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Thermoelastic problems refer to a coupled phenomenon existing in a wide range of practical applications where elastic responses are influenced by temperature variation. Meanwhile, Moving Morphable Void (MMV) approach receives extensive attentions owing to explicit topological geometric information. In MMV method, a closed B-spline curve defined by several design variables is adopted to describe void material in design domain. In present study, we intend to use the MMV method to topologically optimize the thermoelastic structures under uniform temperature increment and varying temperature field. The weak formulations of heat conduction and elasticity are combined to describe the thermoelastic problems. The optimization mathematical model with the aim of compliance minimization and volume constraint is constructed. The sensitivity of design variables is derived by material derivative method and adjoint sensitivity analysis method. The method of moving asymptote (MMA) algorithm is implemented to update the design variables for finding the best material distribution. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

Learning similar motor skills in close succession is limited by interference, a phenomenon that takes place early after acquisition when motor memories are unstable. Interference can be bidirectional, as the first memory can be disrupted by the second (retrograde interference), or the second memory can be disrupted by the first (anterograde interference). The heightened plastic state of primary motor cortex after learning is thought to underlie interference, as unstable motor memories compete for neural resources. While time-dependent consolidation processes reduce interference, the passage of time (~6 h) required for memory stabilization limits our capacity to learn multiple motor skills at once. Here, we demonstrate in humans that prolonged training at asymptote of an initial motor skill reduces both retrograde and anterograde interference when a second motor skill is acquired in close succession. Neurophysiological assessments via transcranial magnetic stimulation reflect this online stabilization process. Specifically, excitatory neurotransmission in primary motor cortex increased after short training and decreased after prolonged training at performance asymptote. Of note, this reduction in intracortical excitation after prolonged training was proportional to better skill retention the following day. Importantly, these neurophysiological effects were not observed after motor practice without learning or after a temporal delay. Together, these findings indicate that prolonged training at asymptote improves the capacity to learn multiple motor skills in close succession, and that downregulation of excitatory neurotransmission in primary motor cortex may be a marker of online motor memory stabilization.

Flow behavior inside rotors can be very complicated and with three-dimensional characteristics. This fact added to a large number of free geometrical parameters that can be varied makes the design of these components a difficult task. Optimization techniques can be applied to generate optimized designs for these machines. In this work, a different approach to design rotors by using topology optimization is proposed. An objective function measured at the boundaries and derived from energy dissipation inside the domain is used with the continuous adjoint approach considering a rotating reference frame for the governing equations. Cyclic boundary conditions are used to represent rotational repeating patterns. The Finite Volume Method is used to solve the direct and adjoint problems, and an implementation of the Globally Convergent Method of Moving Asymptotes (GCMMA) is applied. Numerical examples are presented and an optimized design is compared with a traditional one.

This work reports on optimizing the Indirect Indentation Method for measuring the elastic properties of brittle materials by indentation. The method employs a thin metallic film that protects the brittle material by absorbing the inelastic damage causes by the penetrating indenter. It applies hyperbolic identities to the Zhou-Prorok Model for thin film indentation that approach an asymptote as the indenter advances toward the film/substrate interface. The slope of this asymptote has been shown to be directly related to the elastic modulus of the brittle material being tested. A parameter study was conducted and revealed that the method can be optimized when the film Poisson’s ratio is lower than the brittle material tested. This more directly transfers the indenter load to the substrate, enabling it to participate in the composite elastic response earlier in the indentation process. The result is an expanded range of fit of the experimental data to the models linear asymptote, providing more accurate elastic property measurements. Chromium was identified as an ideal film material due to its low Poisson’s ratio, ductility and ability to be deposited onto most ceramics with a strong interface. The improvement was demonstrated on 5 brittle materials with a wide variety of elastic properties; SiC, Al2O3, MgO, SiO2, CaCO3.

The main purpose of this paper is to propose a novel efficient design optimization technique based on the operational quadrature boundary element method (OQBEM) for a simulation study on the material distribution and influence of rotation on the optimal design of rotating anisotropic viscoelastic porous permeable structures. An implicit differentiation method was developed to calculate the design sensitivities of displacements and pore pressure with respect to design variables and the effects of rotation on these sensitivities are also discussed. The optimization problem is solved using the Moving Asymptotes Method (MAM) which requires the calculation of the sensitivities for objective function and constraints by adjoint variable method. The optimum shape design of an elliptical sandwich structure is used as the numerical example to verify the validity and accuracy of the proposed technique.

This paper aims to develop an efficient concurrent topology optimization approach for minimizing the maximum dynamic response of two-scale hierarchical structures in the time domain. Compared with statics problems, the dynamic response problems usually involve many time steps, which may lead to intensive computational burdens in both dynamic response and sensitivity analyses. This study thus proposes an enhanced decoupled sensitivity analysis method for concurrent topology optimization of the time-domain dynamic response problems. The mode acceleration method is incorporated for efficient dynamic response analysis. The three-field density-based approach is employed for topology optimization of macrostructure and microstructure. A previously proposed aggregation functional is employed to approximate the maximum dynamic response of the structure. The method of moving asymptotes (MMA) is employed to update the design variables. Three numerical examples are presented to demonstrate the effectiveness of the proposed approach. Some discoveries regarding the concurrent topology optimization for dynamics problems are presented and discussed. Furthermore, the potential of the concurrent topology optimization formulation for designing lightweight structures under dynamic loads is also demonstrated.

In current optimization methods for free-form shells, the shape and topology are usually optimized separately. These methods are based on the assumption that the shape and topology of a shell influence each other only slightly, but this is not always correct. Moreover, different parameterization models are used in the shape optimization and topology optimization of free-form shells, which brings difficulties to carry out the integrated optimization. To solve this problem, an integrated method is proposed for simultaneously optimizing shape and topology for free-form shells. A uniform parameterization model based on NURBS solids is established to parameterize the free-form shells. In this model, only a small number of variables are used to describe both the shape and topology of the shell. In this way, the integrated optimization problem can be simplified, thus decrease the computational complexity. The integrated optimization of shape and topology is a complicated and large-scale optimization problem. Solving this problem requires a suitable optimization method. In this paper, the Method of Moving Asymptotes (MMA) is adopted. Finally, numerical examples are presented to address the importance of the optimization sequences and show the effectiveness and application of the proposed method.

In this paper, we present a new approach to identify all material parameters of flexoelectric materials based on electrical impedance curves. This approach combines an Isogeometric Analysis (IGA) formulation with a gradient-based optimization algorithm using the Method of Moving Asymptotes (MMA). The IGA formulation allows for efficient modeling of flexoelectricity taking advantage of the higher order continuity of IGA. The proposed methodology starts with determining preliminary real parts based on resonant modes in order to avoid local minima which gives the numerical impedance curves close to the experimental impedance curve. The results in the preliminary step are used as initial parameters of the refinement step to simultaneously determine both real and imaginary part by minimizing the difference between pseudo-experimental and numerical impedance curve. Some numerical examples are illustrated to show the good agreement between the numerical and pseudo-experimental impedance curves.

The structures in thermal environment often suffer from severe thermal expansion, potentially leading to buckling failure. This study aims to address this issue by proposing multi-material topology optimization for thermomechanical buckling problems. The density-based model with the rational approximation of material properties (RAMP) is adopted here for parameterization of multiple materials. The sensitivities of thermomechanical compliance and buckling are derived through the adjoint technique. The globally convergent version of the method of moving asymptotes (GCMMA) is employed to solve the non-monotonic topology optimization problem. In this study, two numerical examples are presented to illustrate the effectiveness of the proposed method, in which the total volume of multi-materials is minimized subject to thermoelastic compliance and buckling constraints. The examples exhibit significant difference in the final topologies for mechanical buckling and thermomechanical buckling optimization. The study demonstrates the importance of thermomechanical buckling criteria for the design of structures operating in a temperature-varying environment.

Within the platform of unsteady, one-dimensional heat conduction in simple solid objects (large plate, long cylinder and sphere) cooled/heated with uniform surface temperature, the three important thermal quantities that need to be quantified are: the center temperature, the mean temperature and the total heat transfer. One objective of the study is the accurate determination of new dimensionless critical times for the mean and center temperatures that describe the large time sub-domain using a symbolic algebra software. Another objective of the study is to use regression analysis to construct plain correlation asymptotes for the center temperature, the mean temperature and the total heat transfer in the small time sub-domain using as input data the exact, analytical temperature distributions for the plate, cylinder and sphere expressed by infinite series for all time. Excellent agreement for the center temperature, mean temperature and total heat transfer are achieved in the small time sub-domain using the two different computational procedures.

Search for possible ways of the binary information storage evoked an interest in the mechanism of the electrochemical monomer/dimer switching. Thus, determination of the rate of radical-to-dimer conversion became an issue. Mathematical formulation describing the electrochemical generation of a radical followed by a bimolecular chemical reaction contains a quadratic term, in which case the inverse Laplace transformation does not exist. Until now, kinetic data were obtained by using finite difference simulations. We report an alternative and simpler evaluation method, which uses the frequency dependence of the faradaic impedance. Determination of the required surface concentration uses convoluted voltammogram recorded at the same bulk concentration as the impedance data. Functional dependence of the faradaic phase angle on frequency (cot ϕ vs. ω1/2) shows a maximum at lower frequencies containing information on the dimerization kinetics and a linear asymptote at the highest frequency range yields the electron transfer rate. This new procedure was applied to four different known redox systems, all involving radical dimerization process.

We describe the development of a fluid-coupled 2D extended finite element method (XFEM) algorithm to model the propagation of nonplanar radially-symmetric hydraulic fractures. The model determines the fracture propagation trajectory according to the maximum tangential stress criterion of Erdogan and Sih (1963). An implicit level-set algorithm (ILSA) is employed for locating the moving fracture front. The aim of the paper is to validate the radially-symmetric XFEM-ILSA model for nonplanar fracture propagation for mixed modes I and II. First, the results of the model are compared to the analytical solution for viscosity-dominated propagation of a penny-shaped crack. Next, we compare the results of the XFEM-ILSA scheme to the results of laboratory experiments and the results of an axisymmetric displacement discontinuity model for the near-surface propagation of hydraulic fractures with fluid lag (Bunger et al., 2013). For this comparison, a mixed-mode toughness tip asymptote is employed within ILSA to locate the fracture front. An improved algorithm is used for locating the fluid front within the fracture.

Reactive Powder Concrete-Filled Steel Tube (RPC-FST) is a new composite section with ultra-high strength, good plasticity and ductility to withstand blast loading. This paper is devoted to introduce an analytical method for evaluating the damage level of RPC-FST column suffered fire attack and the following blast load. The damage indexes of RPC-FST column has experienced ISO-834 standard fire and subsequent blast load are predicted using Pressure-Impulse (P-I) diagram. The analytical approaches are proposed based on equivalent Single Degree of Freedom (SDOF) model, in which the damping dissipation, thermal effect and axial load are included. In order to clarify the influences of temperature distribution and explosive charge on the damage index, an inclusive P-I function, characterized by three variables: pressure, impulse and fire duration, is presented. Then blast-resistant results of four fire-damaged RPC-FST columns are employed to validate the reliabilities of presented method. Parametric analysis is conducted to investigate the impacts of damping ratio and ductility ratio on the structural damages. It is demonstrated that a larger damping would lead to better structural blast-resistance. The asymptote value of quasi-static zone tends to smaller as the ductility ratio increases, either the asymptote value of impulse zone, which results in a larger safe area for structural member. In addition, the damaged level is governed by impulse load as scaled distance decreases. The analytical damage indexes are well validated by experimental data.

This paper deals with the study of size effect on structural strength for quasi-brittle materials under mode I fracture conditions. By using a linear cohesive crack model, accurate numerical simulations were performed to compute the size effect curves for two test configurations – namely, the three-point bending test with span-to-depth ratio equal to 3 and the center crack panel test – featuring sharp notches and blunt notches whose width is also scaled with the specimen dimension. The analysis of the results shows that, as the specimen size tends to infinity, the asymptotic behavior depends on the type of notch. For sharp notches the size effect curve tends asymptotically to Bažant’s Size Effect Law. On the contrary, for blunt notches the size effect curve tends to a horizontal asymptote corresponding to the elastic limit. The elastic limit can be calculated by the tensile strength reduced by the stress concentration factor at the tip of the blunt notch and it depends on the geometry of the specimen. Furthermore, the numerical results were utilized to derive the expression of a Generalized Cohesive Size Effect Curve (GCSEC) which agrees well with Bažant’s Universal Size Effect Law (USEL) and with some experimental data gathered from the literature.

Nonlinear fluid viscous dampers have been widely used in energy-dissipation structures. This paper is devoted to the stochastic optimal design of viscous dampers for large-scale structures under non-stationary random seismic excitations. The optimization problem is formulated as the minimization of the standard deviation of a target displacement component subjected to the constraint on the standard deviations of damping forces of viscous dampers, and the method of moving asymptotes (MMA), a gradient-based optimization method, is employed to solve the optimization problem involved. An effective dimension-reduced explicit method is first proposed for fast nonlinear time-history analysis of structural responses and the corresponding sensitivity analysis with respect to the parameters of viscous dampers, in which only a small number of degrees of freedom associated with the viscous dampers need to be considered in the iteration scheme, leading to extremely low computational cost in the nonlinear analysis. Then the proposed dimension-reduced explicit method is further used to conduct sample analyses with high efficiency in Monte-Carlo simulation (MCS) so as to obtain the statistical moments of critical responses and the relevant moment sensitivities required in the process of optimal design. To demonstrate the feasibility of the proposed method, the stochastic optimal design of viscous dampers is carried out for a large-scale suspension bridge with a main span of 1688 m, and the mean peak values of critical responses with the optimal parameters of viscous dampers are finally obtained for the design purpose of the bridge.

Energy-dissipation devices have been widely used for seismic mitigation of civil structures. Stochastic optimization of energy-dissipation devices has emerged as an appealing means to achieve optimal seismic performance of structures in uncertain environment. This paper proposes an effective optimization framework for nonlinear viscous dampers of large-scale structures in consideration of both random seismic excitations and uncertain damper parameters. A dimension-reduced explicit time-domain method (ETDM) is employed for nonlinear time-history analysis of seismic responses and response sensitivities with respect to the nominal parameters of uncertain viscous dampers. To obtain the statistical moments of critical responses and the corresponding moment sensitivities, the high-efficient ETDM is then used in conjunction with the Monte-Carlo simulation (MCS) with sufficient samples of seismic excitation and damper parameters. The stochastic response and sensitivity results are further utilized for stochastic optimization of the nominal values of damper parameters with the method of moving asymptotes (MMA). The present optimization framework represents a hybrid approach combining the existing ETDM, MCS and MMA. A large-scale suspension bridge installed with nonlinear viscous dampers with uncertain parameters is analyzed to demonstrate the feasibility of the proposed optimization framework, and the influence of the uncertainties of damper parameters on stochastic optimization is also investigated.

In this work, we revisit a classical problem of Hamiltonian-type systems of second-order elliptic PDE in bounded domains. Recalling the famous critical hyperbola associated with this problem, we propose an approach where one of the nonlinearities has a polynomial growth over this hyperbola’s asymptotes, which allows the other one to have exponential growth. We establish solutions for these critical systems by using the reduction by inversion method and some new results for sharp Adams Inequality and Concentration–Compactness for high order N -Laplace operators.

There are renewed interests in grid-stiffened composite structures due to the high structural stability and damage tolerance enabled by multiple intersected stiffeners . The limited design space of repeated straight grid patterns has been remarkably expanded by introducing non-uniform curved grid-stiffened composite structures (NCGCs). In this work, curved stiffener layout optimization for NCGCs with a central cutout is investigated to maximize the critical buckling load under a given weight constraint. The design framework is developed by calling ABAQUS for simulating stiffened models and using numerical sensitivities in order to adopt gradient-based optimization algorithm, where the computational time depends not only on simulation but also the number of design variables. To increase the efficiency, an improvement is proposed based on globally convergent method of moving asymptotes (GCM), as one of the most popularly used structural optimization algorithms, by relaxing the conservativeness (CR-GCM) with an additional relaxation factor and an adaptive limit of the iteration number . Numerical examples show that optimal curved stiffeners around the cutout have the ability to remarkably increase the structural buckling load and the proposed CR-GCM demonstrates the ability of better balancing the computational efficiency and convergence in the optimization process.

This paper presents a pressure-impulse (P-I) diagram method for predicting failure modes of reactive powder concrete (RPC) one-way slabs subjected to blast loading. This method involves two loosely-coupled single-degree-of-freedom (SDOF) models and the proposed failure criteria. Motion functions, resistance functions and dynamic mechanical properties of RPC are considered in predicting the dynamic response of RPC one-way slabs. Deformation of RPC one-way slabs predicted using a theoretical approach correlate well with the explosion test results. According to previous studies, the flexural-shear failure of structural members occurs at high pressures and impulses. However, analysis results show that only shear failure occurs under these conditions once the shear fracture criterion is introduced. A new shear failure region is found in the P-I diagram. Parametric studies show that the asymptotes of P-I curves increase with increasing slab depth, longitudinal reinforcement ratio, and RPC compressive strength, and decreasing slab length and load level. When the boundary condition changes from clamped to simply-supported, the asymptote values of flexural P-I curves decrease, while the asymptote values of shear P-I curves increase. In addition, the applicability of the improved P-I diagrams approach in practical evaluation is illustrated through a case study.

Compliant mechanism-based microdevices with multiple inputs and multiple outputs have a wide range of applications in precision mechanics, e.g., cell manipulation, electronic microscopy and MEMS (Micro-Electro-Mechanical Systems). In designing this kind of microdevice, the movement coupling among the microdevices becomes critical because many inputs and outputs are involved. This paper presents a systematic method for designing fully decoupled compliant mechanisms with multiple degrees of freedom by using topology optimization. An optimization formulation is posed by considering both output coupling and input coupling issues to achieve fully decoupled motion. The SIMP (Solid Isotropic Material with Penalization) and MMA (Method of Moving Asymptotes) methods are adopted to identify the optimized material distribution in the design domain. Several numerical examples are presented to demonstrate the validity of the proposed method.

Large eddy simulations are conducted to investigate transient three-dimensional flows past arrays of finite plates translating in the vicinity of a wall. Flows around a single plate are examined for a wide range of wall distances at a Reynolds number based on plate height of 50,000. The drag coefficient decreases rapidly when the plate is placed very close to the wall; it reaches a maximum at an intermediate distance and it asymptotes to the value corresponding to unconfined flows as the gap between the wall and the plate is increased. The reduction in drag coefficient is directly related to the pressure drop caused by vortices generated upstream of the plate induced by the close proximity of the wall. Temporal and spatial characteristics of flows past arrays of yawed plates are examined for the wall distance ratio of 1.5 and the spacing ratios of 2.5 and 5. Drag coefficient of the plates is larger than those placed away from the wall. With suitable spacing the wall proximity effects result in an increase of drag force exerted on the plates. The present study aids in optimizing marine energy harvesting systems that have blades translating beneath ocean platforms or floating river docks.

Basic models of the farfield waves created by a monohull ship or a catamaran that travels at a constant speed in calm water of uniform finite depth are considered. A classical basic model is the 1-point ship model introduced by Kelvin in 1887 for deep water and extended to uniform finite water depth by Havelock in 1908. Another basic model is the 2-point ship model, which considers the two dominant waves created by the bow and the stern of a monohull ship or by the twin bows of a catamaran, and therefore accounts for main wave interference effects. These 2-point ship models contain information that cannot be found in the classical patterns for the 1-point ship model commonly used since Kelvin. In particular, whereas Havelock’s classical wave patterns for the 1-point model only depend on the Froude number based on the water depth, the farfield waves for the 2-point models of a monohull ship or a catamaran also depend on the Froude number associated with the length of the monohull ship or the spacing between the twin hulls of the catamaran. Moreover, the ‘apparent wake angles’ associated with the highest waves that result from constructive wave interferences can greatly differ from the cusp or asymptote angles of Havelock’s wave patterns. Keywords: Farfield ship waves, Shallow water, Ship models, Wave interferences

This paper demonstrates that chromaticity shifts in light-emitting diode (LED) devices arise from multiple mechanisms that produce chemical changes in the materials used to construct the LED devices. Each chromaticity change is shown to proceed over a finite period of time, and there is a limit on the impact of each shift. For example, chromaticity shifts in LED devices usually start with a fast-acting component that quickly reaches a maximum value, followed by one or more slower acting component(s). This behavior can be modeled analytically with a bounded exponential component to describe the fast-acting component, followed by one or more generalized logistic models. These analytical models contain several key parameters, including the limiting value of each chromaticity shift (A for the upper asymptote and L for the lower asymptote) and the rate of the change k. This approach to chromaticity modeling is demonstrated with analytical models of the chromaticity shifts caused by the irreversible degradation of phosphors. These analytical models provide insights into the kinetic processes responsible for green and red chromaticity shifts caused by phosphor degradation. A green shift is produced by the surface oxidation of the nitride phosphor that changes the emission profile to lower wavelengths. As the surface oxidation reaction proceeds, surface reactants are consumed thereby slowing the reaction rate, and the bulk oxidation processes become more prevalent. A red chromaticity shift can arise from quenching of the green phosphor which shift the emission in the red direction. This paper concludes by discussing the implications of these models for projecting chromaticity for different operational conditions.

The remarkably simple yet realistic Hogner model of farfield ship waves, previously considered to analyze the apparent wake angle associated with the highest waves that result from constructive interferences among the divergent waves created by a fast ship in deep water, is applied to the more general case of uniform finite water depth. This theory is used to illustrate notable features of ship waves in finite water depth. In particular, numerical applications to a monohull ship and catamarans illustrate two notable features of ship waves in shallow water: specifically, the apparent wake angle can be much smaller than Havelock's classical asymptote or cusp angles, and the apparent wake angle in finite water depth is nearly identical to the apparent wake angle in deep water if the water depth is greater than the ship length. Moreover, the numerical illustrations demonstrate the paramount importance of interferences among divergent waves for fast ships. Indeed, constructive interferences among the divergent waves created by a fast ship largely determine the variation of the amplitude of the waves across the ship wake, and therefore the apparent wake angle and the wave drag of the ship, a critical element of ship design. These numerical illustrations also corroborate main conclusions of an approximate analysis of wave interferences in shallow water for monohull ships and catamarans modeled as 2-point wavemakers.

We consider numerical solutions in which the linear elastic response to an opening- or sliding-mode fracture couples with one or more processes. Classic examples of such problems include traction-free cracks leading to stress singularities or cracks with cohesive-zone strength requirements leading to non-singular stress distributions. These classical problems have characteristic square-root asymptotic behavior for stress, relative displacement, or their derivatives. Prior work has shown that such asymptotics lead to a natural quadrature of the singular integrals at roots of Chebyhsev polynomials of the first, second, third, or fourth kind. We show that such quadratures lead to convenient techniques for interpolation, differentiation, and integration, with the potential for spectral accuracy. We further show that these techniques, with slight amendment, may continue to be used for non-classical problems which lack the classical asymptotic behavior. We consider solutions to example problems of both the classical and non-classical variety (e.g., fluid-driven opening-mode fracture and fault shear rupture driven by thermal weakening), with comparisons to analytical solutions or asymptotes, where available.

In this paper, a new method of patched-conic for designing the interplanetary orbit is proposed. It is based on iterative computation and the equations are derived. The new method avoids the errors caused by assuming the velocity vector at the boundary of planetary sphere of influence parallel to the asymptote of the hyperbolic orbit. Based on the orbit constraint, the spacecraft’s velocity vector and the position vector at the boundary of planetary sphere of influence are calculated during each iteration to meet the continuous condition. This method is suitable for implementation in computer program and has a fast convergence speed.

We establish a two timescale asymptotics of the weakly compressible Stokes system which has dissipation of order e > 0 . For any L 2 initial data, over time scale of order 1, the solutions of the weakly compressible Stokes system converge strongly to those of the acoustic system as e → 0 . Over time scale of order 1 / e , the limit system is the incompressible Stokes system with the initial data projected on the incompressible mode. For the periodic domain, the convergence is weak due to the fast oscillation generated by acoustic waves. For the Navier-slip boundary condition with the reciprocal of slip length being square of the Knudsen number, the acoustic waves are damped by the viscous boundary layer, and consequently the strong convergence is justified.

This work describes a method to reliably measure the elastic modulus of brittle materials from Berkovich indents under the continuous stiffness mode. It involves depositing a metallic film at the surface of the tested material to absorb the inelastic damage caused by the penetrating indenter. The Zhou-Prorok model was employed and rearranged to decouple the film and substrate contributions. This converted it into a hyperbolic form that approached an asymptote as the indenter approaches the film/substrate interface. This asymptote was described by a simple linear approximation whose slope directly revealed the substrate’s elastic modulus. The method enabled the elastic behavior of the brittle ceramic to be assessed without the indenter penetrating it. In fact, this method can assess properties of an unknown film/substrate composite as long as one has an estimate of the film thickness and the film can appreciably plastically deform.

This article presents an analysis of previously published hydraulic conductivity data for a wide range of sediments. All soils exhibit a prevalent power trend between the hydraulic conductivity and void ratio. Data trends span 12 orders of magnitude in hydraulic conductivity and collapse onto a single narrow trend when the hydraulic conductivity data are plotted versus the mean pore size, estimated using void ratio and specific surface area measurements. The sensitivity of hydraulic conductivity to changes in the void ratio is higher than the theoretical value due to two concurrent phenomena: 1) percolating large pores are responsible for most of the flow, and 2) the larger pores close first during compaction. The prediction of hydraulic conductivity based on macroscale index parameters in this and similar previous studies has reached an asymptote in the range of k meas /5 ≤ k predict ≤ 5k meas . The remaining uncertainty underscores the important role of underlying sediment characteristics such as pore size distribution, shape, and connectivity that are not measured with index properties. Furthermore, the anisotropy in hydraulic conductivity cannot be recovered from scalar parameters such as index properties. Overall, results highlight the robustness of the physics inspired data scrutiny based Hagen–Poiseuille and Kozeny-Carman analyses.

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Permeability governs fluid flow in hydrate-bearing sediments (HBSs) and directly affects gas production efficiency. Reported models relating permeability to hydrate saturation are usually embedded with parameters whose physical meaning is not clear or difficult to determine. It limits their applicability in numerical simulations and practices. In this study, we proposed an innovative permeability-hydrate saturation model based on the Poiseuille's law and the Kozeny-Carman equation. The proposed model has single one parameter, the void ratio, which is physically sound and easily determined. This model was verified by experimental data and other existing models, and proved to have a satisfying performance in predicting the permeability of HBSs. The prediction results reached an asymptote in the range of kmeas/2≤kpredict≤2kmeas. For a given hydrate saturation, the normalized permeability decreases nonlinearly as void ratio increases. The sensitivity of permeability of HBS to changes in void ratio is higher at high hydrate saturation. Overall, the proposed model can capture the main feature of permeability with hydrate saturation for coarse-grained HBS. The remaining uncertainty in this model underscores the important role of hydrate distribution, heterogeneity, anisotropy, and pore geometry of HBSs that are not characterized by the hydrate saturation and the void ratio.

The long-term strength and time-to-failure of brittle rocks has become increasingly important with the increased interest in the storage of used nuclear fuel in deep geological repositories . This paper critically reviews and analyzes the currently available time-to-failure data for various brittle rock types. The current best approach on estimating time-to-failure of rock samples at the lab scale under a constant stress is using semi-log data based on the driving stress ratio and the logarithm of time. In most studies, the applied driving stress ratio is calculated based on the average strength of the rock, however, sample strength can vary up to 15%. Therefore, it is proposed that the crack-initiation stress threshold for each sample be used to calculate sample specific ultimate strengths based on relationships determined in literature. It is proposed that if a sample fails during a long-term strength test within the first 1–10 s, the applied stress for that test can be assumed equivalent to the ultimate strength. Additionally, a modified exponential function with a horizontal asymptote at the crack-initiation threshold is explored as an alternative to the typical log-linear approach. The exponential approach is non-linear in semi-log space and does not require an arbitrary cut-off for time-to-failure at the static fatigue limit of the rock as is the case of the semi-log approach. Ultimately, it is shown that although the exponential function does usually provide a better overall fit to data at relatively short times (

Current service life models for predicting the time to chloride-induced corrosion initiation of steel reinforcement in concrete structures are based on a hypothesized surface chloride concentration, Cs, as a boundary condition. This is either assumed to be constant or varies with time, generally disregarding other factors that influence Cs. For example, Fickian models use a constant Cs and existing time-variant models assume Cs is only a function of time. In this paper, an improved time-variant Cs model is hypothesized using general physical concepts and is then validated by an empirical study. The proposed model, as opposed to the existing time-variant models, not only accounts for the variability of Cs with exposure time but also incorporates the effects of time to exposure and the effects of the concentration of chlorides in the exposure environment. The model assumes that Cs is sigmoidal in shape with an asymptote that is a function of the concentration of chlorides in the environment. The input variables for the proposed model were selected based on best subset sampling analysis on the results of the experimental work to determine the influence of water-to-cement ratio, time to exposure, the concentration of chlorides in the exposure environment, and exposure time on Cs. The accuracy of the proposed model is assessed versus existing time-variant Cs models and the results indicate that the proposed model better predicts the Cs in concrete exposed to chlorides. Moreover, results of service life predictions using the proposed model show that the proposed model yields more accurate results, better protecting owners from financial and engineering risks.

In this paper, an analytical model for determining the iso-damage curves for framed monolithic glass panels subjected to blast loading is proposed. Two typical damage levels corresponding to different conditions in GSA/ISC are classified, namely (a) the glass crack limit and (b) glass fragments invading with a certain velocity. The nonlinear dynamic responses and failure modes of framed monolithic glass under different blast loadings are firstly analysed numerically. Then critical states of glass panel in both impulsive region and quasi-static region of the pressure-impulse (P-I) diagram are defined. Based on the energy balance approach, an analytical method is proposed for determining the pressure asymptote and the impulse asymptote of framed monolithic glass for different damage levels. The proposed method is verified through comparison with published experimental data and numerical results. The method can be applied for any framed monolithic glazing with different dimension and thickness and provides a practical approach for engineering design and hazard level estimation of framed monolithic glass against blast loading.

Gradient metallic materials, which can be made by surface mechanical attrition, non-equilibrium growth, or other thermomechanical means, have been deemed as an effective way to overcome the strength-ductility tradeoff as commonly seen in traditional metallic alloys. Although a large number of research works have been devoted to the unique strengthening mechanisms as resulting from the enhanced plastic-strain gradients and back stresses in these novel materials, the disproportionally fewer studies on ductility are rather restricted to the delay of the Considere necking limit due to the elevated work hardening. This view is incomplete, because the onset of necking (i.e., the uniform ductility) depends critically on both the amplitude and wavelength of initial perturbations. Even with a mere simplification of gradient materials by a film-on-substrate or a sandwich structure, this work shows that with random surface perturbations, the upper bound of uniform ductility is dictated by an extremely short-wavelength perturbation at the surface of the outer hard layer (thus denoted as Rayleigh mode). On the other hand, a pre-patterned surface with perturbations of varying periods is practicably unable to evolve into the Rayleigh asymptote and thus can achieve even higher uniform ductility. A revisit of literature experiments is suggested to be undertaken with a particular focus on the spectral growth kinetics of surface morphology and its connection to uniform ductility in these gradient materials.

Looking at wear of incomplete contacts in partial slip we start from an asymptotic description of the contact tractions at the contact edges. We introduce distributed dislocations along the slip zone to account for the profile reduction due to wear and find the long-term time asymptote where the contact is wholly stuck. The resulting stress field is used to find the crack tip stress intensity factors for short contact edge cracks, which are useful in predicting the crack nucleation threshold.

We analyse the influence of fluid yield stress on the propagation of a radial (penny-shaped) hydraulic fracture in a permeable reservoir. In particular, the Herschel–Bulkley rheological model is adopted that includes yield stress and non-linearity of the shear stress. The rock is assumed to be linear elastic, and the fracture is driven by the point source fluid injection with a constant volumetric rate. The fracture propagation condition follows the theory of linear elastic fracture mechanics, and Carter’s leak-off law is selected to govern the fluid exchange process between the fracture and formation. The numerical solution of the problem is found using the algorithm based on Gauss–Chebyshev quadrature and Barycentric Lagrange interpolation techniques. We also construct an approximate solution with the help of the global fluid balance equation and the near-tip region asymptote. The latter approximation is computationally efficient, and we estimate its accuracy by comparing the primary crack characteristics such as opening, pressure, and radius with those provided by the full numerical solution. We present examples corresponding to typical field cases and demonstrate that the addition of yield stress can lead to a shorter radius and wider opening compared to the corresponding case with simpler power-law fluid rheology. Further, we quantify the limiting propagation regimes (or vertex solutions) characterised by the dominance of a particular physical phenomenon. Relative to the power-law results, there are two new vertices that are associated with the domination of yield stress: storage-yield-stress and leak-off-yield-stress. To understand the influence of various problem parameters, we utilise the constructed approximate solution to investigate the dimensionless parametric space of the problem, in which the applicability domains of the limiting solutions are quantified. This enables one to quickly determine whether yield stress provides a strong influence for given problem parameters.

An elastic visco-plastic creep model was combined with the Monte-Carlo probabilistic method incorporating multivariate copula and nonlinear analysis to investigate the effects of uncertainties in the elastic visco-plastic model parameters on time-dependent settlement and the distribution of excess pore water pressure in soft soils under applied loads. The elastic-plastic model parameter ( λ / V ) and creep coefficient ( ψ 0 / V ) were considered as random variables with lognormal distribution while considering the cross correlation between these two random variables. When λ / V and ψ 0 / V were used as random variables, the coefficient of variation of time-dependent deformation gradually decreased approximately 25% over time until reaching an asymptote. By adopting over 50 years of monitoring data from the case study of Vasby test fill and results from the settlement ratio, the most appropriate cross correlation coefficient between selected random variables was introduced. The results revealed that increasing the cross correlation coefficient between λ / V and ψ 0 / V increased the standard deviation and the coefficient of variation of settlement up to 40%. Meanwhile, the corresponding statistical features for the predicted excess pore water pressure decreased as the cross correlation coefficient increased. This study also provides a practical insight into selecting the most suitable cross correlation coefficient between elastic visco-plastic model parameters, while adopting reliability-based design approach that captures the time-dependent deformation of embankments and structures built on soft soils.

Problems involving a transition between dense and dilute dispersed phase regimes often require hybridization of Eulerian-Eulerian (EE) and Eulerian-Lagrangian (EL) methods for accurate and efficient computational modeling. A hybrid EE-EL formulation is developed in this work from first principles, which asymptotes to well-established EE and EL methods in limiting conditions. A smooth and dynamic transition criterion and a corresponding algorithm for conversion between the two representations of the dispersed phase are developed. To use EE and EL in their respective regions of effectiveness, the transition criterion is designed as a function of local volume fraction and local kinetic energy of random uncorrelated motion of particles. Several one-dimensional numerical tests are conducted to analyze limits of the hybrid EE-EL method in dense (up to 65% volume loading) and dilute conditions, at first, without any conversion between EE and EL, and then the ability of the conversion algorithm to smoothly transition from EE to EL and vice versa is evaluated using prespecified and dynamically computed transition criteria for one- and two-dimensional tests. Particle evolution in two-dimensional frozen turbulence is simulated to evaluate the method's ability to dynamically transition from EE to EL and vice versa in regions of particle trajectory crossing. Finally, the hybrid method is used for simulating dispersion of an initially dense particle cloud in a three-dimensional spherical sector blast.

In this paper, the slip length of branched hydrocarbon molecules, i.e., polyalphaolefin oils, under shear in a gap between iron surfaces were investigated utilizing large-scale Molecular Dynamics (MD) simulation. The results showed the expected singularity for the slip length with variation gap height. For large gap height, h → ∞ , the slip length approaches a constant asymptote λ → λ ∞ . This study indicated that as the number of branches of the liquid molecule raise, the slip length λ → λ ∞ as well as viscosity increases. For given apparent shear rate, the friction force increased with increasing temperature due to the reduction of wall slip. MD Simulations demonstrate that the slip length of the polyalphaolefin-iron system increase by decreasing the liquid temperature, indicating an Arrhenius process.

Fatigue crack initiation can be regarded as a generalized phase transformation from the view of breaking energy barrier. A new phase transformation model is proposed to predict fatigue crack initiation based on the second law of thermodynamics. Evolution of dynamic energy during crack initiation and the damage under fatigue loading is considered combining with the entropy theory. The system becomes unstable when the Helmholtz free energy reaches the extremum value, which is adopted to represent fatigue crack initiation. The effects of grain size on the crack initiation and the asymptote of S-shaped S-N curve are discussed. The theoretical predictions are compared with the experimental data and show reasonable accuracy for different metallic materials.

This paper proposes a hybrid multilevel approach of simultaneous optimization design of topology and discrete fiber orientation for maximum stiffness design of constant-stiffness laminated plates. The lamination parameters are selected as the intermediate variables to overcome the local optima behaviors derived from directly optimizing fiber orientation. The hybrid multilevel method incorporates two different types of optimization techniques to benefits from the advantages of them. At the first level, lamination parameters and density are taken as the design variables, the method of moving asymptotes (MMA) is applied to obtain the optimal lamination parameter and topology shape simultaneously. At the second level, taking the discrete fiber orientation angles of individual layers as the design variables, a detailed lay-up design optimization considering some limitations on manufacturing is implemented by an improved direct simulated annealing (IDSA) algorithm. Thus, the hybrid multilevel optimization procedure can achieve a global optimum and obtain a faster convergence. Finally, Numerical examples are tested to illustrate and validate the proposed hybrid method .

The four-parameter Unified Richards model has been applied to the growth of different animal taxa. Traditionally researchers of animal growth have favoured three-parameter models such as the logistic, Gompertz, and von Bertalanffy models. However, the growth-rate parameters of the traditional versions of these models are incomparable, and model forms returning starting points for the curves are not available. Therefore, we have reviewed and developed the family of Unified growth models (U-models), including U-versions of the logistic, Gompertz, and von Bertalanffy models, which each have an inflection placement at a fixed percentage of the upper asymptote. Consequently, in order to accommodate for those who prefer a three-parameter model, we also deduce (show) how to derive from the U-Richards a new, generic, three-parameter U-models with any predetermined inflection placement. This means an indefinite number of U-models, which will cover inflection placements at any percentage of the upper asymptote. All U-models have been re-parameterized to exhibit a unified set of parameters, which measure the same thing cross all family members, hence these models are termed the Unified family (or simply U-family). We also discuss how to interpret parameter values and whether to restrain the asymptote to a fixed value. All U-family models can be fitted to data in either of two forms: the first where one of the parameters represents the time of inflection, and the second with a parameter representing the starting value (intersection with the x-axis). Each parameter in these models only affects a single curve-shape characteristic. We show, also by fitting the models to bird growth data, how only a complete U-Richards family of models and accompanying parameter-translation equations will guarantee that we will be able to choose a model that returns realistic values and provides a consistent interpretation of growth data. There should be no enticement to choose other tools for analysing sigmoidal growth. Traditional versions of the Gompertz, logistic, von Bertalanffy or Richard’s models found in the literature have various shortcomings.

There exist some difficulties in determining aquifer parameters based on pumping test data within a partially penetrated retaining walls using traditional Cooper-Jacob method. Many other site-specific factors, such as the effect of partially penetrating well and the large diameter of the wells, cannot easily be accommodated in theoretical well formulae. The semi-log drawdown-time curves affected by the effects of barrier, wellbore storage, and partial penetration well can be characterised by four distinct stages of drawdown: i) Stage I, drawdown is unaffected by the barrier, ii) Stage II, drawdown is significantly influenced by the barrier, iii) Stage III, the drawdown-time curve runs parallel to that deduced from greenfield conditions, and iv) Stage IV, the drawdown becomes a constant value. To handle the four distinct stages of drawdown, a semi-analytical method using the slope of the late-time drawdown asymptote of Stage III for determining the transmissivity is proposed. The horizontal intercept, resulting from an extension of the late-time drawdown asymptote from Stage II, is used for determining the storage coefficient. Pumping test data from a case history are analysed using the proposed semi-analytical method, and the results obtained are compared with those deduced from the numerical simulation. The comparison between the analytical results and those obtained from the numerical simulation appeared satisfactory.

In this study an elastoplastic hardening model for quasibrittle materials is presented. The yield surface exhibits hyperbolic meridians while its shape on the deviatoric plane is described by an elliptic function. The proposed hardening mechanism is controlled by the slope of the asymptotes of the hyperbolic meridians and thus by the mobilized friction of the material. The yield surface is capped during the first stages of hardening and opens up before reaching the peak strength. On the deviatoric plane the hardening is non-uniform producing changes in both the size and the shape of the yield surface. The proposed plastic potential is related with the yield function through a simple modification of its volumetric part. The model is equipped with a hardening rule that is a monotonically increasing elliptic function of the hardening parameter. The latter is given in its rate form and it is pressure dependent. A proposed ductility rule controls this pressure dependency and leads to brittle behavior in tension and ductile behavior at high confinement compression. All the parameters have physical interpretation and are directly related with measurable mechanical properties of the material in the lab. Most of them could be identified from a uniaxial compression test. The predictions of the model are compared against experimental datasets and it is shown that exhibit very good agreement.

There is an ongoing need to develop alternative penultimate methods for analysing extreme wind speeds, i.e. methods not involving convergence to an asymptote. This need has sharpened given that it is now known that the wind climate is “mixed” at many more sites than previously thought. One penultimate method developed many years ago from work on random electrical noise signals, is the so-called Level Crossing Method. This was used for processing wind speeds without serious examination of the fundamentals. In the paper the original formulation is examined both theoretically and by testing with computer-generated synthetic data. It is found to be based on some incorrect assumptions, which lead to errors. A new theoretical expression is derived for level crossings of wind speeds which fits perfectly those measured from the synthetic data. Thus, given a parent distribution of the Forward Weibull type and the correlation coefficient between successive measured values, the Gumbel plot can immediately be derived. This process also uses the idea that rare crossings of high levels are a Poisson process. The correlation of the parent introduces systematic errors from this assumption, but these are small and have the advantage of decreasing as the wind speed level increases. Given a means of separating “mixed” wind regimes by the newly available OEN analysis, an up-dated version of the Level Crossing Method appears to be a possible new penultimate method for extremes.

Photoassociation of ultracold Cs atoms is reported in magneto-optical trap with the modulation technique. Trap loss spectroscopy of the ultracold Cs2 molecules has been obtained experimentally. Spectroscopy data are expended to the red detuned of 70 cm-1 below the 6S1/2+6P1/2 dissociation limit. Several new low lying vibrational levels belongs to the 0u+ and 1g states are identified and analyzed. The long range molecular coefficients C3 for the 0u+ and 1g states are obtained, and the corresponding empirical potential curves are derived with the spectroscopy data.

Many studies regarding growth in diameter at breast height ( D ) in trees suffer from several problems, including heteroscedasticity, temporal autocorrelation and very low statistical adjustments. In growth ring studies, growth models are sometimes omitted, presenting only a mean curve or smoothings, while studies that use models often do not address the above mentioned problems. For these reasons, this paper proposes a new approach to the classical modeling of D = f ( t ), where t is age (years), using the logarithmic transformation of the relative growth rate ln(1/ D )( dD / dt ) = ln f ( D , A ),where A is the asymptote of D based on the differential growth rate model of von Bertalanffy. High statistically significant adjustments for Cedrela odorata ( ME = 65%, model efficiency, ME , an analogous to R 2 but for non-linear regressions), and Juglans neotropica ( ME = 78%) were obtained and met all regression assumptions. These equations were integrated to obtain D = f ( t ) for both species, followed by self and independent validation. Based on these equations, different life history and silviculture traits were calculated for both species. This procedure does not appear to have been previously used in the study of tree growth.

Radial frequency (RF) patterns, which are sinusoidal modulations of a radius in polar coordinates, are commonly used to study shape perception. Previous studies have argued that the detection of RF patterns is either achieved globally by a specialized global shape mechanism, or locally using as cue the maximum tangent orientation difference between the RF pattern and the circle. Here we challenge both ideas and suggest instead a model that accounts not only for the detection of RF patterns but also for line frequency patterns (LF), i.e. contours sinusoidally modulated around a straight line. The model has two features. The first is that the detection of both RF and LF patterns is based on curvature differences along the contour. The second is that this curvature metric is subject to what we term the Curve Frequency Sensitivity Function, or CFSF, which is characterized by a flat followed by declining response to curvature as a function of modulation frequency, analogous to the modulation transfer function of the eye. The evidence that curvature forms the basis for detection is that at very low modulation frequencies (1-3 cycles for the RF pattern) there is a dramatic difference in thresholds between the RF and LF patterns, a difference however that disappears at medium and high modulation frequencies. The CFSF feature on the other hand explains why thresholds, rather than continuously declining with modulation frequency, asymptote at medium and high modulation frequencies. In summary, our analysis suggests that the detection of shape modulations is processed by a common curvature-sensitive mechanism that is subject to a shape-frequency-dependent transfer function. This mechanism is independent of whether the modulation is applied to a circle or a straight line.

Focusing on the deficiencies of the current liquefaction evaluation methods typically on deep sandy-layers of 10 m to 20 m, a new liquefaction evaluation formula, which is based on the 156 SPT data from liquefaction investigation in China mainland, is proposed. The formula is plausible for wide depth range up to 20 m. The formula which takes a hyperbolic function form fits the liquefaction data at shallow depth and predicts satisfactorily deep liquefaction. The liquefaction dataset available from China earthquakes and foreign earthquakes (i.e., Kobe earthquake and ChiChi earthquake) are statistically summarized. The deficiencies of prevailing liquefaction evaluation methods and the CSR method by Seed are pinpointed. To validate the proposed formula, a liquefaction dataset consist of 312 liquefaction data from China mainland and foreign countries is used for re-evaluation. The results indicate that the new formula is quite feasible for wide sandy-layer buried depth, different seismic intensities and varying groundwater tables. Comparing with the current Chinese code methods and the CSR method, the new formula which approaches to an asymptote eliminates the abnormality of the CSR method that decreases inversely when the depth exceeds a certain value. The new formulae solve the deficiency of Chinese codified liquefaction evaluation methods that are conservative for intensity VII at shallow depth