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In the automotive engineering community, the modified maximum force criterion proposed by Hora and co-workers is considered acceptable for theoretically estimating the forming limit curve (FLC) of sheet metals. Based on this criterion, a graphical method is proposed to simplify evaluation of the FLC. This paper investigates the proposed graphical method in a special case by using a power-hardening law and the Mises yield function, which leads to an explicit expression of the critical strains according the strain paths. The FLC of a DP590 sheet estimated using the proposed method is compared with that estimated using existing analytical methods. The proposed method provides the best prediction of the FLC of the tested material. For verification, the calculated FLC is then adopted into the finite-element method to predict the punch stroke at fracture of several notched specimens subjected to Nakazima tests. The good agreement between the predicted and experimentally determined values of the punch strokes verifies the ability and potential of the proposed method in industrial engineering.

Extended linear Drucker–Prager (DP) model has been a proper choice to capture the stress-strain of cylindrical concrete columns confined by fiber reinforced polymers (FRPs). However, most existing DP models calibrated by uniform active/passive tests are unsuitable for concrete under non-uniform passive confinement. This paper aims to calibrate the key parameters i.e., friction angle, plastic dilation angle and hardening needed for the DP model based on tri-axial test results on concrete cube subjected to non-uniform confinement. The effect of friction angle parameter is isolated from the hardening parameter within the yield function while the friction angle is defined as a function of concrete grade and hardening as a function of lateral confinement stiffness ratio. Here, the plastic lateral strains of non-uniform confined concrete, which could be obtained in cyclic tests but were usually left aside, are used to define a function for plastic dilation angle which works compatibly with the yield parameters. The resultant extended DP model could capture the stress-strain behaviour of concrete under both uniform or non-uniform passive pressure as well as the variable flow rules and different load paths occurring across the section of FRP-confined non-circular concrete.

The thermomechanical coupling constitutive model of concrete is a critical subject for the theoretical investigation and numerical simulation of the mechanical behaviors of concrete members and structures at high temperature. This paper presents a thermomechanical coupling constitutive model for the description of the mechanical behaviors of concrete at different temperatures. The expression of the elastic strain increment is derived with the free energy function including the temperature variable. The expression of the plastic strain increment is derived from the yield function based on the Drucker&ndash, Prager strength criterion. The elastoplastic damage effect is included in this constitutive model. The damage variable is included in the yield function to consider the effect of the damage on the elastoplastic mechanical behaviors of concrete. The proposed constitutive model is validated by the comparison of the simulation results of the uniaxial compression tests of concrete at different temperatures with the corresponding test results. The simulation results accord well with the test results at different temperatures. This indicates that the proposed constitutive model can characterize the mechanical behaviors of concrete at different temperatures with considerable accuracy. The proposed constitutive model was applied to simulate an axially compressive concrete column. The simulation results are consistent with the essential mechanical response behaviors of concrete members at different temperatures.

This article investigates the macroscopic behavior of uniaxially pre-strained large-scale DP780 and CHSP45R sheet specimens. A novel grip system was designed for the pre-straining of the large tensile specimens. After this first loading, the uniformly strained gauge-section of the large-scale specimen was machined to smaller standard specimens. After pre-strain, further uniaxial tension tests at 45° and 90° from the pre-tensile direction, compression test and in-plane biaxial tension tests at 1:1, 2:1 and 1:2 force ratios were conducted. The flow curves and the instantaneous r-values of the pre-strained steel in the aforementioned uniaxial loading directions were compared with their monotonic response. In addition, the pre-strained compression test was incorporated to the π-plane at several incremental offset strains. The yield function- and isotropic hardening-based homogeneous anisotropic hardening (HAH) model (Barlat et al., 2014) was selected to predict the material response after non-linear strain path change. The Swift law characterized the isotropic hardening, while the Yld2000-2d anisotropic yield function (Barlat et al., 2003a) represented the yield locus. All the coefficients of the distortional plasticity model were manually determined and validated with an optimization algorithm. The HAH-predictions of the pre-strained flow curves and yield loci at several offset strains were in reasonable agreement with the experimental data, while the instantaneous r-value evolution was qualitatively well captured.

The non-associated flow rule (non-AFR), which has been proved with advantages in accurately predicting yield stress components and Lankford coefficients, has different definitions for yield function and plastic potential function. Currently, there are two typical approaches to determine the plastic strain for non-AFR, one is called simple method which still uses the equivalent plastic strain (EPS) to calculate the plastic strain tensor, while the other is called full method which adopts the plastic compliance factor. Many researchers prefer to adopt the simple method in calculating the plastic strain due to its higher computation efficiency and its acceptable accuracy like the full method for some materials. However, the limitation and application condition of the simple method are still ambiguous. In the present work, a restriction for calculating the parameters in plastic potential function for the simple method is clarified and the limitation of the simple method has also been investigated. It is found that if the relative error of the difference between the yield function value and that of plastic potential function is within ±5% and hardening exponent is in the range of 0.1–0.3, the maximum absolute value of the relative error of the stress predicted by the simple method can be controlled less than 1.6%. Besides, an effective approach is introduced to reduce the error of the stress predicted by these two methods, which can improve the applicability of the simple method for those materials with the relative error of the difference between the value of yield function and that of plastic potential function is less than 10%. In order to have deeper understanding about their applicability, the two methods are compared under uniaxial tension along different orientations for AA2090-T3 and AA2008-T4 with the fully implicit return-mapping scheme. Fracture simulations of AA2090-T3 have also been conducted by introducing different methods. The results show that during the loading in transverse direction, the difference of EPSs predicted by these two methods is very small for AA2008-T4, while for AA2090-T3, the EPS predicted by the simple method is almost twice of that calculated by the full method. This further indicates that the applicability of the simple method mainly depends on the characteristics of materials.

The forming limit experiments of 5754O aluminum alloy under combined loading paths are carried out and the forming limit diagrams made up of strains under four combined loading paths are obtained. The effects of the loading path on the forming limit under four combined loading paths are analyzed. The corresponding stress path is solved for each experimental strain path based on Yld2000-2d yield function and Chaboche hardening law. Then the theoretical FLDs-strain under the above combined loading paths are obtained based on Yld2000-2d yield function and Chaboche hardening law using M-K theory and validated with the experimental results. The effect of the angle of the groove in M-K theory on the prediction of forming limit is analyzed. The forming limit diagrams made up of the first and second principal stresses and forming limit diagrams made up of equivalent plastic strains are obtained from the experimental FLDs-strain under combined loading paths based on Yld2000-2d yield function and Chaboche type hardening model. The calculated FLDs-stress and FLDs-EP from experimental FLDs-strains are compared with the theoretical ones calculated with M-K theory. It is found that the loading path-dependence of FLD-stress and FLD-EP are much less than that of FLD-strain. The final thickness of 5754O aluminum alloy sheet under different loading paths is obtained from the FLD-strain. Then the thickness reduction rate of sheet metal are adopted to construct the forming limit diagram, which is named FLD-tr for abbreviation. It is found that the effect of strain path on FLD-tr is similar to those on FLD-stress and FLD-EP and is much less than that on FLD-strain. Since the thickness reduction rate can be easily obtained from FLD-strain without yield function and hardening model, FLD-tr is convenient for engineering application. The forming limits under the combined loading paths where the pre-strains are larger than that obtained in experiments are calculated and analyzed. It is found that, besides FLD-strain, the FLD-stress, FLD-EP and FLD-tr are also affected by loading paths when the pre-strain achieves some value and the reason is analyzed in detail. The prediction of forming limit under such combined loading paths with large pre-strains is discussed.

Numerical simulation of void growth from thousands of randomly distributed particles is used to assess the functional dependence of the Gurson model. Shock loading of the model region followed by a ramped pressure release creates a smoothly varying velocity field in which the void growth is inertially stabilized. The pressure, effective stress, and void fraction are obtained from the simulation for comparison with the Gurson model. The results show that the pressure-void fraction relation from the model reasonably follows the simulation data, but the numerical data exhibit significantly greater void fraction dependence on the effective stress than the Gurson model.

Constitutive models developed for simulating plastic response upon strain path changes are combined: 1) a macro-mechanical model based on anisotropic yield function, associated flow rule and distortional hardening using Homogeneous Anisotropic Hardening (HAH) approach; 2) a micro-mechanical model using self-consistent crystal plasticity in conjunction with crystallographic dislocation-density based hardening. The micro-mechanical model is employed to probe the yield surface in order to gain the insight required to construct empirical rules appropriate for the macro-mechanical model. Simulation results of the micro-mechanical model under various loading conditions involving strain path changes and different crystallographic textures are presented. The trends captured in the yield surface evolution predicted by the micro-mechanical model were used to validate and improve the empirical rules used in the HAH model.

Gurson’s model and its numerous modifications are established for simulating ductile failure. However, this model is formulated within the theory of simple materials which is why it predicts a localization of deformation within an infinitesimally thin band for the softening regime. Corresponding FEM simulations exhibit a spurious mesh dependency. In order to overcome this problem, several heuristic extensions of Gurson’s model to non-local or gradient theories were proposed in literature. Although these extensions are computationally effective, the particular implementation and interpretation of the additional terms and the corresponding constitutive parameters is problematic. In contrast, the extension of Gurson’s model by Gologanu et al. (1997) (GLPD model) towards strain gradient media by homogenization does not have these problems but its numerical implementation is considerably more complicated. The present contribution aims in providing a gradient extension of Gurson’s model which combines computational efficiency with a sound micromechanical basis. For this purpose a theory of homogenization towards unconstrained microdilatational media is developed. Based on this theory, a limit-load analysis is performed for a unit cell with void leading to a closed-form yield function of Gurson-type which contains additional terms of the microdilatational theory.

The work described in this paper is the development of a buckling model based on the classical energy method of flange area material using a one-dimensional beam geometry assumption to predict flange wrinkling in hot deep drawing aluminium alloys with macro-textured blankholder surfaces. A series of deep drawing experiments utilising different macro-textured tool surfaces were performed to investigate the effects of process parameters and texture features on flange wrinkling. The results have shown that wrinkling occurs when the hollow dimension of radially grooved textures reached a certain magnitude dependent on process conditions. A dislocation-driven based continuum damage mechanism (CDM) material model for aluminium alloys at elevated temperatures was used to model the viscoplastic behaviour during deformation. The newly developed buckling model was validated by comparison with experimental results. The predicted results showed that the resistance to wrinkling increases with increasing forming temperature and decreasing forming speed, depending on the particular viscoplastic characteristics of the work-piece. The effects of texture ratio and draw ratio on wrinkling were found to be more significant than the effects of the temperature and strain rate. The buckling model developed in this paper can be used to model the flange wrinkling phenomena, as well as the non-isothermal feature in the hot stamping condition using the macro-textured tool surfaces.

Combined with the actual conditions of the middle section of the V# orebody of Xincheng Gold Mine, the criterion, the yield function, and the softening parameter of the double-yield model were studied. And the simulation parameters of the double-yield model were obtained according to the mechanical parameters of the filling body in Xincheng Gold Mine. The FLAC3D numerical simulation method was used to simulate the filling body of first-step mining stage, and the simulation results of the initial and later stages were analyzed. Real-time monitoring equipment was buried in the second layer of the first-step mining stage to get the internal stress-strain law of the filling body. As for double-yield model, the data of the second stratified monitoring, the data of the real-time monitoring, and the data monitored by the Mohr-Coulomb model of the filling body were compared and analyzed. The applicability of the double-yield model in simulating the filling body was verified, which was closer to the results of actual situation. At the same time, the distribution and variation of stress and strain were basically understood. The above analysis results provide a scientific basis for the optimization of deep mining in Xincheng Gold Mine.

A coupled numerical–experimental inverse calibration approach was implemented and systematically validated to evaluate the formability of high-strength, hot-rolled, hyper-burring (HB780) steel sheets and dual-phase (DP780) steel sheets. The proposed methodology featured the determination of hardening behavior beyond the uniform elongation limit at large strain and shapes of 3-D, non-quadratic yield functions: Hosford and Yoshida models. To accurately identify the 3-D yield functions and directly monitor the strain localizations of hemispherical domes for the virtual numerical forming limit analyses, stretching tests were recommended for the investigated hot-rolled sheets. The modeling procedure was evaluated by comparing the forming limits of the stretching tests’ various sample widths to those of the experiments, which confirmed the validity of the identified constitutive model parameters by predicting the localized failure strains and punch force–displacement curves under different deformation modes. For the purpose of validation, simulations and experiments of cylindrical circular cup drawing tests were performed. The proposed numerical procedure could predict the profiles of eared cups, locations of fracture, and drawing limit ratios of the two hot-rolled sheets without the input of the forming limit diagram when proper calibrations of the 3-D, non-quadratic, anisotropic yield function and strain hardening at large strains were guaranteed.

In recent years, in order to improve the precision of the springback prediction, many advanced material constitutive models have been developed to describe the complex material behavior of sheet metal upon load reversals. The Yoshida-Uemori (Y-U) and the homogeneous yield function-based anisotropic hardening (HAH) models are typical models which are able to predict the Bauschinger effect, transient hardening and permanent softening phenomena. The heavy identification efforts raise to be one main chanllenge before their application due to the numerous parameters. Appropriate tests and robust optimal methods are needed to calibrate parameters. In this work, cyclic stress-strain curve of DP780 steel sheets are obtained by tension-compression tests, and then the parameters of modified Y-U and HAH model are identified through global optimization approach. The identified parameters are verified by the comparison between springback results of U-shape draw-bending process and simulation.

The combined loading tests of 5754O aluminum alloy sheet are used to verify the yield function. Three yield functions are implemented into the commercial finite element model (FEM) code ABAQUS as a user material subroutine UMAT for the FEM simulation of the combined loading tests. The comparison of the simulating and experimental results shows that the modified Yld2000-2d yield function can describe the mechanical behavior of 5754O aluminum alloy sheet under combined loading paths reasonably while other three yield functions do not. The performance of the modified Yld2000-2d yield function on describing the mechanical behavior under combined loading paths is analyzed in detail. It is concluded that the modified Yld2000-2d yield function can be adopted to describe the deformation behavior of 5754O aluminum alloy sheet for industrial applications.

Traditional methods for structural damage evolution and failure mode analysis usually depend on specific failure path analysis, which is inefficient and time-consuming to implement for complex structures. In this paper, an efficient failure path-independent methodology for structural damage evolution and failure mode analysis of framed structures is proposed based on the elastic modulus reduction method. The element bearing ratio, uniformity of element bearing ratio and reference element bearing ratio are defined in terms of the homogeneous generalized yield function of spatial beam element, while a dynamic criterion is presented to identify the highly stressed elements. Subsequently, a self-adaptive strategy of elastic modulus adjustment is developed to reduce the elastic moduli of the highly stressed elements for simulation of structural damage evolution. Finally, the reduction rate of elastic moduli of the highly stressed elements is presented to determine the failed sections among the failure elements in the last iteration, based on which the potential failure mode is identified. The applicability, computational accuracy and efficiency of the proposed methodology are validated by comparing with the elasto-plastic methods through two numerical examples.

In the current study, spring-back of DP980 steel sheet was numerically evaluated for U-bending using a yield function with a hardening model. For spring-back prediction, two types of yield functions - Hill'48 and Yld2000-2d - were considered. Additionally, isotropic hardening and the Yoshida-Uemori model were used to investigate the spring-back behavior. The parameters for each model were obtained from uniaxial tension, uniaxial tension-compression, uniaxial tension-unloading and hydraulic bulging tests. The numerical simulations were performed using the commercial software, PAM-STAMP 2G. The results were compared with experimental data from a U-bending process. Key Words : Spring-back, Hardening Model, Yield Function, U-bending, Advanced High Strength Steel 1. 서 론 최근 자동차 연비 규제 및 배기가스 규제가 강화되면서 차체 경량화가 주요 이슈로 대두되고 있다. 차체 경량화를 위한 방안으로 초고강도강을 적용하는 사례가 점점 증가하고 있다. 초고강도강을 차체에 적용할 경우, 탄성회복량의 증가로 인하여 과다한 스프링백이 발생하기 때문에 치수정밀도를 확보하는데 어려움이 있다. 이러한 문제를 해결하기 위해 유한요소해석을 이용하여 스프링백을 사전에 예측하고 이를 생산공정에 반영하고 있다. 하지만 기존의 구성방정식은 바우싱거(bauschinger) 효과, 전이(transient) 거동, 소재의 변형에 따른 탄성계수의 변화 및 이방성 거동 등을 고려하기 어렵고 높은 예측정밀도를 얻는데 한계가 있다. 따라서, 유한요소해석에 사용된 구성방정식이 소재의 거동을 보다 정밀하게 모사할 필요가 있다. 이에 따라 정밀하게 스프링백을 예측하기 위한 연구가 활발하게 진행되고 있다. Park 등[1]은 이동경화 모델에 기반하여 MS1470 강판의 스프링백을 예측하였다. 그 결과, 기존의 등방경화모델을 사용한 경우에 비해 실험 결과와 보다 유사한 형상을 보이는 것을 확인하였다. 또한, Kim 등[2]은 등방-운동성경화 조합모델을 활용하여 zircaloy-4 판재의 경화 거동을 예측하였고 Ha 등[3]은 항복함수의 찌그러짐에 기반한 경화모델을 사용하여 EDDQ 강판의 이방성 경화 거동에 대해 조사하였다.

Strain localization is one of the main sources of failure in sheet forming processes. State of the art forming limit curves allow the prediction of localization for linear strain paths but fall short in case of non-proportional loading. The aim of this contribution is to revisit the Modified Maximum Force Criterion (MMFC) and extend it to accommodate distortional hardening models. This is accomplished by uncoupling its formulation from any particular yield function and thus enabling its use as a generic framework for the prediction of forming limits under arbitrary loading conditions. Furthermore a novel approach is proposed for considering strain rate sensitivity, which substantially improves the predictive capabilities of the model under plane strain tension conditions. The method is applied to steel and aluminum materials and the role of phenomena such as Bauschinger effect, latent hardening and cross-loading contraction on localization are discussed.

The object of this paper is the definition of a generalised constitutive model for geomaterials, based on elastoplasticity. Two are the tasks of the paper: the substantial enhancement of an existing hierarchical yield function and the definition of an isotropic hardening constitutive model for the behaviour of both cohesive and frictional geomaterials. After its definition, the new function will be compared with different yield surfaces existing in literature in both the deviatoric and the meridian representation. Thereafter, the constitutive model will be outlined by defining hierarchical expressions for hardening laws and stress–dilatancy relationship in order to take into account several aspects of soil behaviour. Finally, some comparisons between data from experimental tests on clay and sand will be made to highlight the hierarchical structure of the proposed model.

A simple cyclic elastoplastic constitutive model for sand is proposed based on the UH model for overconsolidated clay. The proposed model has the following features. First, in order to describe the stress-induced anisotropy in sand, a rotational hardening rule is introduced for the evolution of the yield surface axis with development of plastic deviatoric strain in the principal stress space. Second, the relationship between the rotational axis and stress-induced anisotropy is modeled by introducing the slope of rotational axis into the yield function. The flatness of the yield surface can be determined by the slope of rotational axis. Finally, a revised unified hardening parameter is proposed to incorporate the stress-induced anisotropy. The model capability in describing the cyclic response of sand is verified by comparing the simulations with available test results.

In practice, precast concrete structures are often being designed by manual methods and linear finite element analysis in the ultimate limit state. This practice leads to suboptimal structures, and the behaviour of the in situ cast joints are unaccounted for. More accurate and efficient means of design are therefore needed, and a framework based on finite element limit analysis is being developed. In this paper, a one-dimensional multiscale joint element is presented, and a mechanical model is proposed as the yield function of the macro element. The scope of the model is to capture the behaviour of joints in three dimensions subjected to triaxial stress, and the resulting mathematical optimisation problem fits the format of semidefinite programming. The presented joint element is analysed and a real size example of a four-storey stairwell subjected to shear and torsion of precast concrete is presented. The influence of the joints on the behaviour of the stairwell is assessed.

Most of sheet metals belong to orthorhombic aggregates of cubic crystallites. Since both the elasticity tensor and the yield function of sheet metals depend on the crystalline orientation distribution, some correlations between elasticity and plasticity must exist. Employing the correlations, herein we derive the computational expressions of determining all elastic and plastic parameters in the elasticity tensor and the general Hosford yield function only by the data of uniaxial tension tests. By the elastic FEM numerical simulations and the plastic Taylor-Bishop-Hill model's numerical simulations, we verify the correlations and the computational expressions, and compare the general Hosford yield function with the Hill quadratic yield function and the Hill 1990 yield function. The main goal of this paper is to give a method of determining all the elastic and plastic parameters in the elasticity tensor and the general Hosford yield function only by uniaxial tension tests.

This study aimed to evaluate the effect of constitutive equations on springback prediction accuracy in cold stamping with various deformation modes. This study investigated the ability of two yield functions to describe the yield behavior: Hill’48 and Yld2000-2d. Isotropic and kinematic hardening models based on the Yoshida-Uemori model were adopted to describe the hardening behavior. The chord modulus model was used to calculate the degradation of the elastic modulus that occurred during plastic loading. Various material tests (such as uniaxial tension, tension-compression, loading-unloading, and hydraulic bulging tests) were conducted to determine the material parameters of the models. The parameters thus obtained were implemented in a springback prediction finite element (FE) simulation, and the results were compared to experimental data. The springback prediction accuracy was evaluated using U-bending and T-shape drawing. The constitutive equations wielded significant influence over the springback prediction accuracy. This demonstrates the importance of selecting appropriate constitutive equations that accurately describe the material behaviors in FE simulations.

International audience; Granular materials are the most recurrent form of solid-state matter on Earth. They challenge researchers and engineers in various fields not only because they occur with a broad variety of grain sizes, shapes and interactions in nature and industry, but also because they show a rich panoply of mechanical states. Despite this polymorphism, all these different types of soils, powders, granules, ores, pharmaceutical products,. .. are instances of the granular matter with the same least common denominator of being sandlike (psammoid in Greek), i.e. solid grains interacting via frictional contacts. This review describes milestone contributions to the field of granular materials since the early elastic-plastic models developed for soils in the 1950s. The research on granular materials has grown into a vast multidisciplinary field in the 1980s with increasing focus on the microstructure and owing to new experimental tools and discrete simulation methods. It turns out that the granular texture, particle-scale kinematics and force transmission are far more complex than presumed in early micromechanical models of granular materials. Hence, constitutive relations cannot easily be derived from the particle-scale behavior although advanced continuum models have been developed to account for anisotropy, intermediate stress and complex loading paths. The subtle elastic properties and origins of bulk friction will be discussed, as well as the effects of particle shape 19and size distribution. The review covers also recent developments in macroscopic modeling such as the thermomechanical approach, anisotropic critical state theory, nonlocal modeling approach, inertial flows and material instabilities. Finally, a brief account is given of open issues and some new frontiers and challenges in the field.

Although the Hosford yield function is more suitable for describing both the yielding and the plastic deformation of orthorhombic materials than the Hill quadratic yield function, the Hosford yield function suffers from the restriction that the loading has to be coaxial with the orthotropy of the materials. To relax this restriction, herein we present a new general Hosford yield function for the orthorhombic materials. The new general Hosford yield function is suitable to any stress state of the orthorhombic materials. When η = 2, the new general Hosford yield function becomes the Hill quadratic yield function. The new general Hosford yield function is more general than the general Hosford yield function of Huang and Man (Int J Plast 41:97–123, 2013), which covers only weakly-textured sheets of cubic metals. Two examples show that the new general Horsford yield function with suitable η value gives much better fits than those of the Hill quadratic yield function (η = 2).

In the present work the disc compression test used to determine the balanced biaxial strain-ratio $r_b$ is analyzed in terms of the influence of contact friction using non-linear finite element analysis (FEA). The FEA results reveal an unexpectedly strong sensitivity of the $r_b$-value on contact friction, which is discussed in detail. The most important outcome of the present work is that the FEA can reproduce the $r_b$-value imposed by the utilized yield function very well, but only when the prescribed Coulomb friction coefficient has a very small value; for increasing friction coefficients a gradual deviation from the imposed $r_b$-value can be observed. This finding implies that in experiments contact friction must be eliminated to a larger extent than commonly expected, otherwise the determined $r_b$-value using disc compression testing will considerably deviate from the actual one, particularly when $r_b$ is far from one.

Biaxial tensile tests of 6000 series aluminum alloy sheet with different density cube textures were conducted using cruciform specimens. The specimens were loaded under linear stress paths in a servo-controlled biaxial tensile testing machine. The plastic orthotropy remained coaxial with the principal stresses throughout every experiment. Successive contours of plastic work in stress space and the directions of plastic strain rates were precisely measured and compared with those calculated using selected yield functions. The Yld2000-2d yield functions with exponents of 12 and 6 were capable of reproducing the general work contour trends and the directions of plastic strain rates observed for the test materials with high and low density cube textures, respectively. Hydraulic bulge tests were also conducted and the variation of thickness strain along the meridian directions of the bulged specimen was compared with that calculated using finite element analysis (FEA) based on selected yield functions. Differences in the cube texture density caused significant differences in the strain distribution of the bulged specimens, and were in good agreement with the FEA results obtained using the Yld2000-2d yield functions. It is thus concluded that the biaxial tensile testing method with a cruciform specimen is an effective material testing method for accurately detecting and modeling the deformation behavior of sheet metals under biaxial tension.

In this study, an attempt has been made to develop a finite-element numerical procedure for the non-linear transient dynamic analysis of reinforced concrete (RC) beams. New material constitutive relationships have been employed depending on various experimental data. Eight-node serendipity degenerated plate elements have been used to represent the concrete beam elements. A layered approach was adopted to discretise the concrete and steel reinforcement through the thickness of the beam. Strain-hardening plasticity and elastic perfectly plastic models have been used to model the compressive behaviour of the concrete used in this study. Strain rate effect was included by assuming the dynamic yield function to be a function of the current strain rate in addition to being the total plastic strain. Geometrical non-linearity in the layered approach is considered in the mathematical model, which is based on the total Lagrangian approach taking into account Von Karman assumptions. A new model is used to consider the effect of tension stiffening in the cracked concrete. Steel reinforcement is considered as an elastic plastic material with linear strain hardening. Implicit Newmark with a corrector–predictor algorithm is employed for time integration of the equation of the motion. A computer program coded in MATLAB has been developed for the non-linear finite-element dynamic analysis of RC beams subjected to the dynamic loadings. Finally, various numerical examples validating the proposed formulation are given.

Referring to an egg shaped yield function for geotechnical materials, a failure criterion for light-weight aggregate concrete is put forward, in which the tensile and compressive meridians are egg shaped curves and the failure envelopes in deviated plane is smooth elliptic curves. The suggested failure criteria could describe the failure characteristic of lightweight aggregate concrete at different stress state. The precision of the suggested egg shaped failure criteria is verified by comparing with experiment data of lightweight aggregate concrete.

On the basis of Storen-Rice model, the limit strain formula is derived by introducing the plasticity constitutive relation coupling Logan-Hosford yield function. Limit strain of AL6111-T4 and AL2028 is calculated and compared with experimental data. The effect of index a of yield function, anisotropy parameter r on the calculation result is discussed. Index a has a significant effect on the right hand side(RHS) limit strain, while it has less relation with left hand side(LHS) limit strain. The RHS limit strain is smaller while a-value gets larger. Good correlation between the calculation result and experimental data is indicated when a-value equals to 4. The RHS limit strain is smaller while r gets larger when a equals to 2, while it has less relation with r when a equals to 4 or 6.

Recently non-proportional deformation has received increased attention from researchers working in the area of experimental and computational modeling of metal deformation. However, most of them are numerical in nature with limited experimental data available, making it further difficult to model non-proportional deformation. In the present work, two-stage uniaxial tests, along with uniaxial cyclic and biaxial tests for different stress ratios, have been performed to evaluate deformation behavior of ultra-low carbon high strength automotive steel. Behaviors like cross-effect and hardening stagnation, which are attributed to the evolution of complex dislocation structures, were observed in this steel. It was also noticed that this steel exhibits tension–compression asymmetry. As for constitutive modeling, a modified asymmetric yield function is proposed to be used with a combined isotropic–kinematic hardening model. Also methods to account for the hardening stagnation during reverse loading and the cross-effect during two-stage deformation are proposed. The resulting constitutive model showed reasonably good agreement with experimental results.

The initial and subsequent yield surfaces for an anisotropic and pressure-dependent 2D stochastic cellular material, which represents solid foams, are investigated under biaxial loading using finite element analysis. Scalar measures of stress and strain, namely characteristic stress and characteristic strain, are used to describe the constitutive response of cellular material along various stress paths. The coupling between loading path and strain hardening is then investigated in characteristic stress–strain domain. The nature of the flow rule that best describes the plastic flow of cellular solid is also investigated. An incremental plasticity framework is proposed to describe the pressure-dependent plastic flow of 2D stochastic cellular solids. The proposed plasticity framework adopts the anisotropic and pressure-dependent yield function recently introduced by Alkhader and Vural [Alkhader M., Vural M., 2009a. An energy-based anisotropic yield criterion for cellular solids and validation by biaxial FE simulations. J. Mech. Phys. Solids 57(5), 871–890]. It has been shown that the proposed yield function can be simply calibrated using elastic constants and flow stresses under uniaixal loading. Comparison of stress fields predicted by continuum plasticity model to the ones obtained from FE analysis shows good agreement for the range of loading paths and strains investigated.

We apply a nonlocal regularisation method to a breakage model recently proposed for the constitutive modelling of crushable granular materials. Coupling between material points is taken into account through the nonlocal averaging applied to the yield function. This enables us to introduce a length scale to continuum breakage models, and therefore helps to overcome numerical difficulties arising from physical instabilities encountered when the material effectively undergoes softening due to crushing. The numerical implementation of the nonlocal version of a breakage model is briefly presented. To demonstrate its promising features, this nonlocal model is used in a series of numerical analyses of high pressure shearing processes, in which grain crushing mechanism governs the material behaviour.

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.

While potato production on the Canadian Prairies has expanded significantly since the early 1990s and accounted for roughly one third of Canada’s production over the period 1990–2006, few studies have looked at Plant Breeder’s rights and cultivar releases in Canada, and the determinants of potato yield in Manitoba. This paper examines potato breeding developments in terms of cultivar releases, the extent that new cultivar releases are protected by Plant Breeders’ Rights (PBR), and the contribution of cultivar improvements, environmental conditions and fertilizer inputs to potato yield in Manitoba. The results from our study indicate that professional person-years devoted to potato breeding has declined since 1990 and that PBR granted to European and U.S. breeders have exceeded those granted to Canadian domestic breeding institutions. Manitoba processing potato yields have been affected more so by a combination of fertilizer inputs and regional effects than by improved cultivars. In the current study, the limited effect of protected cultivars on yield may be due to the small number of protected cultivars being assessed, and the relatively short time period considered. Lack of adoption of new cultivars in Manitoba may reflect slow adoption of new cultivars by the processing industry as it ensures that quality and processing specifications are met.

In order to better predict the springback for friction stir welded DP590 steel sheet, the combined isotropic-kinematic hardening was formulated with considering the permanent softening behavior during reverse loading. As for yield function, the non-quadratic anisotropic yield function, Yld2000-2d, was used under plane stress condition. For the verification purposes, comparisons of simulation and experiments were performed here for the unconstrained cylindrical bending, the 2-D draw bending tests. For two applications, simulations showed good agreements with experiments.

In this paper we discuss properties of dense granular °ows and elaborate on some properties of a model which generalises the classical plastic potential model using elements of the double shearing model. It is shown how the model is embedded into a Cosserat continuum model. The proposed model recti¯es the ill-posedness of both the non-associated °ow rule and the double shearing model and may be used for both granular materials and also for metals which possess a micro-structure which is capable of rotation.

Recently, many flexible constitutive equations have been proposed for sheet forming simulations. However, various mechanical tests are required to determine the many material parameters needed for such models. In the present work, effort has been made to investigate the correlation between the polycrystal plasticity based yield loci and those determined from mechanical tests, in order to define yield functions easily and accurately with minimum amount of experimental work. The results for different materials indicate that, in many cases, the Hill’48 deviates significantly from the measured yield loci. The yield loci derived from measured texture and polycrystal plasticity perform better than the Hill’48 yield function in general. Based on the two yield loci derived from the Taylor full constraint model and the Pancake model, a new combined model is proposed. The new model uses the averaged biaxial points of the two models but keeps the shape of the yield loci derived from the Taylor full constraint model in the stretching regime. The stress factors in the uniaxial and shear mode are calculated by averaging the stress factors of the two models. The proposed new description has been validated using several steel grades.

The aggregate-objective optimization technique has been used to assess the optimal set of coefficients of the Barlat yield criterion for anisotropic alloy sheets by means of the evolution strategy. The aggregate-objective problem has been quantified by the Euclidean-type objective function. Computational results indicate that standard procedures, based on three uniaxial yield stresses for different directions of loading in-plane, the balanced biaxial yield stress, and three Lankford coefficients of anisotropy determined for three different directions of loading in-plane, cannot be sufficient to assess unequivocally the Barlat yield criterion for anisotropic alloy sheets.

Authors have proposed an analytical method for H-shaped steel beam-column involving local buckling behavior. And we have studied methods to analyze the elastoplastic buckling behavior of truss members. In this paper, we will extend both methods for H-shaped steel truss member. Then, we will propose a consistent and convenient truss element for H-shaped steel member involving overall and local buckling behavior. This truss element is formulated based on thermodynamics. In formulating, the yield function and the evolution equation considering local buckling are confirmed by analytical results of discrete model. And the softening property caused by local buckling is given from study on plate buckling behavior. Finally we will examine the validity and usefulness of our method through some numerical examples.

The present paper deals with material modeling in connection with sheet metal forming analyses. One purpose of the report is to discuss the special needs and demands of industrial analysts. With this in mind, in particular, the demands put on the yield condition are analyzed. Two recent yield criteria for anisotropic metal sheets, in the literature denoted Yld2000 and BBC2000, respectively, are found to be very well suited for industrial use. They do both belong to a group of yield criteria called the ‘‘Hosford family’’. Practical issues with regard to these yield criteria, such as procedures for determining the parameters being part of the models, implementation issues, and numerical efficiency, are thoroughly discussed. A version of the above criteria, using a reduced set of parameters, is proposed, and is shown to offer a significantly reduced computing time at the cost of some loss of accuracy.

According to unified strength parameters obtained from unified strength theory, the slope of critical state line is modified to reflect critical states of different geomaterials under general stress states. Yield function that can consider the effect of the third deviatoricic invariant is proposed, and an elasto-plastic constitutive model is established by adopting non-associated flow rules; furthermore, methods of overcoming singular points on the yield surface are discussed. The proposed model is verified by true triaxial tests of clay, and results show that the model can well predict stress-strain relationships.

The development of high speed computers has encouraged researchers to increasingly utilize the finite element method (FEM) to simulate more realistic pavement structures and loading conditions in their efforts to predict the performance of asphalt pavem ents. Analysis of pavement materials using mechanistic constitutive materials models is an integral part of these efforts. An elastic viscoplastic continuum model based on Perzyna’s viscoplastic theory and the Drucker-Prager yield function is proposed to simula te the permanent deformation of a hot mix asphalt (HMA) mixture at WesTrack. Compressive strength tests were performed at differen strain rates and confinement pressures to obtain the elastic-viscoplastic constitutive material parameters. The test temperature was 60 °C based on the critical temperature for permanent deformation at 12.5 mm of the WesTrack replacement section. Permanent deformation of the replacement section was simulated by the three dimensional FEM program, ABAQUS. The same trend of rutting profiles was obtained for both the measured and the simulated rutting profiles.

In finite element simulation of auto-body panels forming, an accurate forming limit criterion is very important. To evaluate accurately the formability of automotive aluminium alloy sheet, in this paper, a ductile fracture criterion developed by the author is introduced in finite element simulation. Based on Barlat’s yield function and Hollomon’s hardening equation, the simulations of aluminium alloy sheet forming are carried out. Material constants in the ductile fracture criterion are determined by means of uniaxial tension and hemispherical punch stretching tests. The critical punch strokes of the aluminium alloy sheets X611-T4, 6111-T4 and 5754-O in cylindrical complex forming, which includes deep drawing and stretching modes, are calculated by the ductile fracture criterion. The comparison of the calculated results with the experimental values shows that the critical punch strokes of the three sheets mentioned above are predicted successfully by the ductile fracture criterion.

Since the first application of agricultural practices, humans have altered most of the world’s landscapes and adapted them for their own utilization (Lambin et al. in Glob Environ Change 11:261–269, 2001, Ann Rev Environ Res 28:205–241, 2003). Initially, the yield function of the landscape for food production was the major driver of this development.

International audience; In this work, a thermodynamically-consistent framework is used to formulate a non-associative finite strain anisotropic elastoplastic model fully coupled with anisotropic ductile damage. The finite strain assumption is considered using specific large strains kinematics based on multiplicative decomposition of the total transformation gradient and assuming a small elastic strains. The objectivity principle fulfillment is assumed using the well-known rotating frame formulation. The effective variables are defined to introduce the effect of the anisotropic damage on the other variables through the total energy equivalence assumption. The non-associative plasticity framework, for which equivalent stresses in yield function and in plastic potential are separately defined, allows better plastic anisotropy description. The evolution equations for overall dissipative phenomena are deduced from the generalized normality rule applied to the plastic potential while the consistency condition is still applied to the yield function. Applications are made to an RVE with generic material parameters by considering non-proportional loading paths. For each loading path the effect of the anisotropic plasticity on the damage evolution is studied in the context of finite strains.

Most failures of ductile materials in metal forming processes occurred due to material damage evolution - void nucleation, growth and coalescence. In this paper, the modified yield function of Liao et al in conjunction with the Hosford`s yield criterion is studied to clarify the plastic deformation characteristic of voided anisotropic sheet metals. The void growth of an anisotropic sheet under biaxial tensile loading and damage effect of void growth on forming limits of sheet metals are investigated. Also the characteristic length defining the neck geometry is introduced in M-K model to incorporate the effect of triaxial stress in necked region on forming limits. The forming limits theoretically predicted are compared with experimental data. Satisfactory agreement was obtained between the predictions and experimental data.

Most failures of ductile materials in metal forming processes occurred due to material damage evolution- void nucleation, growth and coalescence of neighboring voids. Recently, Gologanu-Leblond-Devaux (J. Mech. Phys. Solids, Vol.41 (1993), pp.1723-1754) extended the classical Gurson model (ASME J. Engng. Mater. Technology, Vol.99 (1997), pp.2-15) to a ductile material containing an oblate ellipsoidal cavity. And, they proposed a new approximate yield function incorporating the initial void shape effects, which is significant especially at low stress triaxiality. In the present work, the Gologanu-Leblond-Devaux's yield function for anisotropic sheet materials containing axisymmetric prolate ellipsoidal cavities is adopted in evaluating analytically forming limits of sheet metals under biaxial stretching by Marciniak and Kuczynski (M-K) model. The effect of a void shape and growth on the forming limits of sheet metals under biaxial tensile loading is introduced and examined within the framework of the M-K model, along with the effect of including a first-order strain gradient term in the flow stress. To confirm the validity of the proposed model, the predicted FLDs were compared with experimental results for steel sheets. The predicted forming limits for the voided sheets were found to agree well with the experimental data.

A coupled plastic damage model with two damage scalars is proposed to describe the nonlinear features of concrete. The constitutive formulations are developed by assuming that damage can be represented effectively in the material compliance tensor. Damage evolution law and plastic damage coupling are described using the framework of irreversible thermodynamics. The plasticity part is developed without using the effective stress concept. A plastic yield function based on the true stress is adopted with two hardening functions, one for tensile loading history and the other for compressive loading history. To couple the damage to the plasticity, the damage parameters are introduced into the plastic yield function by considering a reduction of the plastic hardening rate. The specific reduction factor is then deduced from the compliance tensor of the damaged material. Finally, the proposed model is applied to plain concrete. Comparison between the experimental data and the numerical simulations shows that the proposed model is able to describe the main features of the mechanical performances observed in concrete material under uniaxial, biaxial, and cyclic loadings.