Rate Independent Hysteresis

Multiphase porous media such as soils are known to exhibit hysteresis, e.g. in soils there is a strong hysteretic relationship between the moisture content and the matric potential and to date the Preisach model has been successful in modelling this relationship. Subsequently ODEs with Preisach hysteresis have been developed, such as a hysteretic version of Darcy's law and a hysteretic version of the linear reservoir known as the Preisach reservoir. In this paper we combine the above Hysteretic Differential Equations (HDEs) with three linear reservoirs so as to develop a simple rainfall runoff model. The model can be represented by a block diagram: Rainfall q(t) enters the soil component and either infiltrates and/or runs off when it exceeds the maximum rate of infiltration. The runoff part is fed into two linear reservoirs in series. Next, the drainage from the soil to groundwater is represented by a single linear reservoir, where the output from the soil becomes the input to t...

This paper presents an enriched hysteresis model with damage relying on the Bouc-Wen formulation, in which a single scalar variable is introduced to reproduce effects of strength and stiffness degradation emerging for damaging materials. First, some acknowledged limits of the original Bouc-Wen model are discussed, focusing on its thermodynamic admissibility and compatibility with Drucker's plasticity postulate, and highlighting the effects of the parameters β and γ. Then, a reformulated expression of the dissipated energy is presented, which is consistent from the thermodynamic point of view. This formulation is extended to the case of degrading Bouc-Wen models. Univariate validation analyses are proposed, together with some considerations on the physical and thermodynamic admissibility of the model. The effect of pinching is also introduced by means of the arrangement in parallel of a nondissipative Bouc-Wen and a degrading (damaging) device, resulting in a varied set of hysteresis shapes. Finally, the proposed model is adopted to analyse the cyclic response of masonry structural elements under in-plane horizontal loads. Within the framework of equivalent frame formulation, masonry panels are modelled by an elastic beam arranged in series with nonlinear flexural hinges lumped at the ends and a shear link, whose constitutive relationships are described by means of the enriched hysteretic model with damage. Highlights:

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Hysteresis is a rate-independent non-linearity that is expressed through thresholds, switches, and branches. Exceedance of a threshold, or the occurrence of a turning point in the input, switches the output onto a particular output branch. Rate-independent branching on a very large set of switches with non-local memory is the central concept in the new definition of hysteresis. Hysteretic loops are a special case. A selfconsistent mathematical description of hydrological systems with hysteresis demands a new non-linear systems theory of adequate generality. The goal of this paper is to establish this and to show how this may be done. Two results are presented: a conceptual model for the hysteretic soil-moisture characteristic at the pedon scale and a hysteretic linear reservoir at the catchment scale. Both are based on the Preisach model. A result of particular significance is the demonstration that the independent domain model of the soil moisture characteristic due to Childs, Poulavassilis, Mualem and others, is equivalent to the Preisach hysteresis model of non-linear systems theory, a result reminiscent of the reduction of the theory of the unit hydrograph to linear systems theory in the 1950s. A significant reduction in the number of model parameters is also achieved. The new theory implies a change in modelling paradigm.

unsaturated hydraulic conductivity, K, expressed as a function of the soil water content, , or the soil water Hysteresis has been found in both the hydraulic conductivity, K, pressure head, , and the relation between and must vs. pressure head, , relationship, and the soil water content, , vs. relationship. This limits the application of a unified solution for be specified before analytical or numerical models can infiltration and drainage. A Haines' Jump model of hysteresis is pro-accurately predict water flow during infiltration, evapoposed and combined with the Broadbridge and White form of K() ration, or drainage. Unfortunately, because of hystereand the diffusivity, D, relationship, D(). This allows a unified analytisis, these relationships are not simple functions and show cal solution for infiltration and drainage. This solution accounts for a great deal of variation between wetting and drying hysteresis by allowing the inverse macroscopic capillary length scale, cycles. Hysteresis has been found in both () and K() ␣, to be hysteretic. A method of a priori estimating the hysteretic

Green roofs integrate vegetation into infrastructures to reach benefits that minimize negative impacts of the urbanization. Green roofs use artificial soils (substrates) that have an improved performance compared to natural soils. In this work, we characterized four substrates in terms of their hydraulic and thermal properties, and performed numerical simulations of heat and fluid flow to study the effect of these properties on green roof performance. Simulation results show that the green roof behavior strongly depends on substrate properties and on moisture content prior to a rainstorm, highlighting the need of dynamic biophysical models for design/maintenance of green roofs.

Cyclosporine A induced arteriolopathy in a rat model of chronic cyclosporine nephropathy. Chronic cyclosporine (CsA) nephrotoxicity is a major complication of heart, bone marrow, and renal transplantation, and is characterized in humans by striped interstitial fibrosis, tubular dilatation and atrophy, and hyalinization of hilar arterioles. This last feature is highly specific for cyclosporine injuiy and has been difficult to reproduce in normotensive animal models. Salt-depletion has been shown to sensitize rodents to the effects of CsA and accelerate the disease process. We conducted sequential studies in chronically salt depleted, pair fed rats treated with CsA (15 mg/kg, s.c.) or an equivalent dose of olive oil vehicle, and found a histologic lesion associated with CsA that consisted of striped cortical interstitial fibrosis, tubular dilatation and atrophy, and hyalinization of many afferent arterioles. The arteriolopathy was first detected at day 10 with progressive hyalinization of arterioles continuing until termination of the study at day 35. The arteriolopathy consisted initially of eosinophilic granular transformation of smooth muscle cells comprising afferent hilar glomerular arterioles, and progressed to foci of smooth muscle cell vacuolization and accumulation of discrete hyaline deposits in vessel walls. Electron microscopy demonstrated marked accumulation of typical renin granules throughout the smooth muscle cell cytoplasm, corresponding to the eosinophilic granular transformation revealed histologically. Immunocytochemistry confirmed the up-regulated production of renin in these vessels. This study documents a rodent model for CsA arteriolopathy and CsA-associated interstitial fibrosis that strikingly reproduces the most characteristic nephropathic effects of cyclosporine found in human patients treated with this agent. This model offers an opportunity to test therapeutic interventions that might block or ameliorate the most serious nephrotoxic effects of this drug. Cyclosporine (CsA) has improved organ transplantation survival markedly since its introduction by Borel et al [1], and cyclosporine-based immunosuppression has been used successfully as therapy for a number of primary renal and non-renal disease states as well. A major complication of long-term therapy is chronic CsA nephropathy, characterized by tubular vacuolization, striped cortical interstitial fibrosis, and a prominent vascular injury manifested by hyalinosis of hilar arterioles, and terminal portions of small muscular (interlobular) arteries [2]. This arteriolopathy is thought to be the most pathognomonic lesion of

The Bouc-Wen (BW) model is a successful differential equations model used to describe a wide range of nonlinear hysteretic systems. However, it is unable to describe force degradation, stiffness degradation and pinching effects. Therefore, Baber and Noori proposed a generalisation, developing the Bouc-Wen-Baber-Noori (BWBN) model. Nevertheless, it is composed of many parameters and complex pinching and degrading functions. Thus, it is necessary to develop a simpler and reliable model to be used for practical applications. In this paper, a modified BW model is proposed. It involves a more direct physical meaning of each parameter and allows achieving a substantial reduction of computational effort and numerical deficiencies. This is obtained through simpler pinching and degrading functions that entail a decrease of the number of parameters. The result is a straightforward model, capable of predicting the behaviour of degrading and pinched hysteretic systems. An application of the proposed scheme to a real case is also presented, in which reinforced concrete bridge piers that were physically tested in the laboratory are considered. The force-displacement data are used to perform the identification process of the model parameters via a Genetic Algorithm. The numerical results are accurate since they coincide with the experimental ones.

Direct measurements of the main wetting curve (MWC) of the soil-water characteristic curve are very hard compared to direct measurements of the main drying curve (MDC) of the soil-water characteristic. Both curves are important in agricultural and engineering applications. This study was conducted to predict main wetting curves (MWCs) from main drying curves (MDCs) using Feng and Fredlund (1999) equation by using the two points method for seven soil samples with a wide range of gypsum content including control treatment (0% gypsum). Both MDCs and MWCs were measured. Performed results showed that good fitting was obtained between measured and predicted value using the two points method by using quantitative statistical parameters: coefficient of determination (CD), coefficient of residual mass (CRM), error ratio (å), geometric mean of error ratio (GMSE) and geometric standard deviation of error ratio (GSDER) as well as 1:1 correlation which showed a high fitting between the measured and predicted points for the main wetting curve (MWC) of the soil-water characteristic curve. Feng and Fredlund (1999) is a simplified model for soil-water characteristic curves fitting as well as to predict main wetting curves (MWCs) from main drying curves (MDCs) by using the two points method with a wide range of gypsum in soil samples.

Direct measurements of the main wetting curve (MWC) of the soil-water characteristic curve are very hard compared to direct measurements of the main drying curve (MDC) of the soil-water characteristic. Both curves are important in agricultural and engineering applications. This study was conducted to predict main wetting curves (MWCs) from main drying curves (MDCs) using Feng and Fredlund (1999) equation by using the two points method for seven soil samples with a wide range of gypsum content including control treatment (0% gypsum). Both MDCs and MWCs were measured. Performed results showed that good fitting was obtained between measured and predicted value using the two points method by using quantitative statistical parameters: coefficient of determination (CD), coefficient of residual mass (CRM), error ratio (å), geometric mean of error ratio (GMSE) and geometric standard deviation of error ratio (GSDER) as well as 1:1 correlation which showed a high fitting between the measured ...

This paper presents how the elasto-plastic constitutive relations have been used to predict the hysteretic behavior in unsaturated sands. An efficient method was selected to represent the relation, and the predicted capabilities were assessed on many scanning curves. The proposed method is derived from Gajo and Wood's evolution equation for the plastic modulus to evaluate the suction change during wetting/drying processes. The study proposes the simple formulas for the relationship between the boundary curves and the scanning curves. The results obtained from the proposed formulas were verified through a comparison with the existing experimental data in the literature. The comparison indicates that the elasto-plastic constitutive relations during cyclic loading can be utilized to describe the scanning behavior of Soil Water Characteristic Curves (SWCCs).

Green roofs integrate vegetation into infrastructures to reach benefits that minimize negative impacts of the urbanization. Green roofs use artificial soils (substrates) that have an improved performance compared to natural soils. In this work, we characterized four substrates in terms of their hydraulic and thermal properties, and performed numerical simulations of heat and fluid flow to study the effect of these properties on green roof performance. Simulation results show that the green roof behavior strongly depends on substrate properties and on moisture content prior to a rainstorm, highlighting the need of dynamic biophysical models for design/maintenance of green roofs.

Green roofs integrate vegetation into infrastructures to reach benefits that minimize negative impacts of the urbanization. Green roofs use artificial soils (substrates) that have an improved performance compared to natural soils. In this work, we characterized four substrates in terms of their hydraulic and thermal properties, and performed numerical simulations of heat and fluid flow to study the effect of these properties on green roof performance. Simulation results show that the green roof behavior strongly depends on substrate properties and on moisture content prior to a rainstorm, highlighting the need of dynamic biophysical models for design/maintenance of green roofs.

Green roofs integrate vegetation into infrastructures to reach benefits that minimize negative impacts of the urbanization. Green roofs use artificial soils (substrates) that have an improved performance compared to natural soils. In this work, we characterized four substrates in terms of their hydraulic and thermal properties, and performed numerical simulations of heat and fluid flow to study the effect of these properties on green roof performance. Simulation results show that the green roof behavior strongly depends on substrate properties and on moisture content prior to a rainstorm, highlighting the need of dynamic biophysical models for design/maintenance of green roofs.

The present industry scenario focuses on green manufacturing, in terms of effective reuse and recycling of the industrial wastes generated in enormous amount while preparing the product. The wastes also act as a threat to the society by causing various kinds of pollution. Therefore, the proper safe disposal of the same is a very critical factor. Most of the industries struggled with the enormous disposal of these wastes and finding ways for reuse and disposal. In this chapter, one such way of reuse of these wastes for making composite product is explored. Industrial wastes such as flyash and ricehusk used as fillers of varying weight percentages, 6%, 8%, 30%, 40%, and 50%, wt%, respectively, are reinforced with matrix. The prepared composites were subjected to flexural studies to know the load withstand ability. Results show that the incorporation of both fly ash and rice husk industrial wastes as filler into the polymer matrix increases the flexural strength. In addition, a low-cos...

This paper presents how the elasto-plastic constitutive relations have been used to predict the hysteretic behavior in unsaturated sands. An efficient method was selected to represent the relation, and the predicted capabilities were assessed on many scanning curves. The proposed method is derived from Gajo and Wood's evolution equation for the plastic modulus to evaluate the suction change during wetting/drying processes. The study proposes the simple formulas for the relationship between the boundary curves and the scanning curves. The results obtained from the proposed formulas were verified through a comparison with the existing experimental data in the literature. The comparison indicates that the elasto-plastic constitutive relations during cyclic loading can be utilized to describe the scanning behavior of Soil Water Characteristic Curves (SWCCs).

A one-dimensional vadose zone model was used to simulate flow under natural boundary conditions. The effects of hysteresis and temporal variability of meteorological conditions were evaluated. Simulations were performed in HYDRUS-1D code for the period April 2013–January 2014 (6601 hours) at three different locations in a delineated portion of the sub-quaternary catchment A80A of Nzhelele with different soil textures. Soil hydraulic characteristics were estimated in a Rosetta library dynamically linked to the HYDRUS-1D model which is based on the numerical solution of a one-dimensional Richard's equation. Analysis of the simulation results suggests that ignoring hysteresis for soils of similar textural class does not lead to any significant deviation of the model predicted soil moisture, unlike for soils with different textural classes.

Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit firstorder vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.

Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit firstorder vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.

Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit firstorder vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.

In this paper, a thermodynamic analysis of Bouc-Wen models endowed with both strength and stiffness degradation is provided. It is based on the relationship between the flow rules of these models and those of the endochronic plasticity theory with damage, discussed in a companion paper (Erlicher and Point, 2007). Using the theoretical framework of that extended endochronic theory, it is shown that an elastic Bouc-Wen model with damage, i.e. without plastic strains, can be formulated. Moreover, a proper definition of the dissipated energy of these Bouc-Wen models with degradation is given and some thermodynamic constraints on the parameters defining the models behavior are emphasized and discussed. In particular, some properties of the energetic linear stiffness degradation rule as well as the so-called pivot rule, well-known in the seismic engineering field, are illustrated and commented upon. An improved energetic stiffness degradation rule and a new stiffness degradation rule are proposed.

In this paper, a thermodynamic analysis of Bouc-Wen models endowed with both strength and stiffness degradation is provided. It is based on the relationship between the flow rules of these models and those of the endochronic plasticity theory with damage, discussed in a companion paper (Erlicher and Point, 2007). Using the theoretical framework of that extended endochronic theory, it is shown that an elastic Bouc-Wen model with damage, i.e. without plastic strains, can be formulated. Moreover, a proper definition of the dissipated energy of these Bouc-Wen models with degradation is given and some thermodynamic constraints on the parameters defining the models behavior are emphasized and discussed. In particular, some properties of the energetic linear stiffness degradation rule as well as the so-called pivot rule, well-known in the seismic engineering field, are illustrated and commented upon. An improved energetic stiffness degradation rule and a new stiffness degradation rule are proposed.

A mathematical model of the hysteresis of the water-retention capacity of the soil is proposed. The parameters of the model are interpreted within the framework of physical concepts of the structure and capillary properties of soil pores. On the basis of the model, a computer program with an interface that allows for dialogue with the user is developed. The program has some of options: visualization of experimental data; identification of the model parameters with use of measured data by means of an optimizing algorithm; graphical presentation of the hysteresis loop with application of the assigned parameters. Using the program, computational experiments were carried out, which consisted in verifying the identifiability of the model parameters from data on the main branches, and also in testing the ability to predict the scanning branches of the hysteresis loop. For the experiments, literature data on two sandy soils were used. The absence of an "artificial pump effect" is proved. A sufficiently high accuracy of the prediction of the scanning branches of the hysteresis loop has been achieved in comparison with the three models of the precursors. The practical importance of the proposed model and computer program, which is developed on its basis, is to ensure the calculation of precision irrigation rates. The application of such rates in irrigation farming will help to prevent excess moisture from flowing beyond the root layer of the soil and, thus, minimize the unproductive loss of irrigation water and agrochemicals, as well as reduce the risk of groundwater contamination and natural water eutrophication.

In this paper, the cyclic behavior of a Nitinol cubic block is described by using the Bouc-Wen model [2] coupled to the intrinsic time measure, other than the clock time which governs the behavior of the materials [4]. The modified Bouc-Wen model consists from the classical Bouc-Wen model coupled to the intrinsic time measure, other than the clock time which governs the behaviour of the materials. As a consequence, the thermodynamic admissibility of the Bouc-Wen model is provided by the endochronic theory of plasticity. The role of the intrinsic time measure is described by capturing the stiffness and strength degradation and the opposite phenomena.

Modern day Performance-Based Earthquake Engineering (PBEE) pivots about nonlinear analysis and its feasibility. IDARC-2D is a widely used and accepted software for nonlinear analysis; it possesses many attractive features and capabilities. However, it is operated from the command prompt in the DOS/Unix systems and requires elaborate text-based input files creation by the user. To complement and facilitate the use of IDARC-2D, a pre-processing GUI software package (INSPECT) is introduced herein. INSPECT is created in the C# environment and utilizes the .NET libraries and SQLite database. Extensive testing and verification demonstrated successful and high-fidelity recreation of several existing IDARC-2D input files. Its design and built-in features aim at expediting, simplifying and assisting in the modeling process. Moreover, this practical aid enhances the reliability of the results and improves accuracy by reducing and/or eliminating many potential and common input mistakes. Such benefits would be appreciated by novice and veteran IDARC-2D users alike. c

A one-dimensional vadose zone model was used to simulate flow under natural boundary conditions. The effects of hysteresis and temporal variability of meteorological conditions were evaluated. Simulations were performed in HYDRUS-1D code for the period April 2013-January 2014 (6601 hours) at three different locations in a delineated portion of the sub-quaternary catchment A80A of Nzhelele with different soil textures. Soil hydraulic characteristics were estimated in a Rosetta library dynamically linked to the HYDRUS-1D model which is based on the numerical solution of a one-dimensional Richard's equation. Analysis of the simulation results suggests that ignoring hysteresis for soils of similar textural class does not lead to any significant deviation of the model predicted soil moisture, unlike for soils with different textural classes.

Based on the domain theory of hysteresis, the present study rigorously derives a unified scaling transformation for predicting the wetting scanning retention function, y w (c), following any sequence of wetting and drying processes, from the measured main wetting curve. It is proved theoretically that a shape-similarity exists among the different wetting curves of a given soil. Each wetting scanning curve and the main wetting curve are described by the same normalized equation, over the common interval of c values. This shape-similarity is a direct result of the Mualem domain theory. On this basis, a general unique equation is formulated for prediction of all wetting scanning curves, of all orders, which is compatible with the Mualem dependent, as well as independent, domain theory. On the same theoretical basis, it is proved that no similarity exists among the drying scanning curves. Thus, the use of the scaling transformation for prediction of the drying scans is subjected to inconsistency with the physical principles underlying the dependent domain theory. As a result, scaling in this case would inevitably lead to inaccuracies in the calculated drying curves. A significant step forward has been made in the present study, from Mualem's dependent domain model (1984) with its implicit predictive formulae of the drying scanning curves. A unique explicit equation was theoretically derived, applicable for describing the drying scanning curves of all orders. This unique equation of the drying scanning curves, together with the general single equation of the wetting scanning curves, provided closure of all theoretical wetting and drying scans within the main hysteresis loop. Consequently, the retention function following any sequence of successive wetting and drying processes can be predicted by these two equations determined by the measured boundary curves.

The paper explores the mathematical modeling of economic hysteresis. First, a general definition of hysteresis as history dependent branching is presented and its relevance to macroeconomic hysteresis is discussed. Then, the classical Preisach modeling of macroeconomic hysteresis is reviewed and the basic facts related to this modeling are outlined. It is stressed that the mathematical structure of the classical Preisach model is intimately related to the origin and nature of macroeconomic hysteresis. Next, to account for the continuous evolution of the economy and its effect on hysteresis, the generalized Preisach model of hysteresis is introduced and its advantages in comparison to the classical Preisach model are discussed. Finally, using Preisach models, it is demonstrated that the sluggishness of economic recovery is an intrinsic manifestation of hysteresis branching. It is shown that this sluggishness can be predicted by using the relevant microeconomic data.

The theoretical formulation of the Green-Ampt infiltration model has been extended to conditions of decreasing flooding depth in an isolated system. By defining dimensionless variables of flooding depth s and time τ, an implicit dimensionless equation τ(s) was obtained, which contains a single fundamental dimensionless parameter γ controlling the process, named “infiltration delay parameter”. The characteristics and functional behaviour of

The theoretical formulation of the Green-Ampt infiltration model has been extended to conditions of decreasing flooding depth in an isolated system. By defining dimensionless variables of flooding depth s and time τ , an implicit dimensionless equation τ (s) was obtained, which contains a single fundamental dimensionless parameter γ controlling the process, named "infiltration delay parameter". The characteristics and functional behaviour of γ were analysed, and its physical meaning discussed. A parametric expression s(τ) has been obtained, which uses a unique descriptive parameter a, which in turn depends only on γ and on four generic coefficients valid for a wide range of soil properties and conditions occurring in nature. By means of numerical simulations using different values of soil parameters and initial flooding depths, it was proved that the proposed parametric function generates similar infiltration rates and cumulative storages to those that are obtained starting from Darcy's equation in the extended Green-Ampt scheme.

A one-dimensional vadose zone model was used to simulate flow under natural boundary conditions. The effects of hysteresis and temporal variability of meteorological conditions were evaluated. Simulations were performed in HYDRUS-1D code for the period April 2013-January 2014 (6601 hours) at three different locations in a delineated portion of the sub-quaternary catchment A80A of Nzhelele with different soil textures. Soil hydraulic characteristics were estimated in a Rosetta library dynamically linked to the HYDRUS-1D model which is based on the numerical solution of a one-dimensional Richard's equation. Analysis of the simulation results suggests that ignoring hysteresis for soils of similar textural class does not lead to any significant deviation of the model predicted soil moisture, unlike for soils with different textural classes.

In this paper, a thermodynamic analysis of Bouc-Wen models endowed with both strength and stiffness degradation is provided. It is based on the relationship between the flow rules of these models and those of the endochronic plasticity theory with damage, discussed in a companion paper (Erlicher and Point, 2007). Using the theoretical framework of that extended endochronic theory, it is shown that an elastic Bouc-Wen model with damage, i.e. without plastic strains, can be formulated. Moreover, a proper definition of the dissipated energy of these Bouc-Wen models with degradation is given and some thermodynamic constraints on the parameters defining the models behavior are emphasized and discussed. In particular, some properties of the energetic linear stiffness degradation rule as well as the so-called pivot rule, well-known in the seismic engineering field, are illustrated and commented upon. An improved energetic stiffness degradation rule and a new stiffness degradation rule are proposed.

Hysteresis in the water retention characteristics of a soil is important in prediction of soil hydraulic properties. Although a number of models have been proposed, some are entirely empirical and others are inconvenient to use. We apply a theoretical approach to derive parameters for a more suitable model based on three geometrical scaling conditions. The first condition determines a shape parameter which is identical for all wetting and drying curves; the second defines the relation between the pressure head scale and the water content scale specific to each curve in wetting or drying; and the third condition determines specific water content scale parameters according to the points of departure and arrival of each scanning curve. Given the saturated water content, all curves can be predicted from knowledge of only one curve. The method is illustrated using the van Genuchten water retention function but could also be applied to other functional forms. Results agree well with the existing data.

Several existing equations for solving the non-linear soil-hydraulic properties are introduced and validated to field and laboratory measured data. Models for non-linear hydraulic properties of unsaturated porous media arise from statistical and mathematical fit through the measured data and they can be expressed in forms of unsaturated permeability versus either pressure head or volumetric moisture content. This paper presents the difference models: Gardner, Knuze et al., Haverkamp et al., van Genuchten and Saxton et al. for calculation of hydraulic properties coefficients, typically unsaturated permeability. The accurate and computational efficiency of these five existing models are evaluated for a series of study cases simulating hydraulic properties of unsaturated porous media. The results indicate that all existing models can be applied to homogenous and heterogenous unsaturated porous media, dry and wet cycles and laboratory and field measuring data. Besides, the statistical fit model is inefficient compared to mathematical fit models. Among the mathematical fit models, van Genuchten model is the most promising model. Gardner model can be competitive with van Genuchten model and Haverkamp et al. model is less efficient than others. The mathematical fit models appear to be attractive alternatives to estimate the unsaturated permeability, although there are concerns regarding the stability behaviour of the occupied air in pores, which need to be resolved. The air movement in unsaturated porous media affected the unsaturated permeability, which gives the difference results between wet and dry cycle. Both of unsaturated permeability and volumetric water content of dry cycle were higher than ones of wet cycle. This suggests that the velocity of air-releasing during a wet process was higher than the velocity of air-entering during a dry process. The infiltration is the most important land applications. So, the wet cycle hydraulic properties test might be concerned. Moreover, most of infiltration fields locate on the mixed grain media. So too, the pore-size distribution could affect the unsaturated permeability of porous media. It was observed that the finer material, the lower unsaturated permeability.

The aim of this paper is to investigate the effects of hysteresis and negative stiffness on seismic response reduction. For this reason, the novel Hysteretic Nonlinear Energy Sink (HNES) is used as a passive vibration control device for seismic response mitigation. So far, HNES performance has been tested in shock mitigation and has proved to exhibit exceptional robustness and energy dissipation merits. Apart from a small mass and a nonlinear elastic spring of the Duffing oscillator (type-I NES), HNES is also comprised of a purely hysteretic and a linear elastic spring of potentially negative stiffness, connected in parallel. The Bouc-Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. In this investigation, the response reduction of a primary two-degree-of-freedom model of a shear building is studied against a strong ground motion which is based on the 1999 Athens, Greece earthquake. The response reduction is achieved by using three optimized passive vibration control devices, i.e., an HNES, a type-I NES, and a traditional Tuned Mass Damper (TMD). The optimum configuration of each device is determined using Differential Evolution, a robust metaheuristic algorithm, using the maximum absolute displacement of the top floor as the objective function. Example problems are presented in order to assert that HNES behavior is vastly superior over both NES and TMD. Furthermore, the key advantage of HNES is its inherent insensitivity to drastic changes in the structural characteristics. In particular, it maintains a significant level of performance even if the column stiffness is reduced by half.

Hysteresis is a term that describes macroscopically many phenomena observed in engineering. The complexity of the actual mechanism behind hysteresis has given rise to the extended use of phenomenological models, such as the Bouc-Wen model. This paper presents a new stochastic identification scheme for Bouc-Wen systems that combines Sawtooth Genetic Algorithm and a Bounding technique that gradually focuses into smaller and better regions of the search space. Numerous studies show that the proposed scheme is very robust and insensitive to noisecorrupted data. Apart from frequency-independent hysteretic characteristics, the method is also able to identify viscous-type damping.

Soil suction is an essential parameter for describing the mechanical behavior of unsaturated soils. For analytical purposes, its value is usually inferred from the soil-water characteristic curve. However, the expressions developed up till now to describe this curve, do not properly account for the physical facts involved in the hysteresis phenomenon. It is generally accepted that hysteresis arises because pores of different sizes are interconnected generating the "inkbottle" effect. In this paper, a twofold model that simulates the porous structure of soils is used and the mathematical expressions describing the hysteresis of the soil-water characteristic curves are obtained. This model considers that the voids in the soil mass are composed of two kinds of elements: the sites (cavities) and the bonds (throats), each kind showing its proper size distribution. Based on these premises and making use of the probability theory, the equations corresponding to the main hysteresis loop during wetting or drying are established and it is shownthat the extent of the hysteretic behavior depends on the parameters describing the size distributions. In addition, the equations describing the specific internal (scanning) paths for cyclic wetting and drying are obtained. Finally, these results are compared with experimental results that include the main hysteresis loop, some scanning curves and the poresize distribution.

Two fundamental problems in economic analysis concern the determination of aggregate output, and the determination of market prices and quantities. The way economic adjustments are made at the micro level suggests that the history of shocks to the economic environment matters. This paper presents tractable approach for introducing hysteresis into models of how aggregate output and market prices and quantities are determined.

This memorial note assesses the impact of Alexei Pokrovskii, a pioneer in the mathematical analysis of systems with hysteresis, on economic analysis. Apart from the seminal contributions made, Alexei was a source of inspiration and encouragement to others seeking to understand the imprints of hysteresis on economic behaviour.

In this paper, several variants of Differential Evolution, Particle Swarm Optimization and Genetic Algorithms are employed for the identification of a Bouc-Wen hysteretic system that represents a full-scale bolted-welded steel connection. The purpose of this work is to assess their comparative performance in a highly nonlinear identification problem. Interesting results are produced that reveal the strengths and weaknesses of each algorithm.

The paper defines the average and local soil storage coefficients, for a soil with relatively shallow water table. By means of an adequate law for the suction distribution on soils level and certain parametrical models for the moisture retention curve of soil, the analytical equations for these storage coefficients were determined. Theoretical results are to be applied for a case study and on the basis of a pertinent analysis, and some recommendations were made for the practical use of formulae proposed for the storage coefficients.

A number of improvements have been added to the existing analytical model of hysteresis loops defined in parametric form. In particular, three phase shifts are included in the model, which permits us to tilt the hysteresis loop smoothly by the required angle at the split point as well as to smoothly change the curvature of the loop. As a result, the error of approximation of a hysteresis loop by the improved model does not exceed 1%, which is several times less than the error of the existing model. The improved model is capable of approximating most of the known types of rate-independent symmetrical hysteresis loops encountered in the practice of physical measurements. The model allows building smooth, piecewise-linear, hybrid, minor, mirror-reflected, inverse, reverse, double, and triple loops. One of the possible applications of the model developed is linearization of a probe microscope piezoscanner. The improved model can be found useful for the tasks of simulation of scientific instruments that contain hysteresis elements.

Absrraci: This paper describes the Preisach theory of hysteresis model in a graphical approach. New simple mathematical function which can relate the Preisach diagrams and the B-H limiting loop is developed and presented. With this new function, the Preisach hysteresis model can be implemented easily without the use of any statistical functions. The model is implemented using the Transmission line Modeling (TLM) method and tested in a practical example. Good agreement is obtained from measurements and simulations.

The ground water is recharged by spreading of the water in downward direction and the moisture content of soil increases. The mathematical formulation of the phenomena leads to the governing equation, which is a nonlinear partial differential equation in the form of Burger's equation which has been solved by using q-homotopy analysis method with appropriate initial and boundary conditions. The average diffusivity coefficient over the whole range of moisture content is regarded as constant. It is concluded that the moisture content of soil increases with the depth Z and increasing time T. The numerical solutions of the governing equation have been obtained in the form of tables and graphs by using Mathematica coding. The numerical solution represents moisture content distribution in the vertically downward direction at any depth Z for time T > 0. This type of problems appears particularly in soil mechanics, hydrology, ceramic engineering and petroleum technology.

A review of hysteresis models for soil-water characteristic curves is presented. The models can be categorized into two groups: (i) domain models (or physically based models) and (ii) empirical models. Some models are capable of predicting scanning curves, while other models are capable of predicting the boundary wetting curve and the boundary drying curve. A comparison of the ability of five selected models to predict the boundary wetting curve showed that the Feng and Fredlund model with enhancements by Pham, Fredlund, and Barbour appears to be the most appropriate model for engineering practice. Another comparison among five physically based models for predicting scanning curves showed that the Mualem model-II gives the best overall prediction of scanning curves. The study showed that taking the effect of pore blockage into account does not always give a better prediction of hysteretic soilwater characteristic curves. A scaling method for estimating the initial drying curve, the boundary wetting curve, and the boundary drying curve is also presented in the paper.

The sorptivity S quantifies the effect of capillarity on liquid movement in a porous material. For liquid infiltration into an initially dry material, S is a parameter that is contingent on both liquid and material properties as well as the maximum liquid content behind the infiltrating front, h m . Scaling analyses are used to derive a dimensionless, intrinsic sorptivity S * that is constant for different liquids, Miller-similar materials and different values of h m . The analyses confirm that S is dependent on b 1/2 , where b = cos / is a measure of the wettability of the liquid. They also indicate a power law relationship between S and S e(av) , the average liquid saturation behind the infiltrating front. Seventeen water and eleven Soltrol 220 horizontal infiltration experiments are reported in uniform, dry sand. Test results show that water is partially wetting in the sand. They also confirm that S / S d eðavÞ , where d = 3.2 for the experimental conditions. The usefulness of a general, dimensionless Boltzmann variable is demonstrated to normalize infiltration profiles for the different liquids. An approximate method for sorptivity calculation is shown to provide an accurate estimate of S * .

In this paper an analytical method is developed to identify the Bouc-Wen model parameters from the experimental data of periodic loading tests. The model parameters are determined by closed analytical relationships such as the predicted and experimental hysteresis loops to have exactly the same maximum force values and coordinates of loop-axes crossing points. Asymmetric hysteretic characteristics are modeled by sewing the solutions of two different Bouc-Wen equations, corresponding to negative and positive values of the imposed cyclic displacement. The method efficiency is illustrated by its application to portraying the asymmetric hysteretic behavior of two vibration control devices.