Phenomenological Constitutive Model Research Articles

Numerical simulation of microstructural failure of natural fibre–hydrogel composites

In this article, we conduct a numerical simulation to investigate the failure mechanism of natural fibre–hydrogel composites under tensile deformation and swelling. Firstly, a physical-based constitutive model is chosen to describe the deformation of the hydrogel matrix. Concurrently, a macroscopic phenomenological hyperelastic constitutive model, incorporated into the material database of Abaqus, is employed to describe the mechanical responses of natural fibres. Then, we implement the model for a numerical analysis. The material parameters of the model for the hydrogel matrix and fibres are determined by a trial-and-error method from the experimental curves of pure hydrogel and fibres; the numerically simulated stress–strain curve of the composites is compared with the experimental one to verify the effectiveness of the simulation. Subsequently, several numerical analyses are performed to discuss the failure mechanism of hydrogel composites caused by the microstructural features of fibres. The findings revealed that fibre protrusion, fibre orientation deviation, and interface strength significantly affect the local failure of the composites during tensile deformation and swelling; the composites’ strength and toughness mainly depend on the cooperation of various microstructural features. These results provide valuable insights into the design of fibre–hydrogel composites.

A new effective phenomenological constitutive model for semi‐crystalline and amorphous polymers

A new effective phenomenological constitutive model for semi‐crystalline and amorphous polymers

Stress localization investigation of additively manufactured GRCop-42 thin-wall structure

A full-field crystal plasticity (CP) framework is presented for the GRCop-42 alloy to study microscopic mechanical behavior and local stress heterogeneities. The microstructures of additively manufactured (AM) materials are often unique relative to conventionally processed materials, and the local thermal histories drive these differences during the build process. These thermal histories depend on the process parameters (laser power, scan speed, and scan strategy) and the part geometry. Prior research has shown that the mechanical properties of thin-walled structures can vary significantly with wall thickness due to changes in the thermal boundary conditions during manufacturing. It is, therefore, desirable to perform CP simulations based on the phenomenological constitutive model to predict the local mechanical responses induced by microstructural heterogeneities. This work generates representative microstructures based on experimentally collected grain information (i.e., texture) for grain scale stress analysis, and the material constitutive parameters are calibrated using the experimental mechanical testing data. We specifically investigated the effect of crystallographic texture and grain morphologies on the size-dependent mechanical properties of AM GRCop-42. The selection of appropriate material properties for implementing an effective free surface boundary condition and the influence of adjacent buffer layers are also discussed. Analysis of local field results reveals a strong correlation between stress localization and the initial grain orientation. However, no significant relationship between the misorientation of the individual adjacent grains and the average misorientation is observed.

A Modular Nitinol Model with Lode Angle-Based Asymmetry and Improved Representation of the Superelastic Loops for Medical Device Applications

Abstract We describe a phenomenological constitutive model for representing Nitinol in medical device applications. The intent is to capture some of the response features important to medical device applications that are neglected in prevalent state of the art models. These features include better representation of the response under compression which is needed to assess bending, and asymmetric plastic yield. We will refer to this implementation as the Thornton Tomasetti (TT) model to distinguish it from other existing implementations that have evolved from the baseline underlying theory. We implement the model in a modular form suitable for use in commercial finite element software and describe initialization from laboratory test data.

Microstructure generation and full-field multi-scale analyses for short fiber reinforced thermoplastics: Application to PA66GF composites

Short Fiber Reinforced Thermoplastics (SFRTs) like PA66GF composites are highly heterogeneous materials with a rather complex microstructure such that the characterization and the prediction of their mechanical behavior remain quite challenging. So far, most of the research efforts have employed phenomenological and mean-field multi-scale models to deal with SFRTs. The present contribution rather focuses on a full-field multi-scale approach that incorporates advanced techniques in terms of microstructural representation and material modeling, allowing a deep insight of the dominating deformation mechanisms occurring in PA66GF composites. The proposed approach is based on an automatic periodic mesh generation algorithm for matrix-inclusion Representative Volume Elements (RVE) with randomly positioned fibers that follow a given Orientation Distribution Function (ODF). At the microscopic scale, while the fibers are assumed to be elastic, the behavior of the thermoplastic matrix is described by a phenomenological multi-mechanism constitutive model accounting for viscoelasticity, viscoplasticity and ductile damage. It results an advanced multi-scale model that enables to visualize the local deformation and degradation mechanisms occurring at the microscopic scale while simultaneously analyzing their influence on the macroscopic response of the composite upon monotonic, persistent and cyclic loading. The potential of the proposed approach is further evaluated by comparing the predicted responses against experimental data.

Temperature and Strain Rate Related Deformation Behavior of UHMWPE Fiber-Reinforced Composites.

As they possess the qualities of high specific strength, high specific modulus, high specific energy absorption, and excellent designability, ultra-high molecular weight polyethylene (UHMWPE) fiber-reinforced composites have gradually replaced traditional materials such as ceramics and steel plates as the main ballistic protection materials. Using an improved test method, the uniaxial tensile tests of UHMWPE fiber-reinforced composites at two strain rates of 10-4 s-1 and 10-2 s-1 and a temperature range from -20 °C to 80 °C are carried out to study the effects of strain rate and temperature on the tensile behavior of UHMWPE fiber-reinforced composites. The experimental results indicate that the tensile responses exhibit nonlinear characteristics and the sensitivity of strain rate and temperature. The yield strength and modulus decrease with increasing temperature and increase with the increase in strain rate. A phenomenological viscoelastic constitutive model composed of a nonlinear spring and a nonlinear Maxwell element is proposed to characterize the temperature and strain rate dependent deformation behavior of UHMWPE fiber-reinforced composites before yielding. The results show that the model can accurately predict the tensile nonlinear viscoelastic responses of UHMWPE fiber-reinforced composites before yielding over a wide temperature range under quasi-static loading.

Asymmetric and anisotropic quench sensitivity of ZA81M magnesium alloy

The quench sensitivity of the ZA81M magnesium alloy is studied by combining experiment and crystal plasticity finite element simulation. The quench sensitivity is high in tension and low in compression making the single-valued quench sensitivity calculated from hardness insufficient. So, there is different loss rate of strength, along different test directions of the alloy, due to slow quenching, i.e., the quench sensitivity is asymmetric and anisotropic. The coarsening of the precipitate and widening of the precipitate-free zone are the origin of the quench sensitivity. Crystal plasticity finite element simulation is proposed to calculate the quench sensitivity. The phenomenological constitutive model is used to explicitly consider the strengthening effect of precipitates on different slip and twinning systems. So, the precipitate characteristics of the water-quenched and air-cooled alloy are easily captured. The anisotropy and asymmetry of the quench sensitivity in two perpendicular sample planes are determined by simulation. Such a method can be useful for determining the quench sensitivity of precipitation-hardening alloys with low crystal symmetry and with precipitates having different strengthening efficiencies on different slip or twinning systems.

Topology optimization structure design of shape memory alloy with multiple constraints

As an emerging functional material, shape memory alloy (SMA) exhibits remarkable mechanical properties and finds diverse applications across industries. This paper presents a topology optimization framework based on the bi-directional evolutionary structural optimization (BESO) method for designing SMA structures, which maximizes structural stiffness under multiple constraints of specified volume fraction, displacement, and fundamental frequency. A phenomenological constitutive model is utilized to simulate the mechanical behavior of SMA accurately. The unit virtual load method is employed to determine sensitivities. Several optimized SMA beam structures and simply-supported cube structures are designed under different thermal-mechanical loads, and their displacement, mean compliance, and fundamental frequency are evaluated throughout the optimization process. The results demonstrate that the proposed framework successfully customizes the SMA topology structure with adjustable displacement and fundamental frequency, and the optimized schemes exhibit more considerable deformation and more uniform mechanical properties than their initial counterparts. The proposed framework has higher computational efficiency than the traditional SIMP-based SMA topology optimization design method.

Virtual laboratory enabled constitutive modelling of dual phase steels

Accurate and efficient characterization and modelling of deformation responses are critically essential in the development of advanced metal forming processes. This work presents a virtual laboratory enabled constitutive framework for modelling complex deformation responses of dual phase (DP) steels under complex stress states, based on multi-phase full-field crystal plasticity (CP) and advanced phenomenological modelling. In the CP based virtual testing method, kinematic hardening and degradation of elastic modulus are modelled in particular to improve the capability for describing evolving microstructure induced mechanical responses of DP steels. The workflow of this framework is completely built and numerically implemented, including (i) representative volume element (RVE) generation based on microstructure characterization, (ii) identification of multiphase CP model parameters, (iii) prediction of elastic modulus degradation, (iv) prediction of yield stresses and plastic potentials in uniaxial tension and biaxial tension with various stress ratios, and (v) prediction of stress–strain curves in reverse tension compression. Using DP780 and DP980 as case materials, the corresponding physical experiments are conducted to verify the accuracy of the virtual tests, showing a good agreement between the virtual and experimental approaches. Both experimental and virtual tests are used to calibrate advanced phenomenological constitutive models that include non-linear elasticity, anisotropic yielding, and kinematic hardening. The calibrated models are implemented into the finite element (FE) codes to predict complex deformation and springback behaviours of DP780 and DP980 sheets in U-bending processes. In comparison with forming experiments of U-channel parts, the virtually calibrated models are validated and show good performance in predicting deformation and springback behaviours, providing a high capability for process analysis. The findings support that the virtual laboratory enabled modelling approach could be a substitute for extensive, expensive, and hard-to-access physically mechanical experiments required in the model calibration for a more effective and efficient analysis of metal forming processes.

Crystal plasticity approach for predicting mechanical responses in wire-arc directed energy deposition of NbZr1 refractory alloy

The refractory alloy, such as Niobium-1 wt% Zirconium (NbZr1) alloy, is a promising candidate for diverse applications in extreme environments. This study investigates an integrated experimental and computational methodology that can predict the mechanical properties of wire-arc directed energy deposited (DED) refractory NbZr1 alloy. The effect of large columnar grains with strong texture induced by the wire-DED process has been successfully incorporated into the representative volume element (RVE). Performing crystal plasticity (CP) simulation on RVE of NbZr1, deformation behavior and stress-strain relationship are predicted to explore the process-structure-property (PSP) relationship. The RVE has been created in synthetic microstructure generation software utilizing the grain statistics derived from electron backscatter diffraction (EBSD) analysis, capturing essential microstructural features. A phenomenological constitutive model and appropriate boundary conditions have been applied and solved, using the CP fast Fourier transform method. The CP model has been calibrated and validated utilizing the tensile test data along the build direction and deposition direction, respectively. The error in predicting yield strength and ultimate tensile strength is 0.91% and 0.67%, respectively, for the calibration simulation, whereas these values are 2.51% and 1.81% for the validation simulation. The results suggest strong agreement between the simulation and experimental observation. Even though global deformation behavior remains consistent across multiple RVEs with the same microstructural features, local stress-strain values vary, indicating structural anisotropy, which is also consistent with the digital image correlation (DIC) result. It is proven that this proposed CP method can effectively predict the mechanical responses of components with large grains and strong textures resulting from the wire-arc DED.

Investigation and Validation of a Shape Memory Alloy Material Model Using Interactive Fibre Rubber Composites.

The growing demand for intelligent systems with improved human-machine interactions has created an opportunity to develop adaptive bending structures. Interactive fibre rubber composites (IFRCs) are created using smart materials as actuators to obtain any desired application using fibre-reinforced elastomer. Shape memory alloys (SMAs) play a prominent role in the smart material family and are being used for various applications. Their diverse applications are intended for commercial and research purposes, and the need to model and analyse these application-based structures to achieve their maximum potential is of utmost importance. Many material models have been developed to characterise the behaviour of SMAs. However, there are very few commercially developed finite element models that can predict their behaviour. One such model is the Souza and Auricchio (SA) SMA material model incorporated in ANSYS, with the ability to solve for both shape memory effect (SME) and superelasticity (SE) but with a limitation of considering pre-stretch for irregularly shaped geometries. In order to address this gap, Woodworth and Kaliske (WK) developed a phenomenological constitutive SMA material model, offering the flexibility to apply pre-stretches for SMA wires with irregular profiles. This study investigates the WK SMA material model, utilizing deformations observed in IFRC structures as a reference and validating them against simulated models using the SA SMA material model. This validation process is crucial in ensuring the reliability and accuracy of the WK model, thus enhancing confidence in its application for predictive analysis in SMA-based systems.

Experimental and Modelling of Shape Memory Effect of Shape Memory Natural Rubber

Shape memory natural rubber (SMNR) is a form of smart material that can memorise its permanent shape in response to temperature. In this article, a phenomenological constitutive model was adopted to predict the stress-strain evolution during the shape memory process of SMNR to understand the behavior of SMNR. A standard linear solid (SLS) model with Kelvin Voigt element was extended with two Mooney Rivlin models to account for the mechanical response, while a thermal strain model represented the change of length during the programming process and recovery process. An external temperature law was constructed to govern the volume fraction change between the soft active and frozen phase. The proposed constitutive model is capable of capturing the stress-strain behaviour of each shape memory step.

Thermal deformation behavior investigation of Ti–10V–5Al-2.5fe-0.1B titanium alloy based on phenomenological constitutive models and a machine learning method

The two-phase titanium alloy Ti–10 V–5Al-2.5Fe-0.1 B was taken as the experimental material, and thermal compression experiments were carried out at a deformation temperature of 770–920 °C and a strain rate of 0.0005–0.5 s−1. An Arrhenius model, a modified Johnson-Cook model, and an improved BP neural network model based on the sparrow search algorithm (SSA-BP) model were established to predict the high temperature rheological stress of the alloy. A comparison of the prediction accuracy of the three models was made. When the partial random data in the rheological curves was used for model building and relatively independent data were used for predicting the rheological stress, the SSA-BP model had higher prediction accuracy, which exhibits the highest mean square correlation coefficient (R2) value of 0.9992 and the lowest root mean square error (RMSE) and average absolute relative error (AARE) values of 1.3031, and 2.0947 %, respectively. The ability of three models to predict the rheological stress for the new process parameters was verified. Results show that the SSA-BP model still has better prediction ability, which exhibits the highest mean square correlation coefficient (R2) value of 0.9720 and the lowest root mean square error (RMSE) and average absolute relative error (AARE) values of 5.0099, and 6.0382 %, respectively. The predicted values of SSA-BP for the rheological stress were used to construct the hot processing map. Results show that the trend of the power dissipation factor (η) value from the hot processing map predicted by SSA-BP can well agree with the microstructure evolution of the alloy.

Time–temperature correlations of amorphous thermoplastics at large strains based on molecular dynamics simulations

In this paper, we investigate the time–temperature correlation of amorphous thermoplastics at large strains based on coarse-grained molecular dynamics simulations. This correlation behavior is characterized by the strain hardening modulus in uniaxial tension simulations at different strain rates across the glass transition region. The temperature regime is divided into a melt zone, a glassy zone, and a transition zone between them, according to the storage modulus calculated from dynamic mechanical analysis (DMA) at small strains. In the melt zone, the existence of time–temperature superposition (TTS) at large strains is verified by constructing a master curve of the hardening modulus. The obtained shift factors are then compared to those from DMA at small strains, showing that the TTS behavior is transferable between small and large strains. In the glassy zone, the effects of time and temperature are not superposable at large strains but still can be correlated. To demonstrate this correlation behavior, we introduce a level set of the hardening modulus with a variable pair of strain rate and temperature. Pairs lying in the same level result in coincident stress–strain curves at large strains. The transferability of the correlation behavior between large and small strains is validated by comparing these stress–strain curves at small strains in the pre-yield region. In the transition zone, the correlation behavior is studied with both aforementioned methods, showing that TTS is applicable to large strains but not transferable to small strains. Finally, we propose a phenomenological constitutive model for uniaxial tension to demonstrate the time–temperature correlation at large strains, considering different constant strain rates and temperatures.

A phenomenological constitutive model of Novel Rheo Gravity Die Cast Al-15Mg2Si-4.5Si-0.01Sr-0.015B composite

The present study discusses the high temperature deformation behaviour as well as phenomenological constitutive model development of the novel Rheo gravity die cast (RGDC) Al-15Mg2Si-4.5Si-0.01 Sr-0.015B composite. Within the scope of the study, uniaxial isothermal compression tests are performed on the RGDC Al-15Mg2Si-4.5Si-0.01 Sr-0.015B composite, covering a range of strain rates from 10−3 to 10 s−1 and deformation temperatures spanning from 250 °C to 450 °C. Analysis using X-ray Diffraction (XRD), Energy dispersive spectroscopy (EDS) and Electron Probe Micro Analyzer (EPMA) revealed the presence of distinct phases within the material, including primary Al, Mg2Si, and elemental Si. The study employed three different constitutive models i.e., the Johnson-Cook (JC), modified Johnson-Cook (mJC), and sine hyperbolic Arrhenius (shA) types, to predict the flow stress of the material as a function of strain, strain rate, and deformation temperature. The results indicated that the sine hyperbolic Arrhenius type model and the modified Johnson Cook model effectively accounted the coupling effect of strain, strain rate, and deformation temperature, which affect the flow stress. Statistical analysis, specifically Pearson coefficient correlation (R), average absolute relative error (AARE) and standard deviations, established a reasonable agreement between the predicted flow stress values and the experimental flow stress data. Furthermore, it is observed that the sine hyperbolic Arrhenius type model exhibited superior accuracy compared to the modified Johnson Cook model, particularly at higher strain levels.

A high-efficiency material deployment design method assisted with multiscale analysis

Efficient deployment of the right materials at the right place is a nontrivial problem. Structural components can achieve superior mechanical properties through tunable material deployment. However, such a structure-property-performance relationship is not explicit and requires the trial-and-error procedure. Discovering this relationship is extremely challenging due to a large number of possible material microstructures and deployed position combinations, and the search for the optimal design is computationally expensive. In this study, a data-driven approach is proposed to efficiently discover the underlying relationship between the deployment of a specific material microstructure and the final structural performance. The uniaxial tension of a perforated composite plate was used as a demonstrator. A high-fidelity representative volume element of a unidirectional fiber reinforced composite was constructed and utilized to calibrate the phenomenological constitutive model. A data compression algorithm was applied to the structure geometry in a finite element simulation to mechanically group similar regions and reduce dimensionality. After optimization, the calculated scenarios were selected based on the target performance. High-efficiency multiscale analysis was subsequently conducted on the selected conceptual designs to reveal the micro-deformation mechanism and interpret the interaction between the fibers and the matrix.

A dislocation density-based meshfree computational framework for solid phase processing

This work proposes a computational modeling framework capable of predicting the behavior of materials when subject to solid phase processing (SPP). A macroscopic dislocation density based constitutive model with internal state variables correlated to microscopic dislocation densities is incorporated into a meshfree smoothed particle hydrodynamics (SPH) framework able to handle large deformations and high temperatures typical of what a material undergoes during SPP. Unlike phenomenological constitutive models that typically neglect material microstructural contributions to macroscale response, the dislocation density based constitutive model improves significantly the predictivity of our modeling framework in a wider range of conditions and allows the multiscale material responses to be simulated simultaneously. With dislocation density based model parameters calibrated to AA1100-O aluminum test data, the generality of the proposed framework is tested on two SPP techniques, namely friction extrusion (FE) and friction stir processing (FSP). Simulation results with different process parameters are systematically validated by experimental data for both cases. The validated models are then used to elucidate the inherent physics associated with SPP by revealing the distributions of temperature, strain, strain rate, and dislocation density, stick-slip contact conditions, and heat generation rates. Model-predicted high dislocation density regions in the processed AA1100-O also agree well with the dynamically recrystallized grain refinement zones observed from experiments.

Constitutive modeling and simulation of polyethylene foam under quasi-static and impact loading

In this paper, quasi-static and dynamic compression experiments were carried out on polyethylene foam by a universal material testing machine and a drop tower impact device. The mechanical response characteristics and energy absorption capacity of polyethylene foam under quasi-static and moderate strain rate (4 × 10−3–102s−1) loading conditions were obtained. An improved constitutive model of strain-rate term coupling strain and strain rate was established based on the Sherwood–Frost phenomenological constitutive model and Johnson–Cook constitutive model. Low Density Foam model combined in the finite element software ABAQUS with the improved constitutive model was used as the parameter definition of polyethylene foam material in the simulation. The drop-tower impact tests at different heights were simulated, and the simulation results were compared with the actual drop tower impact test results. The results showed that the peak acceleration errors between simulation and experiment were less than 7.1%, verifying the accuracy of the constitutive model. This study provides a method of constitutive models and finite element simulation to the performance of polymer foams.

Continuum Mechanics Models for Describing the Creep and Physical Aging Behaviors of Laminated Composites

Two types of carbon fiber-reinforced epoxy composite laminates are chosen for long-term tensile creep tests under different temperatures and load levels. Their time-dependent and non-monotonic deformations indicate clearly both temperature effect and physical aging effect. To characterize these viscoelastic behavior, two phenomenological constitutive models and one physical model are developed. The linear viscoelastic model based on the Boltzmann superposition principle is able to describe reasonably the deformations at relatively lower stress levels and temperatures. The nonlinear viscoelastic model of Schapery’s single-integral form, together with a usage of effective time theory, could describe nicely all the effects of temperature, stress, and physical aging. The physical model based on Ngai’s coupling mechanism concept is further combined with the framework of Schapery’s nonlinear viscoelastic theory, which may provide certain physical understanding about the effect of aging behavior on long-term creep deformation of the laminated composites. Numerical modelling by finite element method are implemented, and comparisons between the experimental and simulation results are demonstrated.

One-Dimensional Shape Memory Alloys Material Phenomenological Constitutive Model Based on Stress Due to Mechanical and Chemical Energy Change

One-Dimensional Shape Memory Alloys Material Phenomenological Constitutive Model Based on Stress Due to Mechanical and Chemical Energy Change