Comprehensive Constitutive Model Research Articles

Modeling high-temperature tensile deformation behavior of AZ31B magnesium alloy considering strain effects

The hot tensile deformation behaviors of AZ31B magnesium alloy are investigated over wide ranges of forming temperature and strain rate. Considering the effects of strain on material constants, a comprehensive constitutive model is applied to describe the relationships of flow stress, strain rate and forming temperature for AZ31B magnesium alloy. The results show that: (1) The effects of forming temperature and strain rate on the flow behaviors of AZ31B magnesium alloy are significant. The true stress–true strain curves exhibit a peak stress at small strains, after which the flow stress decreases until large strain, showing an obvious dynamic softening behavior. A considerable strain hardening stage with a uniform macroscopic deformation appears under the temperatures of 523 and 573K. The strain hardening exponent (n) increases with the increase of strain rate or the decrease of forming temperature. There are not obvious strain-hardening stages when the forming temperature is relatively high, which indicates that the dynamic recrystallization (DRX) occurs under the high forming temperature, and the balance of strain hardening and DRX softening is easy to obtain. (2) The predicted stress–strain values by the established model well agree with experimental results, which confirm that the established constitutive equation can give an accurate and precise estimate of the flow stress for AZ31B magnesium alloy.

Simplified Constitutive Model for Simulation of Cyclic Response of Shallow Foundations: Validation against Laboratory Tests

The nonlinear response of shallow foundations has been studied experimentally and analytically. However, the engineering community is not yet convinced of the applicability of such concepts in practice. A key prerequisite is the ability to realistically model such effects. Although several sophisticated constitutive models are readily available in the literature, their use in practice is limited, because (1) they typically require extensive soil testing for calibration; (2) as they are implemented in highly specialized numerical codes, they are usually restricted to simple superstructures; and (3) in most cases, they can only be applied by numerical analysis specialists. Attempting to overcome some of these difficulties, this paper develops a simplified but fairly comprehensive constitutive model for analysis of the cyclic response of shallow foundations. On the basis of a kinematic hardening constitutive model with Von Mises failure criterion (readily available in commercial finite element codes), the mo...

A composite finite element to predict failure progress in composite laminates accounting for nonlinear material properties

SUMMARY The failure initiation and failure progress up to the final failure of the fiber-reinforced composite (FRC) laminated shells, using the finite element method have been studied. A finite element computer program ‘NLINE’ has been used for this purpose. The program uses a 10-node triangular finite element for the analysis of plates and shells developed by the first author. For detecting and controlling the failure of such structures, Abu-Farsakh–Abdel-Jawad (AF-AJ) failure criterion has been employed, which is applicable to nonlinear behavior composite materials. The material nonlinear behavior is simulated using a comprehensive constitutive material model that incorporates the material nonlinearity through the plastic strain energy density of an equivalent linear–elastic system. Results were compared with the corresponding available experimental data and theoretical predictions of a worldwide failure exercise. This exercise was launched to confirm the current state-of-the art of predicting failure in composite laminates. The predictions of failure by ‘NLINE’ were in good agreement with many of the experimental results as well as the other theoretical predictions. Copyright © 2011 John Wiley & Sons, Ltd.

Active shape change of an SMA hybrid composite plate

An experimental study was carried out to investigate the shape control of plates via embedded shape memory alloy (SMA) wires. An extensive body of literature proposes the use of SMA wires to actively modify the shape or stiffness of a structure; in most cases, however, the study focuses on modeling and little experimental data is available. In this work, a simple proof of concept specimen was built by attaching four prestrained SMA wires to one side of a carbon fiber laminate plate strip. The specimen was clamped at one end and tested in an environmental chamber, measuring the tip displacement and the SMA temperature. At heating, actuation of the SMA wires bends the plate; at cooling deformation is partially recovered. The specimen was actuated a few times between two fixed temperatures <TEX>$T_c$</TEX> and <TEX>$T_h$</TEX>, whereas in the last actuation a temperature <TEX>$T_f$</TEX> > <TEX>$T_h$</TEX> was reached. Contrary to most model predictions, in the first actuation the transformation temperatures are significantly higher than in the following cycles, which are stable. Moreover, if the temperature <TEX>$T_h$</TEX> is exceeded, two separate actuations occur during heating: the first follows the path of the stable cycles; the second, starting at <TEX>$T_h$</TEX>, is similar to the first cycle. An interpretation of the phenomenon is given using some differential scanning calorimeter (DSC) measurements. The observed behavior emphasizes the need to build a more comprehensive constitutive model able to include these effects.

A new mathematical model for predicting flow stress of typical high-strength alloy steel at elevated high temperature

Abstract Numerical simulations can be truly reliable only when a proper material flow stress relationship is built because of its effective role on metal flow pattern as well as the kinetics of metallurgical transformation. Based on the hot compressive deformation behaviors of 42CrMo steel, a comprehensive constitutive model has been developed to predict stress–strain curve up to the peak stress. A new material parameter L , which is sensitive to the forming temperature and strain rate, was proposed in the developed constitutive model. Additionally, the mathematical models to predict peak stress and peak strain were established based on experimental results. The stress–strain values predicted by the developed model well agree with experimental results, which confirmed that the developed constitutive equation gives an accurate and precise estimate for the flow stress of 42CrMo steel.

An elastoplatic framework for coupling hydraulic and mechanical behavior of unsaturated soils

Combining theory of mixture with interfaces (TMI) and the continuum theory of plasticity, a theoretical framework for modeling the elastoplastic constitutive behavior of unsaturated soils is presented. We show that capillary hysteresis, i.e., soil water characteristic curves (SWCCs), is associated with a dissipation mechanism due to the irrecoverable change in volume fraction of water. Within this context, plastic deformation and capillary hysteresis can be consistently simulated in a hierarchical way. Plastic deformation is described by using an intergranular stress tensor that does not require any empirical coefficients and the capillary hysteresis is simulated within the framework of cyclic plasticity. This framework preserves all the advantages of unsaturated soil models based on the effective stress, two stress state variables, and the theory of mixtures. As a first step in developing a comprehensive constitutive model within this framework, a detailed model to simulate SWCCs is presented and compared with experimental data and a good comparison is obtained. A brief description of a novel experimental setup used to rapidly measure the SWCCs is also presented. Finally an isotropic coupled hydraulic–mechanical model is presented and the coupling effects between plastic deformation and capillary hysteresis are investigated.

Impact of multidirectional shaking on liquefaction potential of level sand deposits

Multidirectional shearing, as induced by multidirectional shaking, involves variations not only in shear magnitude but also in shear direction, and in general involves deformations non-coaxial with the stress. Experimental results on saturated sand specimens using a biaxial simple shear device suggest that loading involving changes of direction may introduce significant reduction in the liquefaction resistance of cohesionless soil. However, centrifuge test results indicate that biaxial shaking has only limited impact on the liquefaction potential of level sand deposits. From numerical analysis, using a fully coupled ground response procedure (SUMDES) incorporating a comprehensive constitutive model for sand, and a theoretical study on the basis of the theory of plasticity, it was found that the in situ k0 condition, and the fact that the mobilised shear stress under earthquake tends to decrease as the excess pore pressure builds up, abate the effect of multidirectional shearing on level ground response.

Comprehensive constitutive model for immiscible blends of Newtonian polymers

We present a comprehensive constitutive equation to describe the convection, retraction, breakup, and coalescence of single droplets and blends of immiscible Newtonian polymeric components. The model is tested by comparing its predictions to literature data that was collected under a variety of conditions. When the strain rate is below the critical value for breakup, the model shows good agreement with literature data for single-droplet deformation for a range of flow types from simple shear to planar extension. Droplet breakup is accounted for by a term chosen to match the time evolution of anisotropy predicted by the Tomotika theory for the capillary breakup of an elongated cylinder. In start-up of fast shearing flow, the comprehensive constitutive model predicts the transient shear and first normal stress difference qualitatively, but not quantitatively, possibly because of the ad hoc way in which the model combines droplet retraction with droplet breakup. More importantly, we find that the information provided in the anisotropy tensor is alone insufficient to describe the complex behaviors of retraction and breakup concurrently. Despite this deficiency, the comprehensive model predicts a steady-state droplet size for isolated droplets that is in agreement with theoretical predictions of the Taylor theory for the critical capillary number for breakup, and correctly predicts deviations from Doi–Ohta scaling of steady-state stresses with shear rate, due to the influence of the critical film thickness at which droplet coalescence occurs.

Influence of constitutive model parameters on the predicted migration of DNAPL in heterogeneous porous media

This study examines the influence of constitutive models and their parameters on predictions of the spatial and temporal distribution of a finite release of a dense, nonaqueous phase liquid (DNAPL) into a two‐dimensional, spatially correlated random permeability field. The base case simulation employed a comprehensive constitutive model that was validated against relevant one‐dimensional laboratory experiments. The base case was perturbed in the course of nine individual simulations, where each simulation examined the consequences of simplifying a single model characteristic. None of the nine subsequent simulations was able to reproduce, within ±10%, the spatial and temporal migration characteristics of the nonwetting fluid body at late time predicted by the base case. Capillary pressure‐saturation relationships that do not incorporate specific displacement and terminal pressures are demonstrated to severely overpredict the spatial extent of nonwetting fluid advancement. This suggests that van Genuchten‐based models may not be suitable for predicting DNAPL migration in saturated porous media. Not accounting for any one of hysteresis, nonwetting phase trapping, or the proper curvature or end‐point values of the nonwetting phase imbibition relative permeability curve profoundly influenced the time predicted for all nonwetting fluid movement to cease. The practical implication of this study is that an appropriate, comprehensive constitutive model, characterized with suitable parameter values, is necessary to accurately simulate a complete DNAPL release below the water table in both space and time.

Viscoelastic, Viscoplastic, and Damage Modeling of Asphalt Concrete in Unconfined Compression

A comprehensive constitutive model for asphalt concrete was calibrated that included viscoelasticity, viscoplasticity, and irreversible micro-structural damage in unconfined compression. Three different types of laboratory tests were designed and performed to calibrate each of these response components. Small-strain dynamic modulus tests were used to calibrate the undamaged linear viscoelastic properties. Cyclic creep and recovery tests to failure were performed to calibrate the viscoplastic properties. Constant-rate-of-strain tests to failure were used to calibrate the damage behavior. These tests were performed at a wide range of temperatures, loading rates, and stress levels. Upon calibration of each individual response, the model was validated by predicting the results of other constant-rate-of-strain tests at temperatures and strain rates different from those used in the calibrations. The predictions for these different conditions indicate that the comprehensive model can realistically simulate a wide range of asphalt concrete behavior.

Finite element analysis of fibrous composite structures: A plasticity approach

A finite element program which incorporates a new comprehensive constitutive model for in-plane loading of fibre-reinforced composite (FRC) laminates is presented. This material model combines the classical flow theory of plasticity with a failure criterion to formulate a complete plane stress constitutive relationship for orthotropic FRC laminates up to the ultimate stress condition. Numerical integration of the incremental elastoplastic constitutive equations is based on a tangent predictor-normal return algorithm. The resulting nonlinear equilibrium equations are solved using a full Newton-Raphson iterative scheme. The program is tested for symmetric laminated plates with a central hole and the results are compared against previously published experimental data. Progression of failure in the plane of each layer is also illustrated.

Bounding Surface Hypoplasticity Model for Sand

A comprehensive constitutive model for sand is formulated within the general framework of bounding surface hypoplasticity. The distinctive feature of this model is the dependence of the loading and plastic strain rate directions on the stress rate direction. This property renders the model hypoplastic. The model can simulate different features of sand behavior under loading conditions, which range from simple monbtonic to complex cyclic at different amplitudes and directions. In particular, the successful simulation of the response under “rotational shear” is one of the distinctive properties of the model, and it is mainly due to its hypoplastic character. The importance of such predictive capability in practice is related to the phenomenon of liquefaction, which may occur under such cyclic loading conditions of a complex nature, entailing cyclic changes of both principal stress values and principal stress directions. The paper presents a step‐by‐step calibration procedure of the different constants and a...

Fracture Energy‐Based Plasticity Formulation of Plain Concrete

A comprehensive constitutive model is developed for the triaxial behavior of plain concrete. The formulation covers the full load-response spectrum in tension as well as in compression. The concrete model is based on the nonassociated flow theory of plasticity with hardening in the prepeak regime and fracture energy-based softening in the post-peak regime. The constitutive development is guided by recent experimental observations on laboratory specimens which are loaded under “mixed” control in tension, and in triaxial compression at different levels of lateral confinements. The constitutive parameters are calibrated from a series of stroke-controlled laboratory experiments which include direct tension and triaxial compression tests at different confinements. The predictive quality of the fracture energy-based plasticity model is ascertained with a number of separate load-history experiments for which triaxial test data are available in the concrete literature. Pertinent remarks on the numerical implementation of the elastic-plastic constitutive relations with comments on relevant issues related to the uniqueness and stability of nonassociated strain-softening computations, are also presented.