Remote Boundary Research Articles

Generalized effective fields method in peridynamic micromechanics of random structure composites

We consider a static problem for statistically homogeneous matrix linear bond-based peridynamic composite materials (CMs). For the media subjected to remote homogeneous volumetric boundary loading, one proved that the effective behavior of this media is governed by conventional effective constitutive equation as in the local elasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional elasticity of composite materials (CMs) with their adaptation to peridynamics. This is extraction from the material properties a constituent of the matrix properties. Effective moduli are expressed through the introduced new notion of the average local polarization tensor. The average is performed over the surface of the extended inclusion phase rather than over an entire space. Any spatial derivatives of displacement fields are not required. The basic hypotheses of locally elastic micromechanics are generalized to their peridynamic counterparts. In particular, in the generalized effective field method (EFM) proposed, the effective field is evaluated from self-consistent estimations by the use of closing of a corresponding integral equation in the framework of the quasi-crystalline approximation. In so doing, the classical effective field hypothesis is relaxed, and the hypothesis of the ellipsoidal symmetry of the random structure of CMs is not used. One demonstrates some similarity and difference with respect to other methods (the dilute approximation and Mori-Tanaka approach) proposed before in micromechanics of peridynamic CMs. Comparative numerical analyses of these methods are performed for 1D case.

Regional Versus Remote Atmosphere‐Ocean Drivers of the Rapid Projected Intensification of the East Australian Current

AbstractLike many western boundary currents, the East Australian Current (EAC) extension is projected to get stronger and warmer in the future. The CMIP5 multimodel mean (MMM) projection suggests up to 5°C of warming under an RCP85 scenario by 2100. Previous studies employed Sverdrup balance to associate a trend in basin wide zonally integrated wind stress curl (resulting from the multidecadal poleward intensification in the westerly winds over the Southern Ocean) with enhanced transport in the EAC extension. Possible regional drivers are yet to be considered. Here we introduce the NEMO‐OASIS‐WRF coupled regional climate model as a framework to improve our understanding of CMIP5 projections. We analyze a hierarchy of simulations in which the regional atmosphere and ocean circulations are allowed to freely evolve subject to boundary conditions that represent present‐day and CMIP5 RCP8.5 climate change anomalies. Evaluation of the historical simulation shows an EAC extension that is stronger than similar ocean‐only models and observations. This bias is not explained by a linear response to differences in wind stress. The climate change simulations show that regional atmospheric CMIP5 MMM anomalies drive 73% of the projected 12 Sv increase in EAC extension transport whereas the remote ocean boundary conditions and regional radiative forcing (greenhouse gases within the domain) play a smaller role. The importance of regional changes in wind stress curl in driving the enhanced EAC extension is consistent with linear theory where the NEMO‐OASIS‐WRF response is closer to linear transport estimates compared to the CMIP5 MMM.

A numerical study of the effects of overload on fatigue crack growth in plastically compressible hardening and hardening-softening-hardening solids

Variation of cyclic loading effect on fatigue crack growth is investigated under plane strain and small scale yielding (SSY) conditions. The material is characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The influence of cyclic stress intensity factor range (), load ratio (R), number of cycles (N), plastic compressibility ( overload and material softening on near tip deformation was studied in detail. For comparison purpose, a few results pertaining to plastically incompressible solids are also considered. The crack tip opening displacement (CTOD), plastic crack growth, deformed crack tip shape, plastic zone shape and size near the crack tip appear to depend significantly on R, N, overload and material softening. The overload produces strong plastic deformation ahead of the crack tip and decreases the fatigue crack growth substantially. Highlights Variation of cyclic loading effect on fatigue crack growth is investigated for materials characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Both plastically compressible and incompressible solids are considered. The influence of cyclic stress intensity factor range (), load ratio (R), number of cycles (N), plastic compressibility ( overload and material softening on near tip deformation was studied in detail. The crack tip opening displacement, plastic crack growth, plastic zone shape and size near the crack tip appear to depend significantly on R, N, overload and material softening. The combination of softening or softening-hardening material response and plastic compressibility leads to major deviations in crack tip blunting and fatigue crack growth from those that prevail for a hardening material.

Generalized Mori–Tanaka Approach in Micromechanics of Peristatic Random Structure Composites

A statistically homogeneous random matrix medium with the bond-based peridynamic properties (see Silling, J Mech Phys Solids 48:175–209, 2000) of constituents is considered. For the media subjected to remote homogeneous volumetric boundary loading, one proved that the effective behavior of this media is described by conventional effective constitutive equation which is intrinsic to the local elasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional elasticity of CMs and adapted to peristatics. This is extraction from the material properties a constituent of the matrix properties. Effective properties moduli are expressed through the introduced local stress polarization tensor averaged over the extended inclusion phase rather than in an entire space. One proposes a generalization of a dilute approximation method to their peristatic counterpart in the sense that the volume fraction of the particles is small and their mutual interaction can be neglected. As in a classical approach, the essential assumption in the generalized Mori–Tanaka method (MTM) states that each extended inclusion behaves as an isolated one in the infinite matrix and subject to some effective strain field coinciding with the average strain in the truncated matrix. Comparative numerical analyses of both the dilute approximation and MTM method are performed for 1D case.

Very high stratospheric influence observed in the free troposphere over the northern Alps – just a local phenomenon?

Abstract. The atmospheric composition is strongly influenced by a change in atmospheric dynamics, which is potentially related to climate change. A prominent example is the doubling of the stratospheric ozone component at the Zugspitze summit station (2962 m a.s.l., Garmisch-Partenkirchen, Germany) between the mid-seventies and 2005, roughly from 11 to 23 ppb (43 %). Systematic efforts for identifying and quantifying this influence have been made since the late 1990s. Meanwhile, routine lidar measurements of ozone and water vapour carried out at Garmisch-Partenkirchen (German Alps) since 2007, combined with in situ and radiosonde data and trajectory calculations, have revealed that stratospheric intrusion layers are present on 84 % of the yearly measurement days. At Alpine summit stations the frequency of intrusions exhibits a seasonal cycle with a pronounced summer minimum that is reproduced by the lidar measurements. The summer minimum disappears if one looks at the free troposphere as a whole. The mid- and upper-tropospheric intrusion layers seem to be dominated by very long descent on up to hemispheric scale in an altitude range starting at about 4.5 km a.s.l. Without interfering air flows, these layers remain very dry, typically with RH ≤5 % at the centre of the intrusion. Pronounced ozone maxima observed above Garmisch-Partenkirchen have been mostly related to a stratospheric origin rather than to long-range transport from remote boundary layers. Our findings and results for other latitudes seem to support the idea of a rather high contribution of ozone import from the stratosphere to tropospheric ozone.

Boundary Crossing Problems for Compound Renewal Processes

We find sharp asymptotics of the probability that the trajectory of a compound renewal process crosses (or does not cross) an arbitrary remote boundary. In particular, some limit theorems are obtained for the distribution of the maximum of the process in the domain of large deviations. We also give some applications to the classical ruin probability problem in insurance theory.

Vertical Profiling of Aerosols With a Combined Raman‐Elastic Backscatter Lidar in the Remote Southern Ocean Marine Boundary Layer (43–66°S, 132–150°E)

AbstractA combined Raman‐elastic backscatter lidar, deployed aboard the research vessel RV Investigator for two campaigns for a total of 10 week's ship time, is used to quantify the properties of aerosols within the remote Southern Ocean marine boundary layer between Australia and Antarctica in the region 43–66°S and 132–150°E. Eleven Raman case studies are identified for analyses. Particle linear depolarization ratio and height‐resolved lidar ratio S, calculated from the Raman retrievals, are consistent with values expected within the surface mixed layer for clean marine conditions. We determine S=(19±7) sr across the Southern Ocean with the Raman lidar observations. Aerosol optical properties in the marine boundary layer close to Tasmania (43°S) sometimes indicate the influence of continental air masses. Aerosol optical depth at 355 nm calculated from the retrieved Raman extinction profiles within the surface mixed layer is τ=(0.11±0.04). Boundary‐layer height is determined from the lidar observations and decreases from (0.9±0.4) km north of the Polar Front (around 55°S) to (0.7±0.2) km south of the Polar Front. Dried sea salt is present above the midlatitude ocean in the dehumidified decoupled layer in different synoptic‐scale atmospheric conditions including beneath a high‐pressure system and in a post‐frontal air mass. At all latitudes across the Southern Ocean, large aerosol backscatter, low depolarization ratio, and high relative humidity indicate the presence of sea salt droplets within the well‐mixed near‐surface layer.

Integro-Local Theorems in Boundary Crossing Problems for Compound Renewal Processes

We find sharp asymptotics for the probability that the moment when the trajectory of a compound renewal process crosses an arbitrary remote boundary lies in a prescribed small time interval. As a key step in our proof, we obtain limit theorems for the conditional distribution of jumps of the process when the endpoint of the trajectory of a compound renewal process is fixed.

PROCESSING JUMP POINT OF LIDAR DETECTION DATA AND INVERSING THE AEROSOL EXTINCTION COEFFICIENT

Abstract. For a long time, the research of the optical properties of atmospheric aerosols has aroused a wide concern in the field of atmospheric and environmental. Many scholars commonly use the Klett method to invert the lidar return signal of Mie scattering. However, there are always some negative values in the detection data of lidar, which have no actual meaning，and which are jump points. The jump points are also called wild value points and abnormal points. The jump points are refered to the detecting points that are significantly different from the surrounding detection points, and which are not consistent with the actual situation. As a result, when the far end point is selected as the boundary value, the inversion error is too large to successfully invert the extinction coefficient profile. These negative points are jump points, which must be removed in the inversion process. In order to solve the problem, a method of processing jump points of detection data of lidar and the inversion method of aerosol extinction coefficient is proposed in this paper. In this method, when there are few jump points, the linear interpolation method is used to process the jump points. When the number of continuous jump points is large, the function fitting method is used to process the jump points. The feasibility and reliability of this method are verified by using actual lidar data. The results show that the extinction coefficient profile can be successfully inverted when different remote boundary values are chosen. The extinction coefficient profile inverted by this method is more continuous and smoother. The effective detection range of lidar is greatly increased using this method. The extinction coefficient profile is more realistic. The extinction coefficient profile inverted by this method is more favorable to further analysis of the properties of atmospheric aerosol. Therefore, this method has great practical application and popularization value.

Effect of the Lüders plateau on ductile fracture with MBL model

In this study, the effect of Lüders plateau on the ductile crack growth resistance has been investigated with the Gurson damage model and the modified boundary layer (MBL) model, under mode I plane strain condition. The Lüders plateau is modeled as horizontal by keeping the plateau stress equaling to the yield stress. A family of Lüders elongations ranging from 0 to 5% has been considered. The remote boundary condition of the MBL model is governed by the elastic K-field and T-stress. Numerical results show that the existence of the Lüders plateau on the stress-strain curve reduces the ductile crack growth resistance. The degree of reduction depends on the scale of the Lüders elongation. The crack tip stress field analysis indicates that the existence of the Lüders plateau varies the crack tip stress striaxiality distribution and the magnitude. It is also found that the size of plastic zone ahead of the crack tip is reduced, compared with the reference case for material without Lüders plateau. It is demonstrated that the effect of Lüders plateau on ductile crack growth is more significant at lower T-stress or for materials with higher toughness. The dependence of the initial void volume fraction and the T-stress on the ductile crack growth resistance are alleviated when the Lüders elongation is large.

Do remote boundary conditions affect photodetection?

ABSTRACTWe study the photocurrent statistics in a homodyne setup with a mirror in the vacuum port. Conventional photodetection theory predicts a modulation of the photocurrent noise due to the mirror. We show that the mirror changes the quantum efficiency of the detector and affects both the mean and noise of the photocurrent. We discuss detector design parameters that will enhance this effect.

Analysis for T-stress of cracks in 3D anisotropic elastic media by weakly singular integral equation method

This paper proposes an efficient numerical procedure for computing T-stresses of cracks in three-dimensional, linearly elastic, infinite media. The technique is established in a broad framework allowing a medium made of generally anisotropic materials and cracks of arbitrary shape and under general loading conditions to be treated. A pair of weakly singular, weak-form, displacement and traction boundary integral equations is utilized to formulate the key equations governing the unknown crack-face fields. Besides the basic benefits such as the reduction of spatial dimensions of the solution space and the efficient treatment of unbounded domains and remote boundary data, use of such integral equations in the formulation offers additional positive features including the computational simplicity resulting from the weakly singular nature of all involved integrals and the involvement of a complete set of crack-face displacement fields. A weakly singular symmetric Galerkin boundary element method together with the special near-front approximation is utilized to solve for the unknown relative crack-face displacement whereas the sum of the crack-face displacement is obtained from the displacement boundary integral equation for cracks via the Galerkin technique. The latter step is one of the essential aspects of the present study that provides the direct means for determining the T-stress data in terms of the sum of the crack-face displacement in the neighborhood of the crack-front. An extensive numerical study is conducted for various scenarios and a selected set of results is reported to demonstrate both the accuracy and capability of the proposed technique.

Comparison of two key analysis methods for the seismic stability of equipment on the example of a ventilation unit

Results of calculation seismic resistance analysis of light equipment of nuclear power plants performed on the example of a ventilation unit using two most common analytical techniques - linear spectral analysis and direct dynamic methods - are discussed. The basic concepts, assumptions and limitations of the linear spectral method are described. Examples are given of specific calculation cases when the method in question is not applicable in the generally accepted formulation. In particular, the phase difference and, possibly, accelerations (displacements) must be taken into consideration in the calculations of extended spatial structures for mutually remote boundary conditions. Another example are the reservoirs not completely filled with liquids. In such case waves may be formed in the liquid and taking them into account is not possible in the linear spectral method. Specific features are examined of application of the dynamic analysis method including the input data, approaches and methodologies required for synthesizing the calculated accelerograms. A sequence of operations performed during synthesizing calculated accelerograms is provided, materials are provided containing the description of the mathematical apparatus applied for deriving the final mathematical relations for calculating response spectra and the calculation relations as such are given. The concept of the damping coefficient is explained, its influence on the calculated results and the approaches to its determination are demonstrated. Options with complete absence of damping and with absolute damping are discussed. A real ventilation set applied in active ventilation systems of nuclear power plants was accepted as the test model. Results calculated for the detailed finite-element model of the ventilation unit using the Zenith-95 software package are presented. These results include the distribution of the calculated reduced stresses. Analysis of the results obtained using the two methods demonstrated overestimation of calculated results by the linear spectral method as compared to those obtained by the dynamic analysis method, which means that the former method underestimates the equipment’s resistance to seismic effects. In addition, the dynamic method shows additional areas in the ventilation unit where significant reduced stresses are found while the linear spectral method ignores these areas.

Impacts of bromine and iodine chemistry on tropospheric OH and HO<sub>2</sub>: comparing observations with box and global model perspectives

Abstract. The chemistry of the halogen species bromine and iodine has a range of impacts on tropospheric composition, and can affect oxidising capacity in a number of ways. However, recent studies disagree on the overall sign of the impacts of halogens on the oxidising capacity of the troposphere. We present simulations of OH and HO2 radicals for comparison with observations made in the remote tropical ocean boundary layer during the Seasonal Oxidant Study at the Cape Verde Atmospheric Observatory in 2009. We use both a constrained box model, using detailed chemistry derived from the Master Chemical Mechanism (v3.2), and the three-dimensional global chemistry transport model GEOS-Chem. Both model approaches reproduce the diurnal trends in OH and HO2. Absolute observed concentrations are well reproduced by the box model but are overpredicted by the global model, potentially owing to incomplete consideration of oceanic sourced radical sinks. The two models, however, differ in the impacts of halogen chemistry. In the box model, halogen chemistry acts to increase OH concentrations (by 9.8 % at midday at the Cape Verde Atmospheric Observatory), while the global model exhibits a small increase in OH at the Cape Verde Atmospheric Observatory (by 0.6 % at midday) but overall shows a decrease in the global annual mass-weighted mean OH of 4.5 %. These differences reflect the variety of timescales through which the halogens impact the chemical system. On short timescales, photolysis of HOBr and HOI, produced by reactions of HO2 with BrO and IO, respectively, increases the OH concentration. On longer timescales, halogen-catalysed ozone destruction cycles lead to lower primary production of OH radicals through ozone photolysis, and thus to lower OH concentrations. The global model includes more of the longer timescale responses than the constrained box model, and overall the global impact of the longer timescale response (reduced primary production due to lower O3 concentrations) overwhelms the shorter timescale response (enhanced cycling from HO2 to OH), and thus the global OH concentration decreases. The Earth system contains many such responses on a large range of timescales. This work highlights the care that needs to be taken to understand the full impact of any one process on the system as a whole.

Boundary-based finite element method for two-dimensional anisotropic elastic solids with multiple holes and cracks

A special boundary element for the two-dimensional anisotropic elastic solids containing a single elliptical hole or crack is applied. The main feature of this special boundary element is that no meshes are needed along the hole or crack boundary. Take this special boundary element as a base, in this paper a new method called boundary-based finite element method is developed to deal with the problems of two-dimensional anisotropic elastic solids containing multiple holes and cracks. This method is established by using the relation between nodal force of finite element and surface traction of boundary element. With the aid of this relation, a combination of boundary elements can be transformed into a single finite element. By purposely arranging each subregion with a single hole or crack and assembling the entire region according to the rule of finite element method, the problems with multiple holes and cracks can be solved. Furthermore, simple formulae to evaluate the stress concentration factor of hole and the stress intensity factors of crack are derived, by which these factors can be evaluated by using only the remote boundary displacements and tractions. Accuracy and efficiency are illustrated by comparison with analytical solutions, conventional boundary element, and finite element method.

On the Distribution of the First Passage Time of a Random Walk to an Arbitrary Remote Boundary

Under conditions close to the minimal conditions, we find the local and integral asymptotics for the joint distribution of the first passage time by a random walk of an arbitrary remote boundary and the overshoot over that boundary.

Finite deformation analysis of crack tip fields in plastically compressible hardening–softening–hardening solids

Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic–viscoplastic constitutive relation with various hardening–softening–hardening hardness functions. Both plastically compressible and plastically incompressible solids are considered. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The initial crack is taken to be a semi-circular notch and symmetry about the crack plane is imposed. Plastic compressibility is found to give an increased crack opening displacement for a given value of the applied loading. The plastic zone size and shape are found to depend on the plastic compressibility, but not much on whether material softening occurs near the crack tip. On the other hand, the near crack tip stress and deformation fields depend sensitively on whether or not material softening occurs. The combination of plastic compressibility and softening (or softening–hardening) has a particularly strong effect on the near crack tip stress and deformation fields.

Enhanced elastic-foundation analysis of balanced single lap adhesive joints

Conventional single-lap adhesive joints between identical adherends achieve ultimate strength only after significant inelastic deformation of the adhesive and perhaps also the adherends. However purely elastic analysis provides insights and is relevant to fatigue initiation or brittle failure. We extend classical beam-based elastic results, both ‘within the bond’ (deriving more-accurate peak peel stress from the joint-edge moment) and ‘beyond the bond’ (determining the edge moment from adherend dimensions, remote boundary conditions, and load).Within the bond, we show that peak adhesive equivalent stress and principal stress are minimized when the bond length exceeds four characteristic lengths of the elastic-foundation shear stress equation. This makes simplified ‘long’ joint formulas attractive for initial design. We then examine how well the long-joint predicted peak peel stress matches plane strain finite element analysis, and empirically capture a peel-stress end effect due to nonzero adhesive Poisson ratio. With this end-effect correction, the limit of useful accuracy can be expressed as a ratio Ra of (adherend axial stiffness) to (adhesive axial stiffness) being > a number of order 102-103 depending on Poisson ratio. This limit supplements the Goland and Reissner proposed applicability limit for elastic foundation analysis, expressed as a limiting ratio Rv of through-thickness or vertical stiffnesses.Outside the bond, Timoshenko-style beam-column expressions are used to derive a simplified joint-edge moment factor. While similar in spirit to the edge-moment determination of Goland and Reissner for infinite-length pinned adherends, treating the bond region as a rigid block leads to simpler nonlinear expressions, and captures the moment-reducing benefits of shorter (finite-length) adherends and fixed-slope end conditions. Joint rotation effects become dominant when TL2>E̅I (L is adherend free length, T is tensile load), then joint rotation magnitude depends on TD2/E̅I (D is lap length).

A numerical investigation of the interannual-to-interpentadal variability of the along-shelf transport in the Middle Atlantic Bight

A numerical simulation using the Regional Ocean Modeling System (ROMS) indicates that there was significant interannual-to-interpentadal variability of along-shelf transport and water properties over the Middle Atlantic Bight (MAB) from 2004 to 2013. To examine the relative contribution from local atmospheric forcing versus remote oceanic open boundary forcing to such low-frequency variability, we implement a suite of process oriented numerical experiments. Results show that the interannual variability is dominated by remote forcing from the open boundaries of the region rather than by local atmospheric forcing. The penetration of the Labrador Current into the region contributes to a significant increase of along-shelf transport in the winters of 2009 and 2010. By contrast, the anti-cyclonic mesoscale eddies associated with the Gulf Stream decrease the background along-shelf jet and, in certain cases, even reverse the along-shelf transport. In addition, the along-shelf transport appears to possess an interpentadal variation, i.e., weaker during 2004–2008 but stronger during 2009–2013, which is found caused by the migration of the Gulf Stream.

Strip-electro-mechanical yield model for transversely situated two semi-permeable collinear cracks in piezoelectric strip

A strip-electro-mechanical model is proposed for two semi-permeable collinear cracks, symmetrically situated and transversely oriented in a poled piezoelectric strip. The remote boundary of the strip is subjected to mode-III stress and in-plane electric-displacement. Fourier series method together with integral equation method is employed to obtain the analytic solution. Expressions are derived for crack-sliding displacement, crack opening potential drop, intensity factors and energy release rate. Also, explicit expressions for developed slide-yield and saturation zones are derived. An illustrative case study is presented for poled PZT-5H, BaTiO3, PZT-6B and PZT-7A piezoelectric ceramics to study the capability of the strip-electro-mechanical yield model for the crack arrest. Results obtained are graphically presented, discussed and concluded.