Finite Strain Measurements Research Articles

Incompatible Deformations of Elastic Plates

This article considers the methods for mathematical modeling of incompatible finite deformations of elastic plates by using the principles of the differential geometry theory underlying continuously distributed defects. Equilibrium equations were derived by asymptotic expansions of the finite strain measures with respect to two small parameters. One parameter defines the order of smallness of displacements from the reference shape (self-stressed state), while the other specifies the thickness. Asymptotic orders were different for the deflections and displacements in the plate plane, as well as for their derivatives. They were selected in such a way that, with additional assumptions on the possibility of ignoring certain terms in the resulting expressions and the compatibility of deformations, the equations could be reduced to the system of F¨oppl–von Ka´rm´an equations.

Early Paleozoic ductile deformation of the South China Block: the polyphase shear zones in the eastern Jiangnan belt

Three parallel east–west-trending shear zones are components of the polyphase shear zones in the eastern Jiangnan belt. The meso- and microstructural characteristics and the estimates of deformation temperatures, vorticities and geochronology of these shear zones provide significant information regarding the tectonic evolution of the South China Block (SCB) during the early Paleozoic. Most shear sense indicators (e.g. asymmetric folds, S-C fabrics and rotating porphyroclasts) reveal that the kinematics were characterized by east–west dextral shear. Finite strain measurements indicate an oblate strain ellipsoid shape with S-type and SL-type tectonites. The rotated rigid porphyroclasts and Mohr circle methods yield vorticity ( Wk ) values of 0.58–0.80 and 0.66–0.89, respectively, indicating that the flow was generally shear-dominated with almost equal proportions of simple and pure shear. Both mineral deformation thermometers and quartz c -axis fabrics indicate that the deformation occurred at medium temperature conditions of 400–550°C. Combined with our new age and regional geological data, the east–west-trending shear zones might represent an increment of deformation during the last period of the early Paleozoic orogeny in the SCB.

Early Paleozoic oblique convergence from subduction to collision: Insights from timing and structural style of the transpressional dextral shear zone in the Qilian orogen, northern Tibet of China

Transpressional shear zones commonly occur in ancient and modern convergent plate boundaries to accommodate oblique plate convergence. The early Paleozoic Qilian orogen in northeastern Tibet records the subduction of Proto-Tethyan Ocean lithosphere and the accretion-collision of various magmatic arcs and continental terranes. This study focused on the Datong ductile shear zone, which represents the central part of the WNW-ESE−striking ductile shear zone along the northern margin of the Qilian block in the Qilian orogen. This structure bears key information about the evolution of oblique convergence during the early Paleozoic orogeny. The kinematics and timing of the Datong ductile shear zone were investigated via field-based, microstructural, and mica 40Ar/39Ar dating analyses. Mesostructural and microstructural data showed predominantly dextral strike-slip shearing within the Datong ductile shear zone. Microstructural features and quartz c-axis crystallographic preferred orientation patterns indicated that dextral ductile shearing occurred under lower-amphibolite-facies conditions (∼500−550 °C and ∼5.6 kbar) within the shear zone. Microstructures of quartz showed subgrain rotation (SGR) and grain boundary migration (GBM), suggesting dislocation creep−dominated deformation. A strain rate of 10−12 s−1 and a differential stress of 25−39 MPa were estimated by the rheological flow law and quartz paleopiezometry. Finite strain measurements indicated that all deformed rocks of the Datong ductile shear zone exhibit a weakly oblate ellipsoid near the plane strain. Kinematic vorticity (ranging 0.47−0.83) analysis suggested the coexistence of simple shear and pure shear strains within the Datong ductile shear zone, indicating a transpressional setting. Biotite and muscovite 40Ar/39Ar data showed that transpressional shearing deformation started in the Ordovician (before 453 Ma) and lasted to the Silurian (ca. 430 Ma). Our new data combined with regional geological data show that the deformation type, kinematics, and dynamics of the Datong ductile shear zone were controlled by the southward oblique subduction of the Paleo-Qilian Ocean (Proto-Tethyan Ocean) and the following oblique collision between the Qilian block and the Alxa block. The intensive transpressional deformation along the northern Qilian block may reflect strong coupling between the subducting Paleo-Qilian oceanic slab and the overriding Qilian block as well as a high degree of convergence obliquity during the ongoing early Paleozoic convergence.

A unified structure-based constitutive model for both tension and shear of passive myocardium

This paper presents a hyperelastic model for replicating the passive response of ventricular myocardium and pericardium using fourth-order structural tensors. Models that can accurately predict mechanical response of cardiac samples are useful in understanding diseased tissues or postulating potential biomaterials for the replacement of damaged tissue in surgical applications. An orthotropic model is postulated here and is demonstrated to perform well in recreating experimental results in a variety of planar biaxial testing protocols and six modes of simple shear. The work outlines the fourth-order structural tensor (FOST) approach to representations of hyperelasticity for prescribing individual microstructural components (or interaction between them) that contribute to the overall elastic response of a biological tissue, through selection of specific FOSTs and constructing fourth-order material tensors possessing the constitutive properties and directional biases of that constituent. A fourth-order scalar product is then performed between this and an appropriately chosen fourth-order finite strain measure that returns a physically meaningful contribution to the strain energy density function for the overall tissue. A structure-based model for ventricular myocardium and pericardium is presented in this work using this approach. In the case of human myocardium, a consistent set of seven material constants simultaneously replicates five planar biaxial tension protocols and six modes of simple shear response.

쌍안경식 로드셀의 유한요소 해석과 변형률 측정

Binocular loadcells are widely used in low-capacity loadcells such as scales because they are easy to manufacture, and the strain distribution at the area where the strain gage is attached is uniforme. For the design of a binocular load cell, generalized prediction for rated output is required, In this paper, to predict the output strain of a binocular type loadcell, a theoretical equation based on the simple beam theory is proposed. In order to evaluate the theoretical equation, finite element analysis and strain measurement tests were performed. For this purpose, strain analysis and strain measurement were conducted on two loadcells, manufactured in this study and a commercially available binocular loadcell. It is shown that the proposed strain formula assumed with a simple beam can be usefully used to predict the rated output of a binocular load cell. The actually measured strain is about 10% lower than theoretical strain due to difference in shape and area effect of a strain gage, and this difference may vary depending on the thickness of the sensing unit..

Pro-Inflammatory Cytokines are Dysregulated in Depression and Correlated With Measures of Psychopathology

This paper presents a kinematic assumption free and thermodynamically consistent non-linear formulation incorporating finite strain and finite deformation for thermoviscoelastic plates/shells based on the conservation and balance laws of the classical continuum mechanics (CCM) in R3 (see Surana and Mathi, (2020) for linear theory). The conservation and balance laws in Lagrangian description with finite strain measure and the conjugate stress measure in R3 are considered. The conjugate pairs in the second law of thermodynamics (SLT), the consideration of additional physics and the principle of equipresence are utilized to determine the constitutive variables and their argument tensors. The constitutive theory for the contravariant second Piola–Kirchhoff stress tensor is derived using Green’s strain tensor and its convected time derivatives of up to order n as its argument tensors using representation theorem with complete basis (i.e. using integrity). The convected time derivatives of the Green’s strain tensor up to order n provide ordered rate constitutive theory for the dissipation mechanism that is naturally non-linear due to Green’s strain measure. The constitutive theory for heat vector derived using representation theorem and integrity is also a non-linear constitutive theory. Simplified linear forms of these constitutive theories are also presented. The solution methods for the mathematical model for the BVPs as well as the IVPs using p-version hierarchical higher degree and higher order finite element method are presented. Due to dissipation, the energy equation is integral part of the mathematical model that accounts for rate of mechanical work resulting in rate of entropy production, hence heat.The plate/shell geometry (flat or curved) is described by its middle surface containing the nodal vectors (at each of the nine nodes), the ends of which define bottom and top surfaces of the plate/shell (Surana and Mathi, 2020). The geometry is mapped into ξηζ natural coordinate space in a two unit cube. The p-version hierarchical local approximations in ξηζ are constructed to describe the deformation of the plate/shell middle surface as well as its faces that is controlled by p-levels in ξ,η and ζ directions (element local approximation). The formulation presented here is accurate for very thin as well as very thick plate/shells and for small as well as finite deformation and finite strains. Non-linear constitutive theories based on integrity allow more complex constitutive behavior in term of strains as well as strain rates, hence dissipation mechanism. Dissipation mechanism is described by an ordered rate theory based on SLT and additional physics. The formulation presented here always ensures thermodynamic equilibrium during the evolution as it is derived using the conservation and balance laws of CCM in R3. The formulation always preserves three dimensional nature of the deformation physics regardless of the plate/shell thickness and is free of locking problems and shear correction factors that plague most of the currently used plate/shell formulations.

Regional White Matter Diffusion Changes Associated with the Cumulative Tensile Strain and Strain Rate in Nonconcussed Youth Football Players.

The purpose of this study is to assess the relationship between regional white matter diffusion imaging changes and finite element strain measures in nonconcussed youth football players. Pre- and post-season diffusion-weighted imaging was performed in 102 youth football subject-seasons, in which no concussions were diagnosed. The diffusion data were normalized to the IXI template. Percent change in fractional anisotropy (%ΔFA) images were generated. Using data from the head impact telemetry system, the cumulative maximum principal strain one times strain rate (CMPS1 × SR), a measure of the cumulative tensile brain strain and strain rate for one season, was calculated for each subject. Two linear regression analyses were performed to identify significant positive or inverse relationships between CMPS1 × SR and %ΔFA within the international consortium for brain mapping white matter mask. Age, body mass index, days between pre- and post-season imaging, previous brain injury, attention disorder diagnosis, and imaging protocol were included as covariates. False discovery rate correction was used with corrected alphas of 0.025 and voxel thresholds of zero. Controlling for all covariates, a significant, positive linear relationship between %ΔFA and CMPS1 × SR was identified in the bilateral cingulum, fornix, internal capsule, external capsule, corpus callosum, corona radiata, corticospinal tract, cerebral and middle cerebellar peduncle, superior longitudinal fasciculus, and right superior fronto-occipital fasciculus. Post hoc analyses further demonstrated significant %ΔFA differences between high-strain football subjects and noncollision control athletes, no significant %ΔFA differences between low-strain subjects and noncollision control athletes, and that CMPS1 × SR significantly explained more %ΔFA variance than number of head impacts alone.

Feldspar microboudinage paleopiezometer and its applications to estimating differential stress magnitudes in the continental middle crust (examples from west Yunnan, China)

Feldspar, which is the most abundant crustal mineral, exhibits brittle behavior while quartz and mica deform plastically by dislocation creep, under the greenschist-facies conditions (300–450 °C). Pull-apart microboudinage, which formed by repeated cycles of tensile fractures, is a common microstructure observed in feldspar porphyroclasts embedded in the ductile matrix of quartz in granitic mylonites from the Red River, Chongshan and Gaoligong shear zones (Yunnan, China). These crustal-scale shear zones, which lie in the southeastern margin of the Tibet Plateau, have played a critical role in the southeastward lateral extrusion of the Indochina composite block in response to the Indo-Asian continental collision. Here we developed a feldspar microboudinage paleopiezometer. In each feldspar porphyroclast, the differential stresses estimated from microboudins progressively increases with sequential fracturing, depicting an evolution during exhumation of the mylonite upwards the brittle-ductile transition. The results from the feldspar microboudinage piezometer and the quartz recrystallized grain-size piezometer are largely consistent within the range of uncertainties. The microboudinage piezometer, combined with results of finite strain measurements, deformation temperature estimates, and thermochronological data, can yield the valuable information about rheological properties of naturally deformed rocks. It can also be directly used or adapted to a wide range of geological problems, for example, fractured pebbles in an unlithified matrix, chromite pods in serpentinized mantle rocks, and strong boudins in a soft material at any scale.

Strain Localizations in Notches for a Coarse-Grained Ni-Based Superalloy: Simulations and Experiments.

Alloys used for turbine blades have to safely sustain severe thermomechanical loadings during service such as, for example, centrifugal loadings, creep and high temperature gradients. For these applications, cast Ni-based superalloys characterized by a coarse-grained microstructure are widely adopted. This microstructure dictates a strong anisotropic mechanical behaviour and, concurrently, a large scatter in the fatigue properties is observed. In this work, Crystal Plasticity Finite Element (CPFE) simulations and strain measurements performed by means of Digital Image Correlations (DIC) were adopted to study the variability introduced by the coarse-grained microstructure. In particular, the CPFE simulations were calibrated and used to simulate the effect of the grain cluster orientations in proximity to notches, which reproduce the cooling air ducts of the turbine blades. The numerical simulations were experimentally validated by the DIC measurements. This study aims to predict the statistical variability of the strain concentration factors and support component design.

A thermodynamically consistent non-linear mathematical model for thermoviscoelastic plates/shells with finite deformation and finite strain based on classical continuum mechanics

This paper presents a kinematic assumption free and thermodynamically consistent non-linear formulation incorporating finite strain and finite deformation for thermoviscoelastic plates/shells based on the conservation and balance laws of the classical continuum mechanics (CCM) in R3 (see Surana and Mathi, (2020) for linear theory). The conservation and balance laws in Lagrangian description with finite strain measure and the conjugate stress measure in R3 are considered. The conjugate pairs in the second law of thermodynamics (SLT), the consideration of additional physics and the principle of equipresence are utilized to determine the constitutive variables and their argument tensors. The constitutive theory for the contravariant second Piola–Kirchhoff stress tensor is derived using Green’s strain tensor and its convected time derivatives of up to order n as its argument tensors using representation theorem with complete basis (i.e. using integrity). The convected time derivatives of the Green’s strain tensor up to order n provide ordered rate constitutive theory for the dissipation mechanism that is naturally non-linear due to Green’s strain measure. The constitutive theory for heat vector derived using representation theorem and integrity is also a non-linear constitutive theory. Simplified linear forms of these constitutive theories are also presented. The solution methods for the mathematical model for the BVPs as well as the IVPs using p-version hierarchical higher degree and higher order finite element method are presented. Due to dissipation, the energy equation is integral part of the mathematical model that accounts for rate of mechanical work resulting in rate of entropy production, hence heat.The plate/shell geometry (flat or curved) is described by its middle surface containing the nodal vectors (at each of the nine nodes), the ends of which define bottom and top surfaces of the plate/shell (Surana and Mathi, 2020). The geometry is mapped into ξηζ natural coordinate space in a two unit cube. The p-version hierarchical local approximations in ξηζ are constructed to describe the deformation of the plate/shell middle surface as well as its faces that is controlled by p-levels in ξ,η and ζ directions (element local approximation). The formulation presented here is accurate for very thin as well as very thick plate/shells and for small as well as finite deformation and finite strains. Non-linear constitutive theories based on integrity allow more complex constitutive behavior in term of strains as well as strain rates, hence dissipation mechanism. Dissipation mechanism is described by an ordered rate theory based on SLT and additional physics. The formulation presented here always ensures thermodynamic equilibrium during the evolution as it is derived using the conservation and balance laws of CCM in R3. The formulation always preserves three dimensional nature of the deformation physics regardless of the plate/shell thickness and is free of locking problems and shear correction factors that plague most of the currently used plate/shell formulations.

Interpreting Experimental Results from Shock Impacts on Single Crystal PETN in the Context of Continuum Models

AbstractIn this paper we interpret previous experimental measurements of impacts on single crystal PETN in the context of a simple continuum model. Hugoniot calculations using the simple model framework under various limiting assumptions envelope measured Hugoniot states reasonably well and suggest that non‐negligible deviatoric elastic strains may exist in the shock compressed state for weak impacts. An accompanying simple kinematic model for lattice deformation was used to estimate the expected shifts in X‐ray diffraction peaks for the (211) plane under impacts normal to (110) planes. The results suggest that negligible relaxation of the deviatoric lattice deformation occurs on the short (10–20 ns) time and wave propagation (40–80 m) scales of laser‐driven shock experiments, and that the corresponding elastic strains may be large. Because of the potentially large deviatoric elastic strains, the specific finite deformation strain measure used within thermomechanical single crystal models is of significant consequence, which is explored numerically by the comparison of isothermal purely elastic responses under uniaxial and simple shear deformations.

2-D finite displacements and strain from particle imaging velocimetry (PIV) analysis of tectonic analogue models with TecPIV

Abstract. Image correlation techniques have provided new ways to analyse the distribution of deformation in analogue models of tectonics in space and time. Here, we demonstrate, using a new version of our software package (TecPIV), how the correlation of successive time-lapse images of a deforming model allows not only to evaluate the components of the strain-rate tensor at any time in the model but also to calculate the finite displacements and finite strain tensor. We illustrate with synthetic images how the algorithm produces maps of the velocity gradients, small-strain tensor components, incremental or instantaneous principal strains and maximum shear. The incremental displacements can then be summed up with Eulerian or Lagrangian summation, and the components of the 2-D finite strain tensor can be calculated together with the finite principal strain and maximum finite shear. We benchmark the measures of finite displacements using specific synthetic tests for each summation mode. The deformation gradient tensor is calculated from the deformed state and decomposed into the finite rigid-body rotation and left or right finite-stretch tensors, allowing the deformation ellipsoids to be drawn. The finite strain has long been the only quantified measure of strain in analogue models. The presented software package allows producing these finite strain measures while also accessing incremental measures of strain. The more complete characterisation of the deformation of tectonic analogue models will facilitate the comparison with numerical simulations and geological data and help produce conceptual mechanical models.

Quantifying the Partition Between Seismic and Aseismic Deformation Along Creeping and Locked Sections of the North Anatolian Fault, Turkey

Shallow aseismic creep is a key deformation component along plate boundaries that contributes to the energy budget during the seismic cycle. Several major active continental faults show spatial alternation of creeping and locked sections. The present study focuses on the evaluation of the aseismic part of the total displacement along the North Anatolian Fault in Turkey. Detailed microstructural analyses of finite strain were performed using various methods, based on change of length or angle, on six representative samples collected over 32 outcrops along locked and creeping sections of the fault. Chemical analyses were used to map mineral composition of fault rocks and to calculate relative volume changes associated with creep. The relationship between finite strain and volume change allowed quantifying the evolution of the penetrative pressure solution cleavage mechanism of creep. In volcanic and analogous creeping rocks, finite strain measurements revealed two spatial scales of strain that correspond to the alternation of two types of shear zones, with cleavages either oblique or sub-parallel to the fault displacement. Using geodetic and geologic data, cumulative aseismic displacement was calculated in the range 9–49% of the total 80-km displacement in the creping sections and was negligible in locked sections. The large uncertainty in the kilometer-width creeping sections was related to the difficulty of quantifying the high strain values associated with high shear displacement and for which measurement uncertainties are large. A promising way to improve such quantification would be to develop reliable statistical analysis of cleavage orientation in the field.

The Research of Low-profile Load Cell Design Sensitivity

This low profile load cells are referred to the current injection molding machine manufacturers commonly used specifications. This study is about the low-profile load cell design by the finite element analysis and experimental strain measurement verification. In the study, two low-profile load cell were designed and analyzed. The A-type cross-section of the sensor is a generally designed cross-section and has sufficient reliability for commercial use. The B-type curve cross-section load cell from the previous study found that can carry a more significant load. In the study, compare the finite element analysis results with the actual strain measurements to verify the correctness of the analysis. In the experimental verification, the two type sections loadcells were calibrated. The load cells were loading from 0kN to 60kN to measure strain values. The strain values were recorded in experiment processes. When the two types of load cell under loading, the loading force, and strain values regression linearity was 99.99 %. The measured values of the A-type and B-type load cells at 60 kN were 298 με and 170 με, and the results matched finite element analysis strain values. It was shown that the setup of boundary conditions and loading method in finite element analysis were acceptable.

A comprehensive kinematic model of single-manifold Cosserat beam structures with application to a finite strain measurement model for strain gauges

In this paper, we investigate the coupling of Poisson’s and warping effect for a general asymmetric cross-section of Cosserat beam. We present the challenges and inconsistencies observed as a result of our attempt to couple the two effects. The fully-coupled Poisson’s transformation is then developed to describe the in-plane deformation for the prismatic beam. A comprehensive kinematic treatment of geometrically exact and nonlinear Cosserat beam subjected to large deformation and finite strain is finally obtained that extensively captures the deformation due to multiple curvatures, torsion, shear, axial deformation, warping and a fully-coupled Poisson’s effect in the cross-section, all while maintaining the single manifold nature of the problem. The contributions to the strain vector and the deformation gradient tensor due to various deformation effects are interpreted and explained in detail. In the final part of the paper, we use the kinematics developed to establish a measurement model of discrete and finite length strain gauges attached to the surface of the beam (or embedded into the beam). We investigate the relationship between the scalar strain measurement of the strain gauge and the local finite strain parameters of the beam.

Variation of second-order piezoelectric coefficients with respect to a finite strain measure.

In this article the consequence of a change of finite strain measure is theoretically considered for nonlinear piezoelectric crystals. Analytical predictions show that second-order piezoelectric coefficients are finite strain measure dependent. Therefore, the use of any finite strain measure in constitutive modelling of piezoelectric materials requires an adequate choice of higher-order piezoelectric coefficients. This allows one to avoid unwanted corrections to the elastic and electric fields in the case of nonlinear modelling of piezoelectric materials, e.g. for piezoelectric heterostructures such as quantum wells or dots. A general transformation formula for second-order piezoelectric coefficients (elastostriction) is derived. As an example, specific transformation formulae for two common crystallographic classes, namely {\bar 4}3m and 6mm, are presented. The piezoelectric coefficients for GaN and GaAs crystals, as representative cases of these crystal classes, are recalculated and their dependence on the strain measure is demonstrated. A further implication of that effect is that a complete set of second-order piezoelectric coefficients should contain additional information about the strain measure applied during calculations or measurements.

Meso- and Neoarchean Banded Iron Formations and Genesis of High-Grade Magnetite Ores in the Anshan-Benxi Area, North China Craton

AbstractThe Anshan-Benxi area in the North China craton has numerous occurrences of Algoma-type banded iron formations (BIFs) with subordinate high-grade magnetite ores. These ores provide insight into iron metallogenesis and early evolution of the North China craton. In this paper, we present Sm-Nd-Fe-O isotope, mineralogical, and structural data for four BIF-type iron deposits to place constraints on their depositional ages and formation mechanism.Previous SIMS and LA-ICP-MS zircon U-Pb dating results indicated a Mesoarchean age (ca. 3.10 Ga) for the Dagushan BIF and a Neoarchean age (ca. 2.55 Ga) for other regional BIFs (Dai et al., 2012, 2013, 2014).This is confirmed by Sm-Nd isochron ages of these BIFs, high-grade magnetite ores, and host metavolcanics, which yield two regression lines and match apparent ages of 3149 ± 85 Ma (MSWD = 1.2) for Dagushan, and 2671 ± 120 Ma (MSWD = 3.0) for the other three deposits. Our new chronological data thus suggest Meso- and Neoarchean BIF deposition and potentially significant BIF-type iron deposits at depth.The regional high-grade magnetite ores are all hosted in the BIFs that occur in the same orientation and have transitional boundaries between them. They also show similar Sm-Nd isotope compositions and magnetite rare earth elements + yttrium (REY) profiles, indicating that the Anshan-Benxi BIFs were most likely the source beds. The high-grade magnetite ores contain abundant pyrite and actinolite, with systematically lower δ56Fe values (0.67–0.40‰) when compared to the BIFs (1.88–0.64‰), suggesting a hydrothermal origin. In the field, some high-grade orebodies with schistose textures are adjacent to undeformed granitic plutons. This geologic relationship implies that the high-grade magnetite ores were formed earlier and probably did not result from magmatic hydrothermal fluids. Therefore we suggest that the Anshan-Benxi high-grade magnetite ores were most likely produced by infiltration of metamorphic fluids into primary BIFs, based on the following: (1) magnetite δ18O values within the high-grade magnetite ores (+2.5 to −0.6‰) are significantly lower than those in the BIFs (9.2–2.6‰); (2) magnetite (avg 0.39 ppm) and pyrite (avg 0.098 ppm) in the high-grade magnetite ores have much lower REY abundances than magnetite in the BIFs (avg 14.6 ppm); (3) skeletal quartz in the high-grade magnetite ores shows systematically higher FeOtolal contents (1.36–0.56 wt %) than those in laminated chert bands (0.06–0.00 wt %); and (4) hydrothermal zircons within the Nanfen BIF yield a U-Pb age of 2480 Ma, which is comparable to ca. 2.48 Ga regional metamorphism (Zhu et al., 2015).Furthermore, microstructural textures indicate a maximum regional deformation temperature of up to 500°C, which is lower than the plastic flow temperature (>600°C) of magnetite. Finite strain measurements and electron backscatter diffraction analyses suggest a general flattening deformation and similar crystallographic preferred orientation for all magnetite crystals. These structural features reveal that magnetite in the high-grade magnetite ores never experienced a separate tectonic event. Our microscopic studies also show that microfractures at the interfaces of BIF bands contain fragmented quartz crystals and are filled with abundant metamorphic minerals (e.g., actinolite and chlorite). Considering that the Anshan-Benxi high-grade magnetite ores are commonly adjacent to weak structural planes (e.g., faults), we propose that macro- and microscopic fractures probably provided channels for metamorphic fluids.Recent zircon U-Pb geochronology has indicated widespread BIF formation at ca. 2.55 Ga in the North China craton, corresponding to a pronounced peak in BIF deposition of other Precambrian cratons. It is thus implied that a global geologic event triggered the extensive occurrence of BIFs. We correlate the Neoarchean tectonic evolution of the North China craton with the 2.7 to 2.5 Ga Kenorland supercontinent. Significantly, planar distribution signatures of the North China craton BIFs indicate ca. 2.5 Ga cratonization through the amalgamation of at least seven microblocks that were welded by several Neoarchean greenstone belts. Hf-Nd isotope studies have highlighted the Archean episodic crustal evolution of the North China craton, and the Meso- and Neoarchean BIF deposition could have benefitted from these geologic processes. The Anshan-Benxi high-grade magnetite ores that formed at ca. 2.48 Ga were closely related to important metamorphic events during the North China cratonization process.

Neoarchean tectonics: Insight from the Baijiafen ductile shear zone, eastern Anshan, Liaoning Province, NE China

The North China Craton is one of the major Archean to Paleoproterozoic cratons in the world and oldest craton in China, which preserves a large amount of ancient basement and abundant structures showing the early earth tectonics. The controversy over the Archean tectonic regimes has lasted several decades centering around horizontal and vertical tectonics, the two classical tectonic models for Archean times. Thus, more studies of the early crustal growth and tectonic evolution are requisite for better understanding geodynamic regimes in the early Precambrian. This study provides an example for revealing of Archean tectonics. The NWN-trending, ENE-dipping Baijiafen ductile shear zone is located in the eastern Anshan of the northeastern North China Craton and mainly comprises two types of gneisses, including the Chentaigou porphyritic granitic gneiss and the Baijiafen trondhjemitic gneiss. In this study, we have carried out a detailed study on the macrostructure, microstructure and fabric characteristics of the two main types of deformed gneisses within the shear zone. The ribbon structures formed by intensely elongated quartz grains are widespread in these gneisses. Well-developed mineral stretching lineations and asymmetric fabrics indicate an ESE-directed downward shearing. The quartz c-axis fabric patterns obtained by electron backscatter diffraction technique imply low to middle temperature non-coaxial deformation with active rhomb 〈a〉 slip and basal 〈a〉 slip. Deformation behaviors of minerals and quartz crystallographic preferred orientations demonstrate that the rocks underwent mylonitization at a temperature of 400–500°C under greenschist facies metamorphic conditions. Dislocation creep is the main rock deformation mechanism within the shear zone. Finite strain measurement results suggest that the strain types of the shear zone are generally related to elongate-plane deformation, and the tectonites change from L-S- to LS-type across the shear zone. The strain intensity increases obviously towards east, and the Baijiafen gneiss unit is located within the high-strain zone. Kinematic vorticity values of gneisses indicate that the deformed rocks were produced by steady-state simple-shear dominated general shear. Based on abundant structural evidence and previous studies, we infer that the deformation of the Baijiafen ductile shear zone may have resulted from the downward adjoining rock flow during the sagduction of the banded iron formations and synchronous Archean granite dome emplacement, supporting a vertical tectonic regime in Archean times.

On a Physical Field Theory of Micropolar Thermoelasticity

A non-linear mathematical model of thermoelastic micropolar continuum is developed. The model is presented in terms of 4-covariant field theoretical formalism. Lagrangian density for thermoelastic continuum with three micropolar directors is given and the least action principle is formulated. Corresponding field equations of micropolar thermoelasticity are obtained. Variational symmetries of the thermoelastic action are used to formulate covariant conservation laws. Following the usual procedure, micropolar thermoelastic Lagrangians are represented as functions of independent rotationally invariant arguments. The latter constitutes a complete system of objective finite strain measures of micropolar thermoelasticity. Constitutive equations of micropolar thermoelasticity are obtained and discussed.

Oblique collision and deformation partitioning in the SW Iberian Variscides

Abstract. Different transpressional scenarios have been proposed to relate kinematics and complex deformation patterns. We apply the most suitable of them to the Variscan orogeny in SW Iberia, which is characterized by a number of successive left-lateral transpressional structures developed in the Devonian to Carboniferous period. These structures resulted from the oblique convergence between three continental terranes (Central Iberian Zone, Ossa-Morena Zone and South Portuguese Zone), whose amalgamation gave way to both intense shearing at the suture-like contacts and transpressional deformation of the continental pieces in-between, thus showing strain partitioning in space and time. We have quantified the kinematics of the collisional convergence by using the available data on folding, shearing and faulting patterns, as well as tectonic fabrics and finite strain measurements. Given the uncertainties regarding the data and the boundary conditions modeled, our results must be considered as a semi-quantitative approximation to the issue, though very significant from a regional point of view. The total collisional convergence surpasses 1000 km, most of them corresponding to left-lateral displacement parallel to terrane boundaries. The average vector of convergence is oriented E–W (present-day coordinates), thus reasserting the left-lateral oblique collision in SW Iberia, in contrast with the dextral component that prevailed elsewhere in the Variscan orogen. This particular kinematics of SW Iberia is understood in the context of an Avalonian plate salient currently represented by the South Portuguese Zone.