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Since 1980, average wheat (Triticum aestivum L.) yields have remained nearly stagnant in the southern Great Plains (SGP) and stagnant in the state of Oklahoma. Yield stagnation can sometimes be attributed to a relatively small gap between current and potential yields, but the magnitude of the yield gap for this region has not been well quantified. The objective of this study was to determine the wheat yield and production gaps in Oklahoma at state and county levels. This involved estimation of attainable yield (Y a ) using a frontier yield function and water-limited potential yield (Y p ) using estimated transpiration and transpiration efficiency. Yield gap and production gap relative to Y a and Y p were calculated using grain yields and harvested area for 19 counties. Current average yield (Y c ) was 2.06 Mg ha –1 at the state level, well below the maximum recorded yield at the plot level of 6.59 Mg ha –1 . The Y p of current wheat varieties is far above Y c in Oklahoma, and Y c represents 74% of Y a but only 30% of Y p at state level. For growing season rainfall (GSRF) amount

SUMMARY Fabric and its evolution need to be fully considered for effective modeling of the anisotropic behavior of cohesionless granular sand. In this study, a three-dimensional anisotropic model for granular material is proposed based on the anisotropic critical state theory recently proposed by Li & Dafalias [2012], in which the role of fabric evolution is highlighted. An explicit expression for the yield function is proposed in terms of the invariants and joint invariants of the normalized deviatoric stress ratio tensor and the deviatoric fabric tensor. A void-based fabric tensor that characterizes the average void size and its orientation of a granular assembly is employed in the model. Upon plastic loading, the material fabric is assumed to evolve continuously with its principal direction tending steadily towards the loading direction. A fabric evolution law is proposed to describe this behavior. With these considerations, a non-coaxial flow rule is naturally obtained. The model is shown to be capable of characterizing the complex anisotropic behavior of granular materials under monotonic loading conditions and meanwhile retains a relatively simple formulation for numerical implementation. The model predictions of typical behavior of both Toyoura sand and Fraser River sand compare well with experimental data. Copyright © 2013 John Wiley & Sons, Ltd.

SUMMARY Porosity strongly affects the overall ductile behavior of cohesive geomaterials undergoing plastic deformation. In the present paper, we proposed an original micromechanical approach that suitably couples Drucker–Prager-type plasticity, evolving porosity under general triaxial loadings. The resulting model has the advantage to be based on a single macroscopic yield function, which also plays the role of plastic potential. It is shown that this yield function is particularly appropriate to account for the pore collapse and plastic shearing mechanisms that govern the mechanical behavior of the studied Lixhe chalk. Finally, the new model is implemented and validated by comparison to triaxial tests data, covering a wide range of confining pressures. Copyright © 2011 John Wiley & Sons, Ltd.

The prominent high cycle fatigue (HCF) criteria have been generally proposed based on definition of an equivalent stress that is mainly a modified version of a static failure criterion or a static yield function. One or more effects including the mean normal and shear stresses, different phase shifts or random frequencies of the stress components, relative instantaneous time variations of the stress components, relative time locations of the extrema of the time histories of the stress components, etc. have not been considered by many of the previously proposed criteria. In the present paper, based on the proposed instantaneous stress amplitude and mean stress concepts, three new energy-based HCF criteria are proposed to overcome the mentioned shortcomings. A relevant fatigue life assessment algorithm is proposed and results of the prominent criteria are compared with results of the proposed criteria as well as the experimental results prepared by the author. To introduce a comprehensive study, the criteria are examined for components with complicated geometries under proportional, non-proportional and random loadings. Results confirm the efficiency and accuracy of the proposed criteria. Furthermore, it is deduced that the Liu-Zenner type criteria which include the hydrostatic stress implicitly are more accurate than the Papadopoulos-type criteria that consider the hydrostatic stress explicitly.

Das Wachstum landwirtschaftlicher Kulturen als Funktion des Einsatzes von Wachstumsfaktoren folgt grundsatzlich der „Regel vom abnehmenden Ertragszuwachs”, die unter anderem von Mitscherlich (1928) und vonBoguslawski und Schneider (1962, 1963, 1964) mathematisch formuliert wurde. Auf Basis dieser zwei Wachstumsfunktionen wurden EDV-Programme zur Auswertung von Feldversuchen und zur Ableitung des wirtschaftlich optimalen Dungerbedarfs entwickelt und mit deren Hilfe die Dungungsoptima aus 43 mehrjahrig durchgefuhrten Phosphat(P)-Steigerungsversuchen abgeleitet und miteinander verglichen. Drei Versuche mit linearer oder uberproportionaler Abhangigkeit des Ertragszuwachses von der P-Dungung liesen sich mit beiden Methoden nicht sinnvoll verrechnen. Das Gleiche galt fur vier Versuche, bei denen der Hochstertrag bereits in der ersten Dungungsstufe eintrat. In 36 Versuchen, deren Ergebnisse der „Regel vom abnehmenden Ertragszuwachs” entsprachen, ergab sich eine sehr enge Ubereinstimmung beider Verfahren hinsichtlich der errechneten Rentabilitatsoptima (R2 = 0,946). Die Korrelationskoeffizienten zwischen dem P-Saldo im Rentabilitatsoptimum und dem CAL-P-Gehalt im Boden zu Beginn des Versuchs lagen bei R2 = 0,70 (Mitscherlich, 1928) und R2 = 0,65 (von Boguslawski und Schneider, 1962, 1963, 1964). Der daraus abgeleitete Bereich fur den optimalen P-Vorrat im Boden (P-Dungungsoptimum entspricht P-Abfuhr) lag bei 8–10 mg CAL-P (100 g Boden)–1. Beide Verfahren sind zur Ableitung des P-Dungungsoptimums geeignet, wenn der Ertragsverlauf im Sinne der „Regel vom abnehmenden Ertragszuwachs” erfolgt und wenn die Nahrstoffsteigerungsreihe so angelegt ist, dass innerhalb dieser Reihe abnehmende Mehrertrage zu erwarten sind. Comparison of two procedures to evaluate phosphate-fertilizing field trials Growth response of agricultural crops to different input levels (e.g., fertilizer rates) can be described by the “law of diminishing increments”, which has been formulated mathematically amongst others by Mitscherlich (1928) and vonBoguslawski and Schneider (1962, 1963, 1964). In the present paper, the economically optimal phosphate-fertilizer requirements in 43 long-term phosphate (P)-fertilization experiments were calculated using equations on the basis of the yield functions of Mitscherlich or von Boguslawski and Schneider, respectively. For three field trials with linear or disproportionately high yield responses on P fertilization, none of the two procedures could be used. The same held for four trials with maximum yields already appearing at the first fertilization level. Similar P-fertilization optima were calculated for 36 trials following the “law of diminishing increments”, resulting in a highly significant correlation (R2 = 0.946) between both procedures. The correlation coefficients between the phosphate balance at the calculated optimum profitability and CAL-P content in the soils at trial start were R2 = 0.70 (Mitscherlich, 1928) and R2 = 0.65 (von Boguslawski and Schneider, 1962, 1963, 1964), respectively. An optimal soil P content of 8–10 mg CAL-P (100 g soil)–1 was deduced. Both methods are applicable to calculate the optimum phosphate-fertilizer requirement if yield effects due to P fertilization follow the “law of diminishing increments” and the increments of fertilization levels in each trial are established in a way that diminishing yield increments can be expected.

The effect of suction on the behaviour of iron ore has been studied from both physical and mechanical points of view. The porosity and the suction phenomena have been analysed using different experimental techniques. Uniaxial compressive tests on partially saturated samples have shown that the suction is responsible for strength and cohesion improvement. Considering the theory of partially saturated porous soils of Coussy and Dangla (Mecanique des sols non satures (2002 edn). Hermes Science: 2002; 390), we have proposed a constitutive law for partially saturated iron ore. The real increase in the apparent cohesion due to the capillary attraction forces is overestimated if the yield function is written in terms of effective stresses. The effect of the capillary cohesion has been modelled with a function in the expression of the apparent cohesion of the yield function. The effect of suction on the mechanical behaviour has been represented in the effective stresses space and in the total stresses space like the Alonso model (Geotechnique 1990; 40:405–430). Copyright © 2005 John Wiley & Sons, Ltd.

Due to the effect of transformation induced plasticity (TRIP) , TRIP-steels are very promising materials, e.g. for the automobile industry. The material behavior is characterized by very complex inner processes, namely phase transformation coupled with plastic deformation and kinematic hardening. We establish a micromechanical model which uses the volume fractions of the single phases, the plastic strain and the hardening parameter in every grain of the polycrystalline material as internal variables. Furthermore, we apply the Principle of the Minimum of the Dissipation Potential to derive the associated evolution equations. The use of a coupled dissipation functional and a combined Voigt/Reuss bound directly results in coupled evolution equations for the internal variables and in one combined yield function. Additionally, we show numerical results which prove our model's ability to give a first prediction of the TRIP-steels' complex material behavior. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

By now new modern rice varieties (MVs) with multiple pest and disease resistance have completely replaced early MVs, such as IR5 and IR8, except in a few areas of Asia. This study attempts to identify the changing impacts of ‘first-generation’ and ‘second-generation’ MVs on productivity in rice farming by estimating the yield function, while correcting selectivity bias arising from the choice of varieties. For this purpose, we used farm-level survey data collected for eleven cropping seasons in Central Luzon in the Philippines from 1966 to 1990. We found that while the yield advantage of first-generation MVs over traditional varieties was limited, the yield-increasing effect of second-generation MVs over first-generation MVs was highly significant. In particular, the adoption of improved MVs significantly contributed to yield growth under the irrigated condition and during the dry season. Thus, we conclude that the Green Revolution would not have been revolutionary without the development and the diffusion of second-generation MVs with multiple pest and disease resistance.

In this contribution, an approach towards a thermodynamically consistent constitutive model for fluid mud is presented. Fluid mud exhibits highly non-Newtonian, thixotropic behaviour. It can be classified as a structured fluid. Typically, its viscosity is modeled using Bingham-type rheological models of different complexity [1, 2]. Here, the three-dimensional non-Newtonian constitutive behaviour will be modeled based on a visco-elasto-plastic model. At the current stage, a Drucker-Prager-like yield function has been formulated. Viscosity is assumed to be a function of shear viscosity. First results show the general ability to represent experimental data. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A simple and accurate non-layered plastic element which is capable of capturing the development of plastic curvatures across the thickness of the plates is presented in this paper. The influence of transverse shear forces on the plastic behaviour of plates is also investigated here. This non-layered plastic element is based on: (i) the four-node quadrilateral strain element for shear flexible elastic plates given by the authors; (ii) the plastic hinge formulation outlined by Shi and Atluri; and (iii) the modified Ilyushin's yield function which can account for both the development of plastic deformations across the thickness of plates and the effect of transverse shear forces. The numerical examples given here demonstrate that the present non-layered plastic element can achieve the results obtained by the layered element model and the transverse shear forces considerably affect the plastic behaviour of plates under certain load conditions.

To capture the complex elastoplastic response of many materials, classical isotropic and kinematic hardening alone are often not sufficient. Typical phenomena which cannot be predicted by the aforementioned hardening models include, among others, cross hardening or more generally, the distortion of the yield function. However, such phenomena do play an important role in several applications in particular, for non-radial loading paths. Thus, they usually cannot be ignored. In the present contribution, a novel macroscopic model capturing all such effects is proposed. In contrast to most of the existing models in the literature, it is strictly derived from thermodynamical arguments. Furthermore, it is the first macroscopic model including distortional hardening which is also variationally consistent. More explicitly, all state variables follow naturally from energy minimization within advocated framework. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

HCP metals such as magnesium are characterized by a strong interplay between dislocation slip and deformation-induced twinning. These micromechanical processes result in a complex macroscopic behavior. More precisely, in addition to classical isotropic and kinematic hardening, the shape of the macroscopic yield function changes during deformation as well. This effect which is frequently referred to as distortional hardening is particularly pronounced in case of non-radial loading paths typical for most forming processes. Consequently, a physically sound distortional hardening is of utmost importance for several technically relevant applications. In the present contribution, three different of such enhanced hardening models are critically analyzed. Focus is on the modeling of magnesium. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The process chain for components made of sheet metals consists of different forming techniques like hot rolling, cold rolling, and deep drawing as well as heat treatment operations like annealing. For the design and optimization of the whole manufacturing process and the final component behavior, a correct representation of the material behavior and the application of appropriate numerical simulation techniques are required. For our first investigations, a ferritic mild steel DC04, which is a typical steel grade for automotive applications, is analyzed. Therefore, specimens are taken out of a real manufacturing process after hot and cold rolling and after annealing. These specimens are intensively investigated in order to study the texture evolution and the development of other material properties, like yield function during the process chain. In this paper different homogenization methods are used to simulate the texture evolution during cold rolling. The results are compared concerning accuracy and efficiency of the considered models. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Pannell's finding that risk reduces the optimal rate of herbicide use and raises the economic threshold for weed control is found to depend upon the form of the yield function. Pannell's results apply only to convex yield functions. For sigmoidal functions, such as the logistic, risk has the opposite effect over the concave portion of the function's range.

A batch fermentation is modelled with constant and variable yeild terms. It is shown that the model cannot exhibit oscillations if a constant yield term is used. Oscillations in the cell concentration, but not in the limiting substrate concentration, can be simulated if a variable yield function of the limiting substrate is used. Conditions, for which the variable yield needs to satisfy in order to generate oscillations in the cell concentration, are discussed. The primary condition is that the yield must become zero at the same time that the specific growth rate does. Experimental results exhibiting oscillatory behavior are presented and compared with the proposed model.

The general yield function in the hierarchical approach for constitutive modelling of materials is used with Perzyna's theory to characterize viscoplastic behaviour of geologic materials: a sand and rock salt. Particular attention is given to determination of the constants from laboratory quasistatic or short term, and creep tests. The proposed model is verified with respect to observed laboratory response of the sand and salt. It is implemented in a non-linear finite element procedure and applied to analyse time-dependent behaviour of a cavity in the rock salt.

Die radikalisch initiierte Copolymerisation von Butadien/Styrol in Emulsion verlauft zwischen 5 und 50°C bis zu Umsatzen von ca. 60% nach einer Reaktion nullter Ordnung. Bei bekannter Aktivierungsenergie last sich der Reaktionsverlauf in Abhangigkeit von einer vorgegebenen Temperaturfunktion beschreiben. Es werden fur verschiedene Moglichkeiten der Warmeabfuhr im Reaktor Temperaturund Umsatz-Verlauf der Polymerisation, abhangig von der Anfangstemperatur, berehnet. Eine Reaktionsfuhrung mit Endtemperaturen von ca. 55°C ist nur in sehr wenigen Fallen realisierbar. Geringe Abweichungen von diesen stabilen Zustanden fuhren zu uberhohten Endtemperaturen und damit zu hohen Innendrucken im Reaktor. The free-radical copolymerization of butadiene/styrene in emulsion is a zero order reaction between 5 and 50°C for a conversion to about 60% For a known activation energy the course of the reaction can be described in dependence of a given temperature function. For different cases of heat removal the temperature and yield function of the polymerization are calculated in dependence of the starting temperature. Reaction courses with end-temperatures of about 55°C can be realized only in a few cases. Small deviations of such stable conditions lead to increased end-temperatures and therefore to high pressures in the reactor.

An explicit from of the plastic matrix for a Mohr–Coulomb material in two dimensions is presented. The derivation, which assumes elastic–perfectly plastic behaviour is obtained by direct differentiation of a non-invariant expression for the Mohr–Coulomb yield function. A FORTRAN 77 subroutine is also provided.

For many soils experimental evidence suggests that deviation from normality between the plastic strain increments and the yield function is exhibited mainly in the volumetric behaviour, whereas the deviatoric behaviour exhibits normality. An analysis of the consequence of this observation is presented, and it leads to an expression for the plastic potential function as composed of two functions, a yield function and another dependent only on the hydrostatic pressure; the latter is considered to constitute the concept of correction functions presented recently by Desai and Siriwardane13.

A relatively simple yield model is developed for isotropic, porous rocks which yield in a ductile manner. The flow rule and yield function are derived using an adaptation of the work-balance approach of critical state soil mechanics. This adaptation allows for the dissipation of work by frictional and volume change mechanisms, including the dissipation of frictional work at sensibly constant plastic volumetric strain. The yield model uses two material parameters—a basic frictional parameter and a plastic volumetric strain adjustment parameter which is assumed to be constant for the yield locus corresponding to a particular specific volume. The model gives excellent fits to yield loci for two limestones, a chalk and gypsum plaster prepared at different initial void ratios.

There is a serious shortage of yield data for Jojoba (SIMMONDSIA CHINENSIS) from mature and cultivated plantations of ten years or older. Thus, the optimal quantities of water and fertilizers that are needed annually by a Jojoba plantation to achieve maximum profits were estimated from existing plantations. A computer model (IMSL subroutine ZXMWD) was used to determine a Mitscherlich yield function. An economic profit model that incorporates the yield function was then designed to maximize the profits. According to the net present value (NPV) criterion, the maximum yearly net profit is about $7800 per ha, which is achieved during the 11th growth year. The computed cumulative NPV is approximately $21,000 per ha for the entire 15-year period. Similar profits were calculated when the model was tested to examine the NPV using different assumptions with respect to varying costs.

Auf der Grundlage des Traglastprinzips wird mit funktionalanalytischen Methoden das Problem der kritischen Last Prandtl-Reusscher Korper untersucht. Mit Hilfe der Misesschen Fliesfunktion wird auf dem Raum M der Spannungsfelder, die den Gleichgewichtsbedingungen und den Randbedingungen fur die Spannungen genugen, ein nichtnegatives Funktional definiert, das eine positive untere Grenze d genau dann besitzt, wenn M kein statisch zulassiges Feld enthalt. Unter der Voraussetzung der Separabilitat von M wird ein Verfahren zur Konstruktion einer gegen d konvergenten Folge (Minimalfolge) begrundet, das sich in der Anwendung auf die Losung endlicher linearer algebraischer Gleichungssysteme reduziert. Betrachtet werden der dreidimensionale und der ebene Fall. Ein numerisches Beispiel wird angegeben. On the base of limit analysis the problem of the critical load of Prandtl-Reuss bodies is being studied by functional-analytical methods. By Mises yield function on space M of the stress fields, which satisfy the equations of equilibrium and the boundary conditions for the stresses, a non-negative functional is being defined that has a positive infimum d, if and only if M does not contain a statically admissible field. Assuming the separability of M, a method for constructing a sequence, convergent to d, is being proved, what reduces itself in the application to the solution of finite linear algebraic systems of equations. The three- and the two-dimensional case is considered. A numerical example is given.

This paper presents a technique for estimating the physical yield function of a fishery when detailed biological and environmental data are lacking. The physical yield function of the California trawl fishery is incorporated in an economic model to show the relationship between maximum sustainable physical yield of the fishery and maximum economic yield. Maximizing the economic benefit of the fishery to society would involve a drastic reduction in resource use at a catch level considerably below the biological maximum sustainable yield. Only through marginal cost pricing can resources be allocated efficiently to the fishery.