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Forming simulation is an indispensable analysis tool in industry, the most important objective of which being the reproduction of the material deformation behavior during the process as accurately as possible to predict forming defects and determine optimum forming conditions precisely. This paper reviews the material models suitable for metal forming simulations and the material test methods that can reproduce the various types of stress states occurring in real forming operations. These test methods are essential to verify the validity of material models. Examples of forming simulation results for aluminum alloys are presented, illustrating the significant influence of the material models on the accuracy of the process predictions. Finally, the emerging research trends in the field of material modeling and testing are discussed. [ABSTRACT FROM AUTHOR]

This work is carried out to investigate the anisotropic hardening behavior of MS1180 steel through experiment and analytical modeling. Dogbone and hydraulic bulging specimens were machined to test the mechanical behavior of MS1180 steel plate under different loading directions and stress states. The loading process was recorded by the three‐dimensional digital image correction system. The result uncovers that the strength under equi‐biaxial tension is larger than that under uniaxial tension. Mechanical behavior under different loading directions presents the obvious difference related to the plastic strain. Hardening behavior under uniaxial tension and equi‐biaxial tension is characterized by the Swift‐Voce and polynomial equations, respectively. Three yield functions are adopted to describe the anisotropic behavior, including Yld2000‐2d, S‐Y2009, and CQN‐Chen. A convexity analysis method based on geometric definition is used to determine the convex region of the CQN‐Chen yield surface under large strain. By comparing the yield surfaces of the three yield functions under different plastic strain, the CQN‐Chen yield function possesses a more flexible and reasonable characterization ability than the Yld2000‐2d and S‐Y2009 yield functions. The anisotropic hardening behavior of MS1180 steel plate is modeled with an error of less than 0.03 by the CQN‐Chen yield function, showing high prediction accuracy. [ABSTRACT FROM AUTHOR]

Since sheet metal exhibits significant anisotropy in processing and forming, which has a significant impact on its performance during processing, forming, and use, we explore the anisotropic behavior of materials in the forming process of sheet metal. The ability of the Yld2000-2d criterion to describe anisotropic behavior is analyzed, and its accuracy for characterization of the anisotropic behavior of metal plates is improved, based on which anisotropic behavior is predicted in three-dimensional space. Theoretical and experimental results on the anisotropy of sheet metal are compared, and two materials, 5754O aluminum alloy and DP980 steel plate, are tested and analyzed, and the anisotropic behaviors, such as three-point bending and cylindrical deep-drawing, are well predicted. [ABSTRACT FROM AUTHOR]

This paper studies the plastic behavior of the ZK61M magnesium alloy through a combination method of experiments and theoretical models. Based on a dog-bone specimen under different loading directions, mechanical tests under uniaxial tension were carried out, and the hardening behavior was characterized by the Swift–Voce hardening law. The von Mises yield function and the pressure-coupled Drucker yield function were used to predict the load–displacement curves of the ZK61M magnesium alloy under various conditions, respectively, where the material parameters were calibrated by using inverse engineering. The experimental results show that the hardening behavior of the ZK61M magnesium alloy has obvious anisotropy, but the effect of the stress state is more important on the strain hardening behavior of the alloy. Compared with the von Mises yield function, the pressure-coupled Drucker yield function is more accurate when characterizing the plastic behavior and strain hardening in different stress states of shear, uniaxial tension, and plane strain tension for the ZK61M alloy. [ABSTRACT FROM AUTHOR]

This article discusses the thermodynamic constitutive model of gas hydrate-bearing sediments (GHBS) considering anisotropy. The model incorporates anisotropy and accounts for the effects of hydrate swelling and cementing, providing more accurate predictions of the mechanical properties of GHBS. The text also highlights the importance of considering anisotropy in GHBS and discusses various constitutive models for GHBS. It discusses the filling and cementing effects of hydrates in GHBS and the densification mechanism of GHBS. The text introduces an anisotropic thermodynamic model and discusses the relationship between mechanical hydrate saturation and plastic shear strain. It also discusses the thermomechanical theory and the thermodynamic constitutive model of GHBS. The text provides mathematical equations and formulas to describe these concepts. It discusses the analysis parameters of yield surfaces in GHBS and the determination of the anisotropic evolution law. The proposed constitutive model is validated and exhibits good agreement with experimental data. The document also includes references to various scientific papers related to the mechanical properties and behavior of GHBS. [Extracted from the article]

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This work focuses on the limit strains of 5754-O aluminum alloy sheets with consideration of the hardening law effect. Based on uniaxial tension test data, the hardening laws of Swift, Voce, LSV and Hockett–Sherby were applied to determine the mechanical properties. The fitted parameters and the Yld2000-2d yield function were introduced into the Marciniak–Kuczynski (M–K) theory to predict the forming limit curve (FLC). This prediction was not consistent with the Nakajima test results. Assessment of the effect of the hardening law on the predicted FLC indicated that the hardening law affected the yield surface evolution through the hardening rate. Afterward, an improved LSV hardening law was proposed to depict the plastic stress–strain relationship, and both the theoretical prediction and the numerical simulation verified the validity of the improved model. The results were compared with the test data, and good agreement was shown. [ABSTRACT FROM AUTHOR]

Since sheet metal exhibits significant anisotropy in processing and forming, which has a significant impact on its performance during processing, forming, and use, we explore the anisotropic behavior of materials in the forming process of sheet metal. The ability of the Yld2000-2d criterion to describe anisotropic behavior is analyzed, and its accuracy for characterization of the anisotropic behavior of metal plates is improved, based on which anisotropic behavior is predicted in three-dimensional space. Theoretical and experimental results on the anisotropy of sheet metal are compared, and two materials, 5754O aluminum alloy and DP980 steel plate, are tested and analyzed, and the anisotropic behaviors, such as three-point bending and cylindrical deep-drawing, are well predicted.

This paper studies the plastic behavior of the ZK61M magnesium alloy through a combination method of experiments and theoretical models. Based on a dog-bone specimen under different loading directions, mechanical tests under uniaxial tension were carried out, and the hardening behavior was characterized by the Swift–Voce hardening law. The von Mises yield function and the pressure-coupled Drucker yield function were used to predict the load–displacement curves of the ZK61M magnesium alloy under various conditions, respectively, where the material parameters were calibrated by using inverse engineering. The experimental results show that the hardening behavior of the ZK61M magnesium alloy has obvious anisotropy, but the effect of the stress state is more important on the strain hardening behavior of the alloy. Compared with the von Mises yield function, the pressure-coupled Drucker yield function is more accurate when characterizing the plastic behavior and strain hardening in different stress states of shear, uniaxial tension, and plane strain tension for the ZK61M alloy.

Yield surfaces of A5052 aluminum alloy sheets with different tempers are modeled by the simplified identification method using the circumscribing polygon. In this method, a polygon circumscribing the equal plastic work contour is determined by uniaxial tensile, equal biaxial tensile and plane strain tensile tests. Anisotropic yield surfaces of A5052 aluminum alloy sheet are modeled by Yld2000-2d (Barlat et al., 2003) and Yld2004-18p (Barlat et al., 2005) yield functions. Both yield functions can express the inscribed curves of the polygons. The modeled yield surfaces of A5052-O agree with the stress points of the equal plastic work contours measured by the reliable bi-axial tensile tests. The proposed method to identify the yield function is effective for aluminum sheet metal. On the other hand, the two identified yield functions show different in-plane plastic anisotropy in the tension-compression combined stress state. To examine the suitability of identified models, the experiments and numerical analyses of the deep drawing tests are carried out. Comparing the experimental and analyzed results, the predicted ear height of drawn cup using the Yld2004-18p yield function agree with experimental results qualitatively. But the prediction of the ear using the Yld2000-2d cannot express the tendency of the experimental one. [ABSTRACT FROM AUTHOR]

By combining experimental and theoretical models, this research investigates the anisotropic hardening behaviors of TRIP780 steel. The specimens of TRIP780 steel were subjected to uniaxial tensile and bulging tests under different loading conditions to obtain hardening data. The experimental results show that the strength and plastic deformation of TRIP780 steel vary with the loading directions, which indicates that TRIP780 steel has anisotropy characteristics. In this paper, the dichotomous method is used to ensure the convexity of the Chen-coupled quadratic and non-quadratic (CQN) function. Comparing the predictions of the hardening behavior of the TRIP780 steel sheet by the Yld2000-2d, Stoughton-Yoon'2009 and Chen-CQN functions, the results show that the Chen-CQN function exhibits the advantages of simple numerical implementation and a more realistic prediction of yield stress compared to the former two, respectively. Comparing the prediction of Chen-CQN function with the experimental hardening data, the results show that the deviation between the experimental data and the experimental response given by the function is always within 3%, and this function maintains an accurate prediction under different stress states, indicating that the Chen-CQN yield function has accuracy and flexibility for the characterization of the yield surface of TRIP780 steel. [ABSTRACT FROM AUTHOR]

The homogenization method is effective for analyzing macroscopic mechanical properties from the substructure of a material. In perforated sheet metal, macroscopic mechanical properties depend on the pattern of hole arrangement. In this study, the macroplastic properties of perforated sheets with 60° standard staggered and 90° square arrangements are modeled. Biaxial stress is applied to the unit cells given the periodic boundary condition, and the contours of equal plastic work are obtained. The yield surfaces of the perforated sheets on the tensioncompression combined stress state are strongly affected by the hole arrangement. To model the yield surface, a yield function for the rotational symmetry peculiar to the perforated sheet is proposed. The yield surfaces are modeled using the CPB2006 yield function that takes into consideration tensioncompression asymmetry. Also, a surfaceinterpolated differential hardening model is applied to model the changes of yield surfaces. The analysis results obtained using the modeled yield surfaces are compared with the experimental ones obtained on the uniaxial tensile and deep drawing tests. The results of both tests show good agreement. [ABSTRACT FROM AUTHOR]

This study develops a new phenomenological constitutive model to capture the unique evolving cyclic elastoplastic behaviours of hexagonal close-packed (HCP) sheet metals. This new constitutive model is developed by adopting the concepts of multiple-yield surface approaches. Four phenomenological deformation modes, including Monotonic Compression (MC), Monotonic Tension (MT), Reverse Compression (RC), and Reverse Tension (RT), are considered to represent the hardening evolution of the materials, including the twining/untwining behaviours. Reference flow stress equations are introduced, and a Cazacu-Barlat 2004 (CB2004) type yield surface is employed to each deformation mode. In addition, the RT hardening parameters are defined as functions of plastic pre-strains to mitigate the interpolation error caused by parameter determination processes of existing models. For validation, the calculated stress–strain curves of AZ31B magnesium alloy are compared with experimental curves available from literature. Moreover, to show the accuracy of the proposed analytical model, the reproduced stress–strain curves are compared with those of an existing model—the modified homogeneous anisotropic hardening (HAH) model. The obtained results show that the new constitutive model can successfully reproduce experimental Tension–Compression-Tension (TCT) and Compression-Tension–Compression (CTC) stress–strain curves of HCP sheet metals with considerably less percentage errors. [ABSTRACT FROM AUTHOR]

The present work proposes a systematic procedure for evaluation of high temperatures deformation and formability of α+β Brass undergoing the uniaxial tensile test conditions. Firstly, uniaxial tensile tests were conducted on Universal Testing Machine (UTM) with loading capacity of 100 KN at temperature of 773K, 873K and 973K with a quasi-static strain rates of 0.001s-1, 0.01 s-1 and 0.1s-1. Hot tensile flow stress behaviors have been affected significantly by test temperatures and strain rates for Brass. Drop-in yield and ultimate tensile strength have been observed at approximately 58 % and 68 % with a rise in test temperature from 773 K to 973 K. Around 30% improvement has been observed in % elongation with rise in test temperature. Further, flow stress has been predicted by most popular Johnson Cook (JC) uniaxial constitutive model at wide range of temperatures (773K, 873K and 973K) and strain rates (0.001s-1,0.01 s-1 and 0.1s-1). Further, yield loci have been plotted at various temperatures using Hill 1948 and Barlat 1989 yield function. Barlat 1989 has followed experimental results correctly in all test temperatures. [ABSTRACT FROM AUTHOR]

Let Sym 0 be the space of traceless symmetric second-order tensors. We say that a polycrystalline elastic–plastic material is weakly-textured if its yield function f : Sym 0 → R is the sum of a texture-independent isotropic part f iso and an anisotropic part which is linear in the relevant texture coefficients. Let c > 0 and S ≔ f − 1 (c) ⊂ Sym 0 be the yield surface of the weakly-textured material in question. We present a sufficient condition (*), namely that ∇ 2 f (S) be positive definite for each S ∈ S , for a smooth yield surface S to be strictly convex in Sym 0. We apply this sufficient condition to weakly-textured materials with yield functions that satisfy the following conditions: (i) the yield functions f and f iso are smooth; (ii) ∇ 2 f iso (S) is positive definite for each S in S iso ≔ f iso − 1 (c) ⊂ Sym 0 . We prove that the yield surface S ⊂ Sym 0 of such weakly-textured material is strictly convex if the texture coefficients in f are sufficiently small. As illustration for practical applications, by appealing to condition (*) we study the strict convexity of the yield surface pertaining to a weakly-textured orthorhombic aggregate of cubic crystallites which has a quadratic yield function of the type proposed by Hill in 1948. Moreover, we show that all 35 samples of cold-rolled and annealed low-carbon steel sheets studied by Stickels and Mould have their quadratic yield functions and corresponding yield surfaces strictly convex. [ABSTRACT FROM AUTHOR]

Aluminum alloy sheets are widely applied as structure components in automotive, aircraft and other industries to realize lightweight. Nowadays, many high strain rate forming techniques have been developed to improve their formability and widen their application. To ensure the reliability of the aluminum alloy structure components under high strain rate conditions, it is imperative to develop a thorough understanding of the alloy's mechanical properties. In this paper, taking high-strength 6XXX aluminum alloy sheet as an example, the anisotropic deformation characterization and corresponding material models at various strain-rate conditions are investigated systematically. The material hardening curves and anisotropic plastic yielding stresses were achieved based on the quasi-static uniaxial tensile test and the split Hopkinson tensile bar tests. In this study, the Johnson–Cook hardening model and two anisotropic yield functions are applied to well describe the strain-rate-dependent anisotropic plastic deformation behavior. In addition, the fractographic characterization of the fractured samples at various strain-rate conditions are measured and compared. The study systematically investigates the influence of strain rate on the anisotropic deformation behavior of the high-strength aluminum alloy sheets and gives the basic experimental data for their application in engineering fields in the future. [ABSTRACT FROM AUTHOR]

Porous materials have a wide field of application in the biomedical, chemical, pharmaceutical, and automotive industries, among others. In many situations, these materials suffer efforts that can compromise their integrity. To prevent this from happening, a powerful tool, named limit analysis, can be used for the determination of a safe condition of operation for parts made of porous materials. However, there are few studies available that relate the design of parts made of porous material with limit analysis. In this paper, an approach for solving limit analysis problems applied to porous materials is presented. Statical and mixed variational principles are proposed for the limit analysis of porous materials, and a discrete mixed variational principle is presented. Two compaction functions, which relate the relative density to the hydrostatic pressure, are tested: the Helle's and Heckel's expressions. The finite element method is used for the numerical approximation of the discrete limit analysis formulation. Some numerical examples are presented, and the obtained results are close to the numerical and analytical solutions previously published. Among the tested compaction functions, Helle's expression showed the highest compaction. [ABSTRACT FROM AUTHOR]

In this work we implement an analytically derived coupling function between ground-level and primary proton particles for the case of ground-level enhancement events (GLEs). The main motivation for this work is to determine whether this coupling function is suitable for the study of both major cases of cosmic-ray (CR) variation events, namely GLEs and Forbush decreases. This version of the coupling function, which relies on formalism used in quantum field theory (QFT) computations, has already been applied to Forbush decreases yielding satisfactory results. In this study, it is applied to a GLE event that occurred on 10 September 2017. For the analytical derivations, normalized ground-level cosmic-ray data were used from seven neutron-monitor stations with low cutoff rigidities. To assess and evaluate the results for the normalized proton intensity, we benchmark them with the time series for the proton flux, as recorded by the GOES 13 spacecraft during the same time period. The theoretically calculated results for proton energy ≥ 1 GeV are in general agreement with the recorded data for protons with energy > 700 MeV , presenting a least-squares linear best fit with slope 0.75 ± 0.17 and a Pearson correlation coefficient equal to 0.62. We conclude that the coupling function presented in this work is the first coupling function that is well applicable to both cases of cosmic-ray intensity events, namely GLEs and Forbush decreases. [ABSTRACT FROM AUTHOR]

In this paper, a simple sub-loading yield surface model for both normally consolidated and over-consolidated clay is proposed with emphasis on the effect of the yield surface shape. Compared with the modified Cam-clay model, only one additional material parameter is introduced to reflect geometry features of the yield surface. A higher-order stress–dilatancy relation is given in the current study, leading to a new yield function capable of offering an adequate description of the yield surface of soil samples in the p–q plane. By introducing the concept of the sub-loading yield surface and the unified hardening parameter, the proposed model can capture the main features of the over-consolidated clay with dilatancy and strain-softening behavior and the main features of the normally consolidated clay with contraction and strain-hardening behavior. The results show that adjusting the yield surface leads to more accurate predictions than the modified Cam-clay model. The proposed model can also reasonably describe its mechanical behavior for clay samples. [ABSTRACT FROM AUTHOR]

The rutting resistance design of asphalt pavement is full of compromise between technology and economy because it is difficult to predict rutting evolution and distribution. In order to investigate the criterion of rutting, two forms yield function based on the Perzyna theory were contrasted and utilised in the finite element model. Besides, temperature and traffic load, the most important factors of rutting, were taken into consideration to make the analysis of yield function closer to the field condition of pavement. Two resistance points were proposed as criterions in this paper. One can be used in pavement maintenance to figure out the depth of serious rutting, the other can be used in pavement design to determine the usage depth of modified asphalt mixture. The analysis illustrates that the key to controlling rutting at intersections is to use better anti-rutting materials at the top layers instead of deepening the usage of modified asphalt mixture. Besides, the depth of rutting varies dramatically with axle weights. It can be inferred that there may be deviations of the prediction for the rutting distribution and evolution when using the method of equivalent axle weight. [ABSTRACT FROM AUTHOR]

The plastic potential and yield functions are two of the most important components of elastoplastic constitutive models. Because the incremental plastic energy-based equation of the Cam-Clay model does not consider the particle breakage energy, the predicted results for crushable granular material, e.g., rockfills, are not convincing. It should be noted that the particle breakage energy is difficult to be quantified separately, and to avoid directly measuring it, the total input energy during shearing is taken as the equivalent of the energy-based equation in this study. Accordingly, a unified function with two parameters (critical stress ratio Mc and χ) is derived for defining the yield and the plastic potential surfaces for rockfills. When χ = 1.0, the yield locus f is equal to the plastic potential surface g, when χ > 1.0, f is below g, and f tends to become more bullet-shaped with an increasing χ, and when χ < 1.0, f is above g, and f tends to become more drop-shaped with a decreasing χ. Additionally, the experimental plastic strain increment vectors of the Pancrudo slate rockfill (Alonso 2016) are not normal to the yield locus, which demonstrates that the proposed unified function is reasonable. [ABSTRACT FROM AUTHOR]

Recently developed anisotropic yield functions can capture the material anisotropic behaviors through parameter optimization. However, sometimes the parameter optimization is not easy and does not always have a unique solution. This paper introduces an anisotropic yield function that does not require the parameter calibration process. This model simplifies the coupled quadratic and non-quadratic yield function in order to directly use the measured on-set of yielding stress and r-value data without the calibration process. The presented model is validated with five different materials for the prediction of stress and strain anisotropies. In addition, a cup drawing simulation is also presented to validate the simplified model in a practical metal forming simulation with the User-defined subroutine of ABAQUS. The results of this paper show that the simplified model can be effectively employed for the simulation of sheet metal forming processes. [ABSTRACT FROM AUTHOR]

By combining experimental and theoretical models, this research investigates the anisotropic hardening behaviors of TRIP780 steel. The specimens of TRIP780 steel were subjected to uniaxial tensile and bulging tests under different loading conditions to obtain hardening data. The experimental results show that the strength and plastic deformation of TRIP780 steel vary with the loading directions, which indicates that TRIP780 steel has anisotropy characteristics. In this paper, the dichotomous method is used to ensure the convexity of the Chen-coupled quadratic and non-quadratic (CQN) function. Comparing the predictions of the hardening behavior of the TRIP780 steel sheet by the Yld2000-2d, Stoughton-Yoon’2009 and Chen-CQN functions, the results show that the Chen-CQN function exhibits the advantages of simple numerical implementation and a more realistic prediction of yield stress compared to the former two, respectively. Comparing the prediction of Chen-CQN function with the experimental hardening data, the results show that the deviation between the experimental data and the experimental response given by the function is always within 3%, and this function maintains an accurate prediction under different stress states, indicating that the Chen-CQN yield function has accuracy and flexibility for the characterization of the yield surface of TRIP780 steel.

The plastic anisotropy behavior of ferritic stainless steel (FSS) sheets was analyzed and modeled under associated and nonassociated flow rule approaches. Three orthotropic flow functions, known as quadratic Hill48 and nonquadratic (Yld2000-2d and BBC2005), were developed and employed under an associated and nonassociated flow rule hypothesis. For the NAFR based on the initial anisotropy, the mechanical behavior was described by the nonexponential model functions of Yld2000-2d and BBC2005 to predict the directional dependence of mechanical parameters. It provided a considerable advantage in terms of flexibility and good agreement with the experiment. According to the results, the polynomial fit functions of the transverse versus longitudinal true plastic strain curve were used to describe the designated properties corresponding to a selected level of strain. To describe the evolution of anisotropic hardening and potential plastic hardening, seven different loading conditions were considered. The proposed evolutionary non-AFR Yld2000-2d and BBC2005 criteria showed good accuracy in predicting the evolution of hardening yield and Lankford coefficients depending on the plastic deformation. [ABSTRACT FROM AUTHOR]

The influence of yield function parameters on hole-expansion (HE) predictions are investigated for an anisotropic AA6022-T4 aluminum sheet. The HE experiment is performed in a fully-instrumented double-action hydraulic press with a flat-headed punch. Full strain fields are measured by a stereo-type digital image correlation (DIC) system. The stress state gradually changes from uniaxial to plane-strain tension to biaxial tension in the radial direction. Besides HE, the plastic anisotropy of AA6022-T4 is characterized by uniaxial tension and plane-strain tension experiments. Uniaxial tension is considered as the most important, since it is the stress state along the hoop direction in the hole. For the finite element (FE) simulation, the Yld2000-2d non-quadratic anisotropic yield function is used with two different parameter sets, calibrated by: (1) uniaxial tension only (termed Calib1) and, (2) both uniaxial and plane-strain tension (Calib2). The strain field predictions show a good agreement with the experiments only for Calib2, which takes into account plane-strain as well uniaxial tension. This indicates the importance of biaxial modes, and in particular plane-strain tension, for the adopted yield function to produce accurate HE simulations. [ABSTRACT FROM AUTHOR]

In this paper, a wide range of linear transformation-based orthotropic yield functions are reformulated in terms of only independent parameters, as they were originally formulated with too many parameters. This allows to perform a well-posed yield surface calibration. The effect of the hydrostatic part of the transformed stress is discussed for all existing formulations of transformation-based yield functions. The need for a parameter reduction for yield functions with a higher number of parameters is even more significant, as their use is becoming increasingly important for multiscale modelling based on virtual experiments by crystal plasticity. Use of independent parameters is critical for efficient training of neural networks linking crystal and continuum plasticity. • Unique description of linear transformation-based yield functions is proposed. • Simple rules for choosing the dependent parameters for yield functions are given. • The proposed yield function formulations allow well-posed calibrations. • Natural notation shown advantageous in expressing anisotropy matrices. [ABSTRACT FROM AUTHOR]

Abstract Earings appear easily during deep drawing of cylindrical parts owing to the anisotropic properties of materials. However, current methods cannot fully utilize the mechanical properties of material, and the number of earings obtained differ with the simulation methods. In order to predict the eight-earing problem in the cylindrical deep drawing of 5754O aluminum alloy sheet, a new method of combining the yield stress and anisotropy index (r-value) to solve the parameters of the Hill48 yield function is proposed. The general formula for the yield stress and r-value in any direction is presented. Taking a 5754O aluminum alloy sheet as an example in this study, the deformation area in deep drawing is divided into several equal sectorial regions based on the anisotropy. The parameters of the Hill48 yield function are solved based on the yield stress and r-value simultaneously for the corresponding deformation area. Finite element simulations of deep drawing based on new and existing methods are carried out for comparison with experimental results. This study provides a convenient and reliable way to predict the formation of eight earings in the deep drawing process, which is expected to be useful in industrial applications. The results of this study lay the foundation for the optimization of the cylindrical deep drawing process, including the optimization of the blank shape to eliminate earing defects on the final product, which is of great importance in the actual production process.

Aluminum alloy sheets are widely applied as structure components in automotive, aircraft and other industries to realize lightweight. Nowadays, many high strain rate forming techniques have been developed to improve their formability and widen their application. To ensure the reliability of the aluminum alloy structure components under high strain rate conditions, it is imperative to develop a thorough understanding of the alloy’s mechanical properties. In this paper, taking high-strength 6XXX aluminum alloy sheet as an example, the anisotropic deformation characterization and corresponding material models at various strain-rate conditions are investigated systematically. The material hardening curves and anisotropic plastic yielding stresses were achieved based on the quasi-static uniaxial tensile test and the split Hopkinson tensile bar tests. In this study, the Johnson–Cook hardening model and two anisotropic yield functions are applied to well describe the strain-rate-dependent anisotropic plastic deformation behavior. In addition, the fractographic characterization of the fractured samples at various strain-rate conditions are measured and compared. The study systematically investigates the influence of strain rate on the anisotropic deformation behavior of the high-strength aluminum alloy sheets and gives the basic experimental data for their application in engineering fields in the future.

In elastoplastic analyses, a yield function needs convexities and C1 continuities, to meet the requirement of return mapping algorithms. However, many classic criteria in geotechnical engineering have shortages: either numerical issues (nonconvexity and gradient discontinuities) or insufficient physical properties (lack of tensile strength and compressive cap). To overcome these deficiencies, a smoothed classic (SC) yield function is proposed after combining the generalized classic yield function, a robust smoothing technique, and investigations on physical meanings. It can reflect general soil properties, including basic shear strength, tensile strength, compressive cap, and the impact of intermediate principal stress. The yield function is convex and C2 continuous; therefore, it avoids many numerical issues in describing general strength behavior. In addition, it can provide a close approximation to the Mohr–Coulomb criterion to avoid discontinuous gradients. Formulas for the gradient, the Hessian, and the calibration procedure are provided. [ABSTRACT FROM AUTHOR]

In this paper, a simple sub-loading yield surface model for both normally consolidated and over-consolidated clay is proposed with emphasis on the effect of the yield surface shape. Compared with the modified Cam-clay model, only one additional material parameter is introduced to reflect geometry features of the yield surface. A higher-order stress–dilatancy relation is given in the current study, leading to a new yield function capable of offering an adequate description of the yield surface of soil samples in the p–q plane. By introducing the concept of the sub-loading yield surface and the unified hardening parameter, the proposed model can capture the main features of the over-consolidated clay with dilatancy and strain-softening behavior and the main features of the normally consolidated clay with contraction and strain-hardening behavior. The results show that adjusting the yield surface leads to more accurate predictions than the modified Cam-clay model. The proposed model can also reasonably describe its mechanical behavior for clay samples.

Summary: Many models of plasticity are built using multiple, simple yield surfaces. Examples include geomechanical models and crystal plasticity. This leads to numerical difficulties, most particularly during the stress update procedure, because the combined yield surface is nondifferentiable, and when employing implicit time stepping to solve numerical models, because the Jacobian is often poorly conditioned. A method is presented that produces a single C2 differentiable and convex yield function from a plastic model that contains multiple yield surfaces that are individually C2 differentiable and convex. C2 differentiability ensures quadratic convergence of implicit stress‐update procedures; convexity ensures a unique solution to the stress update problem, whereas smoothness means the Jacobian is much better conditioned. The method contains just one free parameter, and the error incurred through the smoothing procedure is quantified in terms of this parameter. The method is illustrated through three different constitutive models. The method's performance is quantified in terms of the number of iterations required during stress update as a function of the smoothing parameter. Two simple finite‐element models are also solved to compare this method with existing approaches. The method has been added to the open‐source "MOOSE" framework, for perfect, nonperfect, associated, and nonassociated plasticity. [ABSTRACT FROM AUTHOR]

[Display omitted] • A geometry-inspired numerical convex analysis (GINCA) method is proposed to investigate the convexity of yield functions. • Its reliability is verified by application to Drucker, Cazacu-Barlat2004, Gao2011, Cazacu2018 and Hu2017 functions. • GINCA is utilized to investigate the convexity of the evolving yield surface of the CQN-Chen anisotropic hardening function. Convexity of a yield function must be guaranteed to ensure unique relationship between plastic strain increments and stress components. A geometry-inspired numerical convex analysis (GINCA) approach is developed to analyze the convexity of a yield function. The numerical approach is verified by the computation of convex domains for several typical yield functions of Drucker, Cazacu-Barlat2004, Hu2017, Cazacu2018 and a newly proposed function for differential-anisotropic hardening. The verified GINCA is applied to analyze the convexity of the Gao2011 yield function since it was not determined yet. The numerical approach is also used to determine the convex domain evolution with respect to plastic deformation in an anisotropic hardening function. It is also applied to investigate the convexity of polynomial yield functions for strong anisotropic metals. The result shows that the GINCA can effectively and correctly compute the convex domain for different yield functions. Besides, the numerical approach only needs to compute the effective stress from a yield function without any computation of the first- and second-order partial derivatives, compared to the complicated convex analysis by the Hessian matrix. Therefore, the proposed GINCA is user-friendly, effective and accurate to analyze the convexity of a yield function both for isotropic hardening and anisotropic/differential hardening. The Matlab codes are shared as electric attachments for scientists and engineers to check the convexity of a yield surface under biaxial loading, plane stress with shear stress and triaxial loading conditions. [ABSTRACT FROM AUTHOR]