Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture

A coupled plasticity-damage model for plain concrete is presented in this paper. Based on continuum damage mechanics (CDM), an isotropic and anisotropic damage model coupled with a plasticity model is proposed in order to effectively predict and simulate plain concrete fracture. Two different damage evolution laws for both tension and compression are formulated for a more accurate prediction of the plain concrete behavior. In order to derive the constitutive equations and for the easiness in the numerical implementation, in the CDM framework the strain equivalence hypothesis is adopted such that the strain in the effective (undamaged) configuration is equivalent to the strain in the nominal (damaged) configuration. The proposed constitutive model has been shown to satisfy the thermodynamics requirements. Detailed numerical algorithms are developed for the finite element implementation of the proposed coupled plasticity-damage model. The numerical algorithm is coded using the user subroutine UMAT and then implemented in the commercial finite element analysis program Abaqus. Special emphasis is placed on identifying the plasticity and damage model material parameters from loading-unloading uniaxial test results. The overall performance of the proposed model is verified by comparing the model predictions to various experimental data, such as monotonic uniaxial tension and compression tests, monotonic biaxial compression test, loading-unloading uniaxial tensile and compressive tests, and mixed-mode fracture tests.     

中高应变率和不同温度下离子型中间膜的拉伸力学性能及本构关系

为系统研究中高应变率和不同温度下离子型中间膜的拉伸力学性能,进行了1 s-1～800 s-1和-40℃～60℃下的系列动态拉伸试验.基于试验结果,确定了离子型中间膜的关键力学参数,并着重分析了温度和应变率的影响:随着应变率的升高和温度的降低,离子型中间膜的初始弹性模量、屈服强度和抗拉强度均普遍提高,但极限应变有所降低....     

The equivalent plastic strain-dependent Yld2000-2d yield function and the experimental verification

An equivalent plastic strain-dependent anisotropic material model was developed for 5754O aluminum alloy sheet. In the developed model, the anisotropy coefficients for Barlat’s Yld2000-2d anisotropic yield function were established as a function of the equivalent plastic strain. The developed anisotropic material model was implemented into the commercial FEM code ABAQUS as a user material subroutine (UMAT) for simulations. In order to evaluate the accuracy of the developed material model, biaxial tensile tests were carried out using cruciform specimens and a biaxial loading testing machine. The results show that the developed material model predicts the experimental results better than the other three material models (Yld2000-2d, Mises and Hill48 yield functions). It is also found that the developed material model describes the uniaxial tensile test curves better than Yld2000-2d yield function. The deep drawing test for 5754O aluminum alloy sheet was carried out and was simulated with different material models. The comparison between the experimental and simulation results indicates that the developed material model predicts the earing profile better than other material models. It is concluded that the equivalent plastic strain-dependence of the material coefficients should be considered for the accurate prediction of the anisotropic deformation behavior of materials.     

双轴受压状态下的高延性纤维增强水泥基复合材料本构模型

基于Darwin和Pecknold考虑混凝土双轴力学行为的方法,建立一个同时考虑双轴受压状态下非线性力学行为和抗压强度变化的高延性纤维增强水泥基复合材料(ECC)二维正交各向异性本构模型。在因双轴加载而产生的正交各向异性的2个方向上引入等效单轴应变,建立非线性应力-等效单轴应变关系以考虑ECC的双轴非线性行为,并采用一条双轴强度包络线确定2个方向上的抗压强度。推导模型的显式数值算法,编写包含该算法的用户自定义材料子程序UMAT,并嵌于有限元计算程序ABAQUS v6.14中。通过对两组不同配合比的ECC试件在不同应力比下的双轴受压加载试验进行数值分析验证本模型的有效性。数值计算得到的主压应力方向上的应力-应变曲线及预测的抗压强度与试验结果吻合较好,表明该文提出的本构模型能够有效地预测ECC在双轴受压状态下的非线性力学行为和破坏强度。     

Analytical evaluation on uniaxial tensile deformation behavior of fiber metal laminate based on SRPP and its experimental confirmation

Uniaxial tensile tests have been carried out to accurately evaluate the in-plain mechanical properties of fiber metal laminates (FMLs). The FMLs in this paper comprised of a layer of self-reinforced polypropylene (SRPP) sandwiched between two layers of aluminum alloy 5052-H34. In this study, nonlinear tensile and fracture behavior of FMLs under in-plane loading conditions has been investigated with numerical simulations and theoretical analysis. The numerical simulation based on finite element modeling using the ABAQUS/Explicit and the theoretical constitutive model based on the volume fraction approach using the rule of mixture and the modified classical lamination theory, which incorporates the elastic–plastic behavior of the aluminum alloy and SRPP, are used to predict the in-plain mechanical properties such as stress–strain response and deformation behavior of the FMLs. In addition, the pre-stretching process is used to reduce the thermal residual stresses before the uniaxial tensile tests of the FMLs. Through comparing the numerical simulations and the theoretical analysis with the experimental results, it is concluded that the adopted numerical simulation model and the theoretical approach can describe with sufficient accuracy of the actual tensile stress–strain curve.     

A cyclic viscoplastic and creep damage model for lead free solder alloys

The reliability of microelectronic components under cyclic thermomechanical loading is an important problem especially for new leadfree solder alloys. To investigate the low cycle fatigue strength of solder joints, material models are required, that can describe the constitutive inelastic deformation and damage behavior of solder materials. Such models form the basis for advanced numerical analyses by the finite element method. In the present contribution an appropriate material model that combines the viscoplastic constitutive model of Chaboche-type with the damage law of A.C.F. Cocks for porous creep will be introduced. The algorithm is reported for an implementation as a user defined material subroutine into the FEM-code ABAQUS®. The necessary parameters of the material model are identified using results of miniaturized double lap-shear experiments and tensile tests for a Sn96Ag3Cu1 solder alloy at various temperatures. The comparison of experimental and numerical results shows a good agreement with respect to strain rate sensitivity, relaxation and damage behavior of the investigated solder material. Finally, some numerical applications to surface mounted microelectronic devices are presented.     

Numerical implementation of strain rate dependent thermo viscoelastic constitutive relation to simulate the mechanical behavior of PMMA

In this work, a nonlinear viscoelastic constitutive relation was implemented to describe the mechanical behavior of a transparent thermoplastic polymer polymethyl methacrylate (PMMA). The quasi-static and dynamic response of the polymer was studied under different temperatures and strain rates. The effect of temperature was incorporated in elastic and relaxation constants of the constitutive equation. The incremental form of constitutive model was developed by using Poila–Kirchhoff stress and Green strain tensors theory. The model was implemented numerically by establishing a user defined material subroutine in explicit finite element (FE) solver LS-DYNA. Finite element models for uniaxial quasi-static compressive test and high strain rate split Hopkinson pressure bar compression test were built to verify the accuracy of material subroutine. Numerical results were validated with experimental stress strain curves and the results showed that the model successfully predicted the mechanical behavior of PMMA at different temperatures for low and high strain rates. The material model was further engaged to ascertain the dynamic behavior of PMMA based aircraft windshield structure against bird impact. A good agreement between experimental and FE results showed that the suggested model can successfully be employed to assess the mechanical response of polymeric structures at different temperature and loading rates.     

A temperature- and strain-rate-dependent isotropic elasto-viscoplastic model for glass-fiber-reinforced polyurethane foam

The primary aim of the present study is to provide a new constitutive model and its computational procedure for a glass-fiber-reinforced polyurethane foam (RPUF) subjected to various cryogenic temperatures and compressive loading rates. A Frank–Brockman-type isotropic elasto-viscoplastic model was introduced to describe the hardening and softening phenomena of RPUF under compressive loads. In addition, the increase of the yield strength and plateau according to the change of temperature and strain rates was demonstrated using the given constitutive model. The introduced numerical model was transformed as an implicit form and was implemented into a user-defined subroutine of commercial finite element analysis (FEA) code, i.e., ABAQUS UMAT. Based on the developed material library, the complex elasto-plastic behavior of RPUF under various cryogenic temperatures and strain rates was numerically estimated. The variation of material internal variables, such as hardening and softening control parameters, was quantitatively investigated, and the temperature- and strain-rate-dependent empirical formulae, namely, a polynomial multiple regression model, were proposed. Finally, the simulation results were compared with a series of compressive test results to validate the proposed method. On using the developed numerical method, it might be feasible to predict the unknown stress–strain behavior of RPUF under arbitrary severe environments.     

Modeling multiaxial impact behavior of a glassy polymer

In many applications of polymers, impact performance is a primary concern. Impact tests experimentally performed on molding prototypes yield useful data for a particular structural and impact loading case. But, it is generally not practical in terms of time and cost to experimentally characterize the effects of a wide range of design variables. A successful numerical model for impact deformation and failure of polymers can provide convenient and useful guidelines on product design and therefore decrease the disadvantages that arise from purely experimental trial and error. Since the specimen geometry and loading mode for multiaxial impact test provides a close correlation with practical impact conditions and can conveniently provide experimental data, the first step of validating a numerical model is to simulate this type of test. In this paper, we create a finite element analysis model using ABAQUS/Explicit to simulate the deformation and failure of a glassy ABS (acrylonitrile-butadiene-styrene) polymer in the standard ASTM D3763 multiaxial impact test. Since polymers often exhibit different behavior in uniaxial tensile and compression tests, the uniaxial compression or tensile tests are generally not representative of the three-dimensional deformation behavior under impact loading. A hydrostatic pressure effect (controlled by the parameter γ) is used to generalize a previously developed constitutive model ("DSGZ" model) so that it can describe the entire range of deformation behavior of polymers under any monotonic loading modes. The generalized DSGZ model and a failure criterion are incorporated in the FEA model as a user material subroutine. The phenomenon of thermomechanical coupling during plastic deformation is considered in the analysis. Impact load vs. displacement and impact energy vs. displacement curves from FEA simulation are compared with experimental data. The results show good agreement. Finally, equivalent stress, strain, strain rate and temperature distributions in the polymer disk are presented. Electronic Publication     

基于实验的钛合金优化动态本构模型与有限元模拟

为确定钛合金材料的Johnson-Cook模型中5个待定本构参数,克服传统单因素分析法的弊端并提高参数识别效率和精度,采用拉丁超立方抽样、Spearman秩相关分析的参数敏感度整体分析方法,并在参数敏感度分析结果和基本遗传算法的基础上,建立了一种基于改进小生境算法、可疑峰值点判断策略和局域精确搜索技术的改进遗传算法,基于实验数据建立了精细的钛合金Johnson-Cook本构模型。采用隐式应力积分法将该模型嵌入到ABAQUS用户材料子程序UMAT中,并通过隐函数求导方法推导出一致切线刚度矩阵。通过ABAQUS有限元软件对钛合金材料的动态响应进行数值模拟分析,计算结果与已有的实验数据吻合良好,UMAT子程序的准确性得到验证,可用于钛合金材料的动态响应预测分析中。     

Multi-Scale Modeling the Mechanical Properties of Biaxial Weft Knitted Fabrics for Composite Applications

In this paper a multi-scale numerical model for simulating the mechanical behavior of biaxial weft knitted fabrics produced based on 1×1 rib structure is presented. Fabrics were produced on a modern flat knitting machine using polyester as stitch yarns and nylon as straight yarns. A macro constitutive equation was presented to model the fabric mechanical behavior as a continuum material. User defined material subroutines were provided to implement the constitutive behavior in Abaqus software. The constitutive equation needs remarkable tensile tests on the fabric as the inputs. To solve this drawbacks meso scale modeling of the fabric was used to predict stress–strain curves of the fabric in three different directions (course, wale and 45°). In these simulations only the yarn properties are needed. To evaluate the accuracy of the proposed macro and meso models, fabric tensile behavior in 22.5 and 67.5° directions were simulated by the calibrated macro model and compared with experimental results. Spherical deformation was also simulated by the multi scale model and compared with experimental results. The results showed that the multi-scale modeling can successfully predict the tensile and spherical deformation of the biaxial weft knitted fabric with least required experiments. This model will be useful for composite applications.     

2024-T3铝合金动力学实验及其平板鸟撞动态响应分析

通过电子万能试验机和分离式霍普金森拉杆（SHTB）拉伸试验分别获得2024-T3铝合金材料准静态和高应变率两种应变率下的应力-应变曲线。铝合金材料的本构关系由能够反映材料硬化效应和应变率强化效应的Johnson-Cook材料模型描述,方程中的4个参数通过不同应变率下的应力-应变曲线拟合得到。基于瞬态动力学软件PAM-CRASH,结合材料动态力学性能试验所获得的2024-T3铝合金Johnson-Cook模型方程,耦合光滑粒子流体动力学（SPH）方法和有限元（FE）方法建立2024-T3铝合金平板的鸟撞数值模型,数值计算所得动态响应与鸟撞试验结果吻合较好,表明建立的鸟撞数值计算模型是合理、可靠的,整个分析流程从材料动态力学性能试验、鸟撞数值计算到最终的鸟撞试验验证为飞机结构的抗鸟撞设计与分析提供了有力的参考。     

On the selection of constitutive equation for modeling the friction stir processes of twin roll cast wrought AZ31B

Proper numerical modeling of the Friction Stir Processes (FSPs) requires the identification of a suitable constitutive equation which accurately describes the stress-strain material behavior under an applicable range of strains, strain rates, and temperatures. While some such equations may be perfectly suitable to simulate processes characterized by low (or high) strains and temperatures, FSPs are widely recognized for their relatively moderate ranges of such state variables. In this work, a number of constitutive equations for describing flow stress in metals were screened for their suitability for modeling Friction Stir Processes of twin roll cast (TRC) wrought magnesium Mg–AL–Zn (AZ31B) alloy. Considered were 4 different reported variations of the popular Johnson–Cook equation and one Sellars–Tegart equation along with their literature–reported coefficients for fitting AZ31B stress–strain behavior. In addition, 6 variations of the (rarely used in FSPs simulations) Zerilli–Armstrong equation were also considered along with their literature–reported coefficients. The screening assessment was based on how well the considered constitutive equations fit experimental tensile stress–strain data of twin roll cast wrought AZ31B. Goodness of fit and residual sum of squares were the two statistical criteria utilized in the quantitative assessment whereas a ‘visual ’ measure was used as a qualitative measure. Initial screening resulted in the selection of one best fitting constitutive equation representing one of each of the Johnson–Cook, Sellars–Tegart, and Zerilli–Armstrong equations. An HCP–specific Zerilli–Armstrong constitutive equation (dubbed here as ZA₆ ) was found to have the best quantitative and qualitative fit results with an R² value of 0.967 compared to values of 0.934 and 0.826 for the Johnson–Cook and Sellars–Tegart constitutive equations, respectively. Additionally, a 3D thermo–mechanically coupled FEM model was built in DEFORM 3D to simulate the experimental tensile test from which the experimental load–deflection data was obtained. The three ‘finalist ’ equations were fed into the FEM simulations and were compared based on the 1) simulations’ running times and 2) goodness of fit of the simulation results to the experimental load–deflection data. It was found that the ZA₆ constitutive equation exhibited favorable run times even when contrasted against the simpler mathematical form of the Sellars–Tegart equation. On average, the ZA₆ equation showed improvements in solution time by 5.4% as compared with the Johnson–Cook equation and almost identical solution time (0.9% increase) with that of the ST equation. This result indicates that the proposed equation is not numerically expensive and can be safely adopted in such FEM simulations. Based on the favorable running times and goodness of fit, it was concluded that the HCP–specific Zerilli–Armstrong constitutive equation ZA₆ holds an advantage over all other considered equations and was, therefore, selected as most suitable for the numerical modeling of FSP of twin roll cast AZ31B.     

Modeling of Nonlinear Mechanical Behavior for 3D Needled C/C-SiC Composites Under Tensile Load

This paper established a macroscopic constitutive model to describe the nonlinear stress–strain behavior of 3D needled C/C-SiC composites under tensile load. Extensive on- and off-axis tensile tests were performed to investigate the macroscopic mechanical behavior and damage characteristics of the composites. The nonlinear mechanical behavior of the material was mainly induced by matrix tensile cracking and fiber/matrix debonding. Permanent deformations and secant modulus degradation were observed in cyclic loading-unloading tests. The nonlinear stress–strain relationship of the material could be described macroscopically by plasticity deformation and stiffness degradation. In the proposed model, we employed a plasticity theory with associated plastic flow rule to describe the evolution of plastic strains. A novel damage variable was also introduced to characterize the stiffness degradation of the material. The damage evolution law was derived from the statistical distribution of material strength. Parameters of the proposed model can be determined from off-axis tensile tests. Stress–strain curves predicted by this model showed reasonable agreement with experimental results.     

一种钢板材料动态拉伸本构方程确定以及试件尺度效应研究

采用数值模拟方法,优化设计了Hopkinson拉伸实验中,QP980CR钢的片状试件尺度。对所设计的试件,在MTS(810材料试验机)上进行了准静态拉伸试验,在Hopkinson拉杆装置上进行了不同应变率及不同温度的动态拉伸试验。由准静态及动态拉伸试验结果,确定了试件材料的J-C型动态拉伸本构方程。基于确定的试件动态拉伸本构方程,采用数值模拟方法,研究了Hopkinson拉伸试验中,试件的形状和尺度对测试结果的影响。     

纤维金属层板低速冲击试验和数值仿真

为开展纤维金属层板（FML）低速冲击有限元数值仿真研究,改进了传统的连续损伤力学（CDM）模型,然后对FML落锤低速冲击试验进行数值仿真,并与实验结果进行对比验证。分别采用5.11 J 和10.33 J冲击能量对FML进行落锤低速冲击试验,得到冲击载荷、位移和能量时程曲线,分析FML的动态响应和失效模式。建立了考虑塑性应变、压缩刚度衰减特征和纤维拉伸断裂损伤的新CDM模型,描述S2-玻璃纤维/环氧树脂（S2-galss/epoxy）复合材料的损伤本构,并编写VUMAT子程序,通过ABAQUS/Explicit求解器对FML落锤冲击试验进行数值仿真。研究结果表明：低能量冲击条件下,FML背面主要为鼓包和裂纹等失效模式,位移峰值随冲击能量的提高而增加,冲击载荷峰值在穿透前也随冲击能量的提高而增加;采用改进的CDM模型描述FML中S2-galss/epoxy复合材料铺层后,有限元数值计算可以较好地预测FML低速冲击载荷下的动态响应;有限元数值仿真结果表明,FML中第2层复合材料铺层发生的纤维断裂损伤比第1层的更严重。     

Temperature and strain rate dependent constitutive model of TRIP steels for low-temperature applications

The aim of this study was to develop a constitutive model that takes into consideration the strain rate and temperature dependent characteristics of TRIP steels, in conjunction with a damage mechanics approach. The martensitic-transformation-induced strain hardening of type 300 series austenitic stainless steels at low temperature is a remarkable phenomenon. From a mechanical point of view, the temperature and strain rate play critical roles in such material nonlinearities. A series of tensile tests for 304L ASS, which is representative of TRIP steels and cryogenic materials, were conducted at various temperatures and strain rates. The experimental results revealed nonlinear material characteristics of TRIP at low temperature and were simulated by the proposed numerical model. A strain-induced martensitic transformation model was implemented in a unified viscoplastic constitutive equation. The damage evolution equation was also incorporated into the proposed constitutive model to simulate material degradation. Using a series of finite element analyses, quantitative verification of the proposed numerical technique was carried out by comparing the experimental and numerical results.     

应变率对T300/Al(L2)复合丝拉伸性能的影响

利用MTS810试验机和自行研制的冲击拉伸试验装置对T300／Al复合丝实施了不同应变率下的拉伸试验,获得了材料从0．001s^-1到1300s^-1应变率范围内完整的应力应变曲线。结果表明：T300／Al是一种应变率敏感复合材料,随着应变率的提高,材料的拉伸强度、失稳应变均相应提高,具有明显的应变率强化效应和动态韧性现象,这主要是由铝基体的应变率强化效应和应变率历史效应引起的。根据材料在不同应变率下的试验结果以及对其不同变形阶段机理的分析,提出了弹塑性复合丝束模型,并由此建立了相应的应变率相关的一维统计损伤本构方程,模型拟合结果与试验结果一致。     

An unusual elastoplastic response of thermoplastic elastomers at cyclic deformation

Observations are reported on a thermoplastic elastomer (ethylene–octene copolymer) in uniaxial tensile tests. The experimental data reveal a rather unusual mechanical response: unlike particle-reinforced rubbers, for which preconditioning causes a monotonic decrease in tensile stress compared with that in a virgin specimen, cyclic preloading of the thermoplastic elastomer induces a reduction in stress at small strains and its noticeable growth at relatively large elongation ratios.A constitutive model is derived for the elastoplastic behavior of a polymer network with constrained chains at three-dimensional deformations with finite strains. The stress–strain relations involve five adjustable parameters that are found by fitting the experimental data. Good agreement is demonstrated between the observations and the results of numerical simulation. It is shown that the material parameters are affected by intensity of preloading in a physically plausible way.