Anisotropic plasticity model coupled with Lode angle dependent strain-induced transformation kinetics law

A phenomenological macroscopic plasticity model is developed for steels that exhibit strain-induced austenite-to-martensite transformation. The model makes use of a stress-state dependent transformation kinetics law that accounts for both the effects of the stress triaxiality and the Lode angle on the rate of transformation. The macroscopic strain hardening is due to nonlinear kinematic hardening as well as isotropic hardening. The latter contribution is assumed to depend on the dislocation density as well as the current martensite volume fraction. The constitutive equations are embedded in the framework of finite strain isothermal rate-independent anisotropic plasticity. Experimental data for an anisotropic austenitic stainless steel 301LN is presented for uniaxial tension, uniaxial compression, transverse plane strain tension and pure shear. The model parameters are identified using a combined analytical–numerical approach. Numerical simulations are performed of all calibration experiments and excellent agreement is observed. Moreover, we make use of experimental data from ten combined tension and shear experiments to validate the proposed constitutive model. In addition, punch and notched tension tests are performed to evaluate the model performance in structural applications with heterogeneous stress and strain fields.     

Experiments and Material Parameter Identification Using Finite Elements. Uniaxial Tests and Validation Using Instrumented Indentation Tests

In this article, we focus our attention on the relation between instrumented indentation tests and the prediction by means of finite element calculations. To this end, a finite strain viscoplasticity model of Perzyna-type with non-linear isotropic and kinematic hardening is calibrated at experimental data of steel S690QL. A particular concept for conducting uniaxial tensile and compression tests is taken up in order to represent the basic rate-dependent material behavior. In this respect, an algorithmic framework of material parameter identification using finite elements is proposed leading to a two-stage procedure in the case of the underlying rate-dependent constitutive model. On the basis of the termination points of relaxation the rate-independent equilibrium stress state can be identified and all viscous parts of the model are obtained using rate-dependent loading paths. Finally, use is made of finite elements for predicting indentation experiments, which results in a critical view on modeling and parameter identification on the basis of experimental results occurring in instrumented indentation tests.     

Effects of texture on shear band formation in plane strain tension/compression and bending

In this study, effects of typical texture components observed in rolled aluminum alloy sheets on shear band formation in plane strain tension/compression and bending are systematically studied. The material response is described by a generalized Taylor-type polycrystal model, in which each grain is characterized in terms of an elastic–viscoplastic continuum slip constitutive relation. First, a simple model analysis in which the shear band is assumed to occur in a weaker thin slice of material is performed. From this simple model analysis, two important quantities regarding shear band formation are obtained: i.e. the critical strain at the onset of shear banding and the corresponding orientation of shear band. Second, the shear band development in plane strain tension/compression is analyzed by the finite element method. Predictability of the finite element analysis is compared to that of the simple model analysis. Third, shear band developments in plane strain pure bending of a sheet specimen with the typical textures are studied. Regions near the surfaces in a bent sheet specimen are approximately subjected to plane strain tension or compression. From this viewpoint, the bendability of a sheet specimen may be evaluated, using the knowledge regarding shear band formation in plane strain tension/compression. To confirm this and to encompass overall deformation of a bent sheet specimen, including shear bands, finite element analyses of plane strain pure bending are carried out, and the predicted shear band formation in bent specimens is compared to that in the tension/compression problem. Finally, the present results are compared to previous related studies, and the efficiency of the present method for materials design in future is discussed.     

Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys

A crystal-inelasticity-based constitutive model for martensitic reorientation and detwinning in shape-memory alloys (SMAs) has been developed from basic thermodynamics principles. The model has been implemented in a finite-element program by writing a user-material subroutine. We perform two sets of finite-element simulations to model the behavior of polycrystalline SMAs: (1) The full finite-element model where each finite element represents a collection of martensitic microstructures which originated from within an austenite single crystal, chosen from a set of crystal orientations that approximates the initial austentic crystallographic texture. The macroscopic stress-strain responses are calculated as volume averages over the entire aggregate: (2) The Taylor model (J. Inst. Metals 62 (1938) 32) where an integration point in a finite element represents a material point which consist of sets of martensitic microstructures which originated from within respective austenite single-crystals. Here the macroscopic stress-strain responses are calculated through a homogenization scheme.Experiments in tension and compression were conducted on textured polycrystalline Ti-Ni rod initially in the martensitic phase by Xie et al (Acta Mater. 46 (1998) 1989). The material parameters for the constitutive model were calibrated by fitting the tensile stress-strain response from a full finite-element calculation of a polycrystalline aggregate to the simple tension experiment. With the material parameters calibrated the predicted stress-strain curve for simple compression is in very good accord with the corresponding experiment. By comparing the simulated stress-strain response in simple tension and simple compression it is shown that the constitutive model is able to predict the observed tension-compression asymmetry exhibited by polycrystalline Ti-Ni to good accuracy. Furthermore, our calculations also show that the macroscopic stress-strain response depends strongly on the initial martensitic microstructure and crystallographic texture of the material.We also show that the Taylor model predicts the macroscopic stress-strain curves in simple tension and simple compression reasonably well. Therefore, it may be used as a relatively inexpensive computational tool for the design of components made from shape-memory materials.     

A plasticity and anisotropic damage model for plain concrete

A plastic-damage constitutive model for plain concrete is developed in this work. Anisotropic damage with a plasticity yield criterion and a damage criterion are introduced to be able to adequately describe the plastic and damage behavior of concrete. Moreover, in order to account for different effects under tensile and compressive loadings, two damage criteria are used: one for compression and a second for tension such that the total stress is decomposed into tensile and compressive components. Stiffness recovery caused by crack opening/closing is also incorporated. The strain equivalence hypothesis is used in deriving the constitutive equations such that the strains in the effective (undamaged) and damaged configurations are set equal. This leads to a decoupled algorithm for the effective stress computation and the damage evolution. It is also shown that the proposed constitutive relations comply with the laws of thermodynamics. A detailed numerical algorithm is coded using the user subroutine UMAT and then implemented in the advanced finite element program ABAQUS. The numerical simulations are shown for uniaxial and biaxial tension and compression. The results show very good correlation with the experimental data.     

不同本构模型对橡胶制品有限元法适应性研究

为确定不同本构模型对橡胶制品进行非线性有限元分析的适应性,采用HyperMesh 和ABAQUS软件建立了橡胶标准试件和防尘罩制品的非线性有限元模型. 根据标准试件单轴拉伸试验数据,利用ABAQUS软件拟合了Mooney——Rivlin, Ogden 及Yeoh 3 种本构模型的特征参数,并给出了试件和制品轴向拉伸和压缩工况有限元分析结果. 实测试验与有限元分析结果对比发现:在应变不大于100% 时,两参数的Mooney——Rivlin本构模型计算误差较小;在应变大于100% 时, 用Yeoh 和Ogden 本构模型计算误差较小. 该结论对大变形橡胶元件的非线性特性理论分析具有实际意义.     

A theory for amorphous viscoplastic materials undergoing finite deformations, with application to metallic glasses

This study develops a finite-deformation, Coulomb-Mohr type constitutive theory for the elastic-viscoplastic response of pressure-sensitive and plastically-dilatant isotropic materials. The constitutive model has been implemented in a finite element program, and the numerical capability is used to study the deformation response of amorphous metallic glasses. Specifically, the response of an amorphous metallic glass in tension, compression, strip-bending, and indentation is studied, and it is shown that results from the numerical simulations qualitatively capture major features of corresponding results from physical experiments available in the literature.     

基于机器学习软骨细胞的时间依赖性力学行为及本构参数反演

探究软骨细胞机械负载下的力学特性对于理解软骨细胞的正常和病理状态以及骨性关节炎的病因至关重要. 基于软骨细胞有限元计算模型的力学响应与其本构参数之间的高度复杂非线性, 本文提出了分别利用双向深度神经网络TW-Deepnets模型和随机森林RF模型并结合有限元方法来识别软骨细胞本构参数的两种反演方法. 首先, 建立了软骨细胞的无侧限压缩实验有限元模型, 收集MSnHS本构参数空间点与对应的有限元计算模型的压缩反作用力响应数据集. 其次, 结合贝叶斯超参数优化算法搭建了用于软骨细胞本构参数反求的TW-Deepnets模型和RF模型, 对有限元收集的数据进行训练, 并利用单个软骨细胞受到50%压缩程度下的实验数据对软骨细胞的MSnHS本构参数进行了反求. 最后, 通过与实验曲线的对比验证了所提出的反演方法的有效性, 并引入决定系数R2对两种模型的预测准确性进行了对比评估, 检验了模型对各本构参数的预测性能, 分析了MSnHS本构模型中各参数影响软骨细胞力学响应的重要性占比. 结果表明, 本研究提出的本构参数反演方法能够有效获取软骨细胞的本构参数值, 从而准确描述软骨细胞的时间依赖性力学特性, 该方法也可进一步推广到生物细胞在静态或动态负载条件下的复杂参数反演问题.      

Formulation and numerical implementation of a constitutive law for concrete with strain-based damage and plasticity

A triaxial constitutive law for concrete within the framework of isotropic damage combined with plasticity is proposed in this paper. It covers typical characteristics of concrete like non-linear uniaxial compression and tension, bi- and triaxial failure criteria and dilatancy with a unified strain-based approach. Thus, this model is quite simple and especially suitable for strain-driven methods like common finite elements. It is complemented with a regularization method based on the crack band approach. A further issue is discussed with procedures for the model parameter determination for a wide range of concrete grades. The application of the model is demonstrated with typical benchmark tests for plain concrete.     

Nonlinear dependence of viscosity in modeling the rate-dependent response of natural and high damping rubbers in compression and shear: Experimental identification and numerical verification

The rate-dependent behavior of filled natural rubber (NR) and high damping rubber (HDR) is investigated in compression and shear regimes. In order to describe the viscosity-induced rate-dependent effects, a constitutive model of finite strain viscoelasticity founded on the basis of the multiplicative decomposition of the deformation gradient tensor into elastic and inelastic parts is proposed. The total stress is decomposed into an equilibrium stress and a viscosity-induced overstress by following the concept of the Zener model. To identify the constitutive equation for the viscosity from direct experimental observations, an analytical scheme that ascertains the fundamental relation between the inelastic strain rate and the overstress tensor of the Mandel type by evaluating simple relaxation test results is proposed. Evaluation of the experimental results using the proposed analytical scheme confirms the necessity of considering both the current overstress and the current deformation as variables to describe the evolution of the rate-dependent phenomena. Based on this experimentally based motivation, an evolution equation using power laws is proposed to represent the effects of internal variables on viscosity phenomena. The proposed evolution equation has been incorporated in the finite strain viscoelasticity model in a thermodynamically consistent way. Simulation results for simple relaxation tests, multi-step relaxation tests and monotonic tests at different strain rates using the developed model show an encouraging correlation with the experiments conducted on HDR and NR in both compression and shear regimes. Finally, an approach to extend the proposed evolution equation for rate-dependent cyclic processes is proposed. The simulation results are critically compared with the experiments.     

基于仿真和智能算法骨骼肌超弹性本构参数的反演方法研究

从事高强度的体力工作者经常会发生肌肉软组织的损伤,因此对骨骼肌的变形特性和应力分布的研究受到了越来越多的重视.获取正确的本构参数对于生物软组织的力学行为的研究至关重要,而本构参数的确定本质上是一个逆过程,具有很大的挑战性.本文分别采用K近邻(K-nearest neighbor,KNN)模型和支持向量机回归(suppo...     

A special mechanical behavior of gels and its micro mechanism

It is found in experiment of gel specimen that the elastic modulus under tension can be 1.6 times of that under compression. In order to explain this phenomenon, a micro model that consists of network and water is proposed. It is assumed that the macromolecular chains can only sustain tensile force but not compression along chains. Based on this constitutive model, the elastic moduli of gels under tension, compression and shear are derived for small strain case. The irregular behavior of gels predicated by this model are consistent with the results of experiment.     

利用材料拉压异必无损检测残余应力的新方法

用实验手段研究了若干种材料在弹性范围内的拉压异性,发现某些材料的拉伸弹性模量与压缩弹必模量相差高达60%,从分析拉压异性产生的机理,描述了拉压导师性材料的应力应变关系,在此基础上提出了一种基于材料拉压异性的残余应力无损检测新方法,并进行了弯曲和扭转残余应力的典型实验,结果证明在某些条件下它是十分有效的,具有简便、精度高的特点。     

Thermoviscoplastic modelling of asymmetric effects for polymers at large strains

Glassy polymers such as polycarbonate exhibit different behaviours in different loading scenarios, such as tension and compression. To this end a flow rule is postulated within a thermodynamic consistent framework in a mixed variant formulation and decomposed into a sum of weighted stress mode related quantities. The different stress modes are chosen such that they are accessible to individual examination in the laboratory, where tension and compression are typical examples. The characterisation of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the Lode angle, such that stress mode dependent scalar weighting functions can be constructed. Furthermore the numerical implementation of the constitutive equations into a finite element program is briefly described. In a numerical example, the model is used to simulate the laser transmission welding process.     

Constitutive equations for metal powders: application to powder forming processes

A new constitutive model for cold compaction of metal powders is developed. The plastic flow of metal powders at the macroscopic level is assumed to be representable as a combination of a distortion mechanism, and a consolidation mechanism. For the distortion mechanism the model employs a pressure-sensitive, Mohr–Coulomb type yield condition, and a new physically based non-associated flow rule. For the consolidation mechanism the model employs a smooth yield function which has a quarter-elliptical shape in the mean-normal pressure and the equivalent shear stress plane, together with an associated flow rule. The constitutive model has been implemented in a finite element program. The material parameters in the constitutive model have been calibrated for MH-100 iron powder by fitting the model to reproduce data from true triaxial compression experiments, torsion ring-shear experiments, and simple compression experiments. The predictive capability of the constitutive model and computational procedure is checked by simulating two simple powder forming processes: (i) a uniaxial strain compression of a cylindrical sample, and (ii) forming of a conical shaped-charge liner. In both cases the predicted load–displacement curves and density variations in the compacted specimens are shown to compare well with corresponding experimental measurements.     

Lonsdaleite Model of Open-Cell Elastic Foams: Theory and Calibration

We formulate a unit-cell model of open-cell elastic foams. In this model, a foam consists of four-bar tetrahedra arranged in the hexagonal diamond structure known as Lonsdaleite. The parameters of the model are the Young??s modulus of the bars and a few geometric parameters, the values of which may be roughly estimated for any given foam. We use the model to simulate a set of experiments in which elastic polyether polyurethane foams in a broad range of densities were tested under five loading conditions, namely tension along the rise direction; compression along the rise direction; compression along a transverse direction; simple shear combined with compression along the rise direction; and hydrostatic pressure combined with compression along the rise direction. With a suitable choice of values of the parameters of the model, the stress?Cstretch curves that we compute using the model compare favorably with the stress?Cstretch curves that were measured in the experiments. In some of the experiments a stress plateau in the stress?Cstretch curve was accompanied by heterogeneous stretch fields, even though the attendant stress fields were homogeneous. For these experiments we show that the model can be used to predict the occurrence of a second-order phase transition, so that the plateau stress can be interpreted as a Maxwell stress and the attendant heterogeneous stretch fields as two-phase fields, consistent with the experimental evidence. In other experiments the stress?Cstretch curve evinced a sudden and pronounced loss of stiffness, but no genuine stress plateau, and the attendant stretch fields remained homogeneous. For these experiments we show that the model can be used to predict the occurrence of a bifurcation of equilibrium in which the stress keeps rising as the deformation continues to increase in the post-buckling stage, so that the stretch fields remain homogeneous throughout, consistent with the experimental evidence. In general, to appraise the goodness of our model we put emphasis on the relation between the stress?Cstretch curve measured in an experiment and the nature of the attendant stretch fields. We submit that this emphasis should remain a guiding methodological trait in the appraisal of constitutive models of open-cell elastic foams.     

Deformation of plastically compressible hardening-softening-hardening solids

Motivated by a model of the response of vertically aligned carbon nanotube (VACNT) pillars in uniaxial compression, we consider the deformation of a class of compressible elastic-viscoplastic solids with a hardening-softening-hardening variation of flow strength with plastic strain. In previous work (Hutchens et al. 2011) a constitutive relation was presented and used to model the response of VACNT pillars in axisymmetric compression. Subsequently, it was found that due to a programming error the constitutive relation presented in the paper (Hutchens et al. 2011) was not the one actually implemented. In particular, the plastic flow rule actually used did not satisfy plastic normality. Here, we present the constitutive formulation actually implemented in the previous work (Hutchens et al. 2011). Dynamic, finite deformation, finite element calculations are carried out for uniaxial compression, uniaxial tension and for indentation of a "half-space" by a conical indenter tip. A sequential buckling-like deformation mode is found in com- pression when there is plastic non-normality and hardening-softening-hardening. The same material characterization gives rise to a Lüders band-like deformation mode in ten- sion. When there is a deformation mode with a sharp front along mesh boundaries, the overall stress-strain response contains high frequency oscillations that are a mesh artifact. The responses of non-softening solids are also analyzed and their overall stress-strain behavior and deformationmodes are compared with those of hardening-softening- hardening solids. We find that indentation with a sharp in- denter tip gives a qualitatively equivalent response for hardening and hardening-softening-hardening solids.     

Effects of stress invariants and reverse loading on ductile fracture initiation

Recent research studies on ductile fracture of metals have shown that the ductile fracture initiation is significantly affected by the stress state. In this study, the effects of the stress invariants as well as the effect of the reverse loading on ductile fracture are considered. To estimate the reduction of load carrying capacity and ductile fracture initiation, a scalar damage expression is proposed. This scalar damage is a function of the accumulated plastic strain, the first stress invariant and the Lode angle. To incorporate the effect of the reverse loading, the accumulated plastic strain is divided into the tension and compression components and each component has a different weight coefficient. For evaluating the plastic deformation until fracture initiation, the proposed damage function is coupled with the cyclic plasticity model which is affected by all of the stress invariants and pervious plastic deformation history.For verification and evaluation of this damage-plasticity constitutive equation a series of experimental tests are conducted on high-strength steel, DIN 1.6959. In addition finite element simulations are carried out including the integration of the constitutive equations using the modified return mapping algorithm. The modeling results show good agreement with experimental results.     

Anisotropic Mullins stress softening of a deformed silicone holey plate

Rubber like materials parts are designed using finite element code in which more and more precise and robust constitutive equations are implemented. In general, constitutive equations developed in literature to represent the anisotropy induced by the Mullins effect present analytical forms that are not adapted to finite element implementation. The present paper deals with the development of a constitutive equation that represents the anisotropy of the Mullins effect using only strain invariants. The efficiency of the modeling is first compared to classical homogeneous experimental tests on a filled silicone rubber. Second, the model is tested on a complex structure. In this aim, a silicone holey plate is molded and tested in tension, its local strain fields are evaluated by means of digital image correlation. The experimental results are compared to the simulations from the constitutive equation implemented in a finite element code. Global measurements (i.e. force and displacement) and local strain fields are successfully compared to experimental measurements to validate the model.     

Finite elasto-viscoplastic modeling of polymers including asymmetric effects

Asymmetric effects between compression and tension are a pronounced behavior for glassy polymers such as polycarbonate. For its simulation an elasto-viscoplastic framework is formulated within a geometrically nonlinear theory. Here a new approach within the concept of stress mode dependent weighting functions is used, where each material parameter is additively decomposed into a sum of weighted stress mode-related quantities. The characterization of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the mode angle, such that stress mode dependent scalar weighting functions can be constructed. The constitutive equations are formulated for large strains in terms of logarithmic Hencky strains and its work conjugated Hill stresses. The resulting evolution equations are updated using a semi-implicit Euler scheme, and the algorithmic tangent operator is derived for the finite element equilibrium iteration. The numerical implementation is also used to identify the material parameters thus resulting into a good agreement with experimental data. Furthermore, the model is used to simulate the cold drawing processes for a dumbbell-shaped specimen in tension and a perforated strip in compression and tension.