shadows and ribbons that help define the mylonitic fabric. All D3 reactions require the introduction of H⁺ and/or H₂O, indicating an open system, and typically result in a volume decrease. Syntectonic D3 muscovite + quartz + chlorite preferentially grew in an orientation favourable for strain localization, which produced a strong textural softening. Strain localization occurred only where reactions progressed with the infiltration of aqueous fluids, on a scale of hundreds of micrometre. Local fracturing and microseismicity may have induced reactivation of the fault zone and the initial introduction of fluids. However, the predominant greenschist facies deformation (D3) along discrete shear bands was primarily a consequence of the localization of replacement reactions in a partially open system.     

Dynamic analysis of strain localization in water‐saturated clay using a cyclic elasto‐viscoplastic model

A computational framework is presented for dynamic strain localization and deformation analyses of water‐saturated clay by using a cyclic elasto‐viscoplastic constitutive model. In the model, the nonlinear kinematic hardening rule and softening due to the structural degradation of soil particles are considered. In order to appropriately simulate the large deformation phenomenon in strain localization analysis, the dynamic finite element formulation for a two‐phase mixture is derived in the updated Lagrangian framework. The shear band development is shown through the distributions of viscoplastic shear strain, the axial strain, the mean effective stress, and the pore water pressure in a normally consolidated clay specimen. From the local stress–strain relations, more brittleness is found inside the shear bands than outside of them. The effects of partially drained conditions and mesh‐size dependency on the shear banding are also investigated. The effect of a partially drained boundary is found to be insignificant on the dynamic shear band propagation because of the rapid rate of applied loading and low permeability of the clay. Using the finer mesh results in slightly narrower shear bands; nonetheless, the results manifest convergency through the mesh refinement in terms of the overall shape of shear banding and stress–strain relations. Copyright © 2013 John Wiley & Sons, Ltd.     

Reaction softening by dissolution–precipitation creep in a retrograde greenschist facies ductile shear zone,New Hampshire,USA

We describe strain localization by a mixed process of reaction and microstructural softening in a lower greenschist facies ductile fault zone that transposes and replaces middle to upper amphibolite facies fabrics and mineral assemblages in the host schist of the Littleton Formation near Claremont, New Hampshire. Here, Na‐poor muscovite and chlorite progressively replace first staurolite, then garnet, and finally biotite porphyroblasts as the core of the fault zone is approached. Across the transect, higher grade fabric‐forming Na‐rich muscovite is also progressively replaced by fabric‐forming Na‐poor muscovite. The mineralogy of the new phyllonitic fault‐rock produced is dominated by Na‐poor muscovite and chlorite together with late albite porphyroblasts. The replacement of the amphibolite facies porphyroblasts by muscovite and chlorite is pseudomorphic in some samples and shows that the chemical metastability of the porphyroblasts is sufficient to drive replacement. In contrast, element mapping shows that fabric‐forming Na‐rich muscovite is selectively replaced at high‐strain microstructural sites, indicating that strain energy played an important role in activating the dissolution of the compositionally metastable muscovite. The replacement of strong, high‐grade porphyroblasts by weaker Na‐poor muscovite and chlorite constitutes reaction softening. The crystallization of parallel and contiguous mica in the retrograde foliation at the expense of the earlier and locally crenulated Na‐rich muscovite‐defined foliation destroys not only the metastable high‐grade mineralogy, but also its stronger geometry. This process constitutes both reaction and microstructural softening. The deformation mechanism here was thus one of dissolution–precipitation creep, activated at considerably lower stresses than might be predicted in quartzofeldspathic rocks at the same lower greenschist facies conditions.