Constitutive Model Parameters Research Articles

Metrics to evaluate constitutive model fitness based on DIC experiments

AbstractFull‐field optical experimental techniques such as Digital Image Correlation (DIC) enable measurement of information‐rich heterogeneous strain states. The aim of Material Testing 2.0 is to capitalise on this and design experimental setups for efficient material characterisation using inverse identification techniques such as the Virtual Fields Method (VFM). In that case, however, a priori knowledge of the constitutive model is required, which sometimes is not a trivial task. This limitation can be overcome by identifying multiple constitutive models using the same DIC strain fields and comparing their performance. In this work, we present a methodology to evaluate model performance and compare different constitutive models based on quantitative metrics. DIC experiments were performed on an S‐shaped high density polyethylene test sample under uniaxial load. The heterogeneous DIC strain fields were used in combination with the VFM to identify parameters of hyperelastic constitutive models with increasing complexity. Two deterministic metrics, the equilibrium gap indicator (EGI) and the reconstructed axial force ratio (RAFR), were defined and used to compare the performance of these constitutive models. The impact of spatial smoothing on DIC strain fields was studied by calculating the EGI and RAFR using a digital twin of the DIC experiments. EGI and RAFR metrics provide complementary information regarding the material behaviour, and both are necessary to make an informed choice. In this case study, hyperelastic constitutive models were found not to capture the material stiffness well in the small strain regime. A linear‐elastic contribution exponentially decaying with the equivalent shear stress was added to the hyperelastic models and the corresponding model parameters identified using the VFM. The elastic‐hyperelastic constitutive models were found to perform better than their purely hyperelastic counterparts.

Effects of C and Al Alloying on Constitutive Model Parameters and Hot Deformation Behavior of Medium-Mn Steels.

Single-pass isothermal hot compression tests on four medium-Mn steels with different C and Al contents were conducted using a Gleeble-3500 thermal simulation machine at varying deformation temperatures (900-1150 °C) and strain rates (0.01-5 s-1). Based on friction correction theory, the friction of the test stress-strain data was corrected. On this basis, the Arrhenius constitutive model of experimental steels considering Al content and strain compensation and hot processing maps of different experimental steels at a strain of 0.9 were established. Moreover, the effects of C and Al contents on constitutive model parameters and hot processing performance were analyzed. The results revealed that the increase in C content changed the trend of the thermal deformation activation energy Q with the true strain. The Q value of 2C7Mn3Al increased by about 50 KJ/mol compared with 7Mn3Al at a true strain greater than 0.4. In contrast, increasing the Al content from 0 to 1.14 wt.% decreased the activation energy of thermal deformation in the true strain range of 0.4-0.9. Continuing to increase to 3.30 wt.% increased the Q of 7Mn3Al over 7Mn by about 65 KJ/mol over the full strain range. In comparison, 7Mn1Al exhibited the best hot processing performance under the deformation temperature of 975-1125 °C and strain rate of 0.2-5 s-1. This is due to the addition of C element reduces the δ-ferrite volume fraction, which leads to the precipitation of κ-carbides and causes the formation of microcracks; an increase in Al content from 0 to 1.14 wt.% reduces the austenite stability and improves the hot workability, but a continued increase in the content up to 3.30 wt.% results in the emergence of δ-ferrite in the microstructure, which slows down the austenite DRX and not conducive to the hot processing performance.

A 3D peridynamic model for fracture analysis of transversely isotropic solids

The classical continuum mechanics (CCM) has limitations in simulating crack initiation and propagation, and the peridynamic (PD) theory overcomes these shortcomings. This study proposed a 3D transversely isotropic PD model based on the micro-beam bond model. Firstly, the micromoduli of the micro-beam bond applied to the transversely isotropic 3D solid model are derived based on the elastic matrix relationship between the different coordinate systems. Secondly, the strain energy density expressions of arbitrary material points are expressed in both the PD theory and the CCM theory using strain and elastic matrix under the assumption of homogenization, respectively. Finally, by equating the strain energy density expressions under the two theories based on the conservation of energy, the constitutive model parameters of the 3D transversely isotropic PD model are solved. Numerical examples of crack propagation demonstrate the effectiveness of the proposed model in addressing dynamic 3D fracture problems.

Brain Material Properties and Integration of Arachnoid Complex for Biofidelic Impact Response for Human Head Finite Element Model.

Finite element head models offer great potential to study brain-related injuries; however, at present may be limited by geometric and material property simplifications required for continuum-level human body models. Specifically, the mechanical properties of the brain tissues are often represented with simplified linear viscoelastic models, or the material properties have been optimized to specific impact cases. In addition, anatomical structures such as the arachnoid complex have been omitted or implemented in a simple lumped manner. Recent material test data for four brain regions at three strain rates in three modes of loading (tension, compression, and shear) was used to fit material parameters for a hyper-viscoelastic constitutive model. The material model was implemented in a contemporary detailed head finite element model. A detailed representation of the arachnoid trabeculae was implemented with mechanical properties based on experimental data. The enhanced head model was assessed by re-creating 11 ex vivo head impact scenarios and comparing the simulation results with experimental data. The hyper-viscoelastic model faithfully captured mechanical properties of the brain tissue in three modes of loading and multiple strain rates. The enhanced head model showed a high level of biofidelity in all re-created impacts in part due to the improved brain-skull interface associated with implementation of the arachnoid trabeculae. The enhanced head model provides an improved predictive capability with material properties based on tissue level data and is positioned to investigate head injury and tissue damage in the future.

Damage constitutive model of rock and application based on strength theory

Abstract Extending the one-dimensional damage constitutive model of rock materials to 3 dimensions using classical methods fails to capture the significant differences in tensile, compressive, and shear strengths exhibited by the rock materials. Consequently, it is necessary to revise the existing damage constitutive model to describe the damage evolution law and constitutive relationship of rock materials more accurately and provide a theoretical basis for the safety and stability analysis of underground engineering more scientifically, thus ensuring the sustainable development of underground engineering. By introducing the Weibull distribution function and building upon strength theory, a correction function was established. This correction function adjusted the equivalent strain, enabling the development of a 3-dimensional damage constitutive model that accounted for the varying tensile, compressive, and shear strengths of rock materials. The impact of various parameters on the model's fitting effectiveness was evaluated, and a comparative analysis was conducted against pertinent experimental results. Using the theory of neutral axis deviation, the relationship between bending moment and damage variables in a purely bending rock beam was derived. The study revealed that all parameters of the damage constitutive model could be derived from the uniaxial stress-strain curve, and its theoretical findings exhibited strong agreement with experimental results obtained from rock and rock-like materials under uniaxial tension, compression and triaxial compression. Based on the examined cases, it was concluded that, when considering both tensile and compressive damage, the ultimate bending moment of a rock beam was approximately one-third of its elastic limit bending moment in an undamaged state. The results have verified the feasibility of the damage constitutive model.

Investigation on effects of thermo-mechanical coupling on residual stress in lithium niobate in surface acoustic wave device

Surface acoustic wave (SAW) devices are subject to thermomechanical coupling during operation, and when the temperature rises sharply to 180 °C, the surface of the lithium niobate crystal substrate generates nonuniform thermal stresses, thus leaving large residual stresses after complete cooling, which seriously influences its service performance and life. In this study, the thermal residual stresses of lithium niobate wafers were tested by nanoindentation tests, and the nanoindentation test process was simulated. The inverse calculation of the parameters of the lithium niobate constitutive model was carried out by comparing the load-displacement curves obtained from the finite element calculations with the experimental results. A multiscale model of the SAW device was established, its operation process was simulated, and then the generation law of residual stress was further discussed. The nanoindentation test results show that the thermal residual stress is positively correlated with the heating time under the effect of the same temperature; however, at the heating temperature up to about 180 °C, the lithium niobate crystal enters the high-temperature hyperelastic interval, and the yield stress of the crystal increases significantly at this stage. The constitutive model curves obtained by finite element calculations are in good agreement with the experimental results, and the thermal residual stress value of lithium niobate can reach 2/3 of its yield stress outside the high-temperature hyperelastic interval by comparison tests. The calculation results of the multi-scale model of the SAW device indicate that excessive thermal stress is the main cause of damage during the thermo-mechanical coupling of the SAW device. The polarization direction of lithium niobate crystals may cause the development of damage cracks, increasing the heat dissipation can effectively reduce the thermal stress to which it is subjected, and better extend the service life of the SAW device.

Determination of Parameters of Soil Constitutive Models Based on Field Test Data

Determination of Parameters of Soil Constitutive Models Based on Field Test Data

Interface stress transfer model and modulus parameter equivalence method for composite materials embedded with tensile pre-strain shape memory alloy fibers.

The constitutive model and modulus parameter equivalence of shape memory alloy composites (SMAC) serve as the foundation for the structural dynamic modeling of composite materials, which has a direct impact on the dynamic characteristics and modeling accuracy of SMAC. This article proposes a homogenization method for SMA composites considering interfacial phases, models the interface stress transfer of three-phase cylinders physically, and derives the axial and shear stresses of SMA fiber phase, interfacial phase, and matrix phase mathematically. The homogenization method and stress expression were then used to determine the macroscopic effective modulus of SMAC as well as the stress characteristics of the fiber phase and interface phase of SMA. The findings demonstrate the significance of volume fraction and tensile pre-strain in stress transfer between the fiber phase and interface phase at high temperatures. The maximum axial stress in the fiber phase is 705.05 MPa when the SMA is fully austenitic and the pre-strain increases to 5%. At 10% volume fraction of SMA, the fiber phase's maximum axial stress can reach 1000 MPa. Ultimately, an experimental verification of the theoretical calculation method's accuracy for the effective modulus of SMAC lays the groundwork for the dynamic modeling of SMAC structures.

An automated system for determining soil parameters: Case study

The success of numerical analysis depends on several factors. One of the keys factors is the accurate determination of constitutive model parameters. Determining these parameters from in-situ tests has several advantages compared to laboratory tests, from lower costs to minimal disturbance of the soil. However, it is not possible to derive soil parameters directly from in-situ tests results, since correlations are required. The literature offers a wide range of correlations which increases the uncertainty during interpretation. The ongoing research project APD (Automated Parameter Determination) investigates the possibilities of automated parameter identification from in-situ tests using a graph-based approach. In the present paper, existing correlations – developed for cone penetration tests - are validated by comparing their output to laboratory results. The Norwegian GeoTest Sites (NGTS) infrastructure project consists of five tests sites in different soils in Norway. The data from the soft clay site located in Onsoy, south-eastern Norway was used in the validation process. A web-based application “Datamap” that has been developed to capture, organize, and classify geotechnical research data has been used to obtain in-situ and laboratory tests data. The further validation of existing correlations to derive accurate constitutive parameters from in-situ tests is part of ongoing research.

Parameter inversion method for target plate constitutive model based on BP neural network

In this paper, a neural network-based inversion method that can be used to streamline the acquisition of polymethyl methacrylate (PMMA) material constitutive model parameters for explosive cutting simulations is presented. This approach mitigates the need for multiple tests, a requirement of traditional methods. Initially, three categories of the damage, penetration depth, impact fracture thickness and spallation damage thickness, were distinguished and quantified by cutting the14 mm PMMA target plate with a 2.5 mm wide linear shaped charge, and the adjustment interval for the constitutive model parameters could be determined by combining the explosive cutting experiment data and the empirical parameters of the Johnson Holmquist Ceramics (JH-2) constitutive model. Subsequently, the numerical simulations of the cutting process of the performed target plate tests were carried out using LS-DYNA, and a dataset of target plate damage incorporating the three types of damage data was amassed. Ultimately, a neural network model correlating the parameters of the PMMA target plate constitutive model with the damage data was developed and trained using the plate damage dataset, and several supplementary experiments as well as finite element numerical simulations involving a 4.2 mm wide linear shaped charge cutting a 19 mm PMMA target plate were conducted. The numerical results displayed minimal variance from the experimental results in terms of fracture characteristics and damage data, suggesting that the inverted JH-2 constitutive model parameters can be effectively applied to PMMA target plate explosive cutting simulations. The parameter inversion method allows for the acquisition of more accurate material constitutive model parameters with fewer experiments and will be beneficial for further theoretical studies and practical applications of target plates in the future.

Numerical sensitivity analysis for stress-strain simulation and flow liquefaction assessment of tailings storage facilities using the NorSand constitutive model

With the advent of critical state Soil Mechanics (CSSM), the void ratio began to be recognized as a key parameter, along with the stress state, which defines the mechanical behavior of soils and other particulate geomaterials by using the state parameter. The state parameter is the difference between the current and critical void ratio so that its definition requires the critical state line (CSL) identification. This work presents numerical calibration results, using the NorSand constitutive model, from three sets of triaxial compression tests selected from the literature. The SIGMA/W module of the Geostudio® System was adopted to perform the simulations of the triaxial compression tests, and the results showed adequate fit between real tests and numerical simulations. The parameters necessary for the modeling with NorSand model, defined from the numerical calibration, were used in a stress-strain evaluation of a hypothetical upstream tailings dam. These simulations allowed the evaluation of the differences in the tailings storage facility (TSF) responses in terms of both deformation behavior and flow liquefaction instability. Flow liquefaction instability is described in the literature as a complete loss in shear strength and the development of excessive strains due to the contractive response of tailings when subjected to low confining stress. The results suggest that the use of the NorSand model is, in general, a good option to reproduce the typical strain-softening behavior of such structures. Furthermore, it was clear the high sensitivity of the constitutive model parameters, drawing attention to the importance of best laboratory practices for carrying out triaxial tests to obtain reliable parameters for NorSand modeling.

High-temperature sealing performance and structure optimization of rubber core for conical blowout preventer

Conical blowout preventer is a vital sealing component in the process of petroleum and gas development, if it were to malfunction, which will result in extremely severe consequences. In order to investigate sealing performance of conical blowout preventer at high temperature and reduce failure rate of rubber core. Firstly, high-temperature tensile and compression experiments for the rubber were conducted, then the constitutive model parameters for rubber core material was confirmed. A numerical model for wellhead sealing of conical blowout preventer was established. Stress distribution and sealing performance of rubber core at different temperatures were investigated. Finally, structural optimization was performed of rubber core, support rib and piston. The results show that the lower end of rubber core is the primary sealing area. Stress concentration on rubber core and significant deformations are the primary reasons for the cracking and detachment of rubber core. As the temperature increases, sealing performance of rubber core gradually decreases. After optimizing structures of rubber core, support ribs and piston, sealing performance of rubber core has been improved. Those results hold significant importance in improving sealing performance of conical blowout preventer and ensuring the safety of operational processes, providing theoretical guidance for the optimization of blowout preventer structures.

Study on the propagation and attenuation characteristics of tunnel blasting vibration waves at different blast center distances

Accurately determining the parameters of the dynamic constitutive model is significant to analyzing the dynamic response characteristics of the surrounding rock at the proximal and distal ends of a railroad tunnel blasting. Hence, this paper analyzes the propagation and attenuation of blasting vibration waves in the rock by utilizing the vibration velocity monitoring data of the Xinbin Tunnel at the Liaoning section of the Shenbai High-speed Railway. The data are provided by the drilling and blasting method. Additionally, the IA-BP inverse analysis method was established to invert the parameters of the JH-2 constitutive model of the rock by numerically analyzing the simulated blasting vibration waves using the inversion parameters. The results highlight that the inversion value obtained by the IA-BP algorithm is slightly different from the calculated test value but still highly accurate, demonstrating the rationality of the inverse analysis method. Meanwhile, the numerical simulation results supplement the proximal vibration velocity, which is difficult to monitor in the project. This is because the vibration velocity of the tunnel surrounding the rock has a noticeable directional effect. Specifically, the vibration velocity law varies as the blast center distance increases, where the peak vibration velocity direction at the far end of the blast changes from the Y direction (vertical direction) to the Z direction (blast direction). The linear attenuation formula of the vibration velocity in the three principles of the tunnel arch, arch shoulder, and arch foot is obtained by fitting, which is an adequate prediction of the safety of the subsequent construction.

Modification of Johnson–Cook Constitutive Parameters in Ball Burnish Simulation of 7075-T651 Aluminum Alloy

The Johnson–Cook model is widely used because of its ability to meet the simulation material requirements in various situations. However, under different working conditions, the accuracy of the model may have errors. In this work, based on Abaqus (Abaqus R2022 Education Edition, Dassault Systèmes, Paris, France) simulation software, Johnson–Cook (JC) constitutive model parameters and compression parameters were selected to simulate the improvement of surface roughness during the ball milling of a 7075-T651 aluminum alloy. In the numerical simulation of ball polishing, the changes in the residual stress field when the Johnson–Cook parameters change are analyzed. By comparing the numerically simulated residual stress fields under the JC parameters calculated at different strain rates, a set of parameters that agrees with the experimental values is selected. The results show that the residual stresses are in line with the experimental values when the strain rate is 10−4s −1. The changes in roughness corresponding to the selected parameters are analyzed. The results indicate that the simulated trend of roughness variation is consistent with the experimental values, and the optimal surface roughness value under a static pressure of 300 N is obtained.

Calibration of constitutive models using genetic algorithms

Constitutive models, describing material response to load, are an essential part of computational materials engineering. Semi-empirical constitutive laws including the Johnson–Cook and Zerilli–Armstrong models are widely used in finite element simulation for easy computability and rapid run time. The reliability of these models depends on accurate and reproducible fitting of parameters. This work presents a genetic algorithm (GA) based tool to fit parameters in constitutive models. The GA approach is capable of finding the global optimum parameter set in a robust, repeatable, and computationally efficient manner. It has been demonstrated that the obtained fits are better than those using traditional term-wise optimisation. Allowed to fit freely, the GA method will be likely to produce non-physical parameter values. However, by constraining the fit, the GA method can produce parameters that are physically reasonable and minimise the error when extrapolating to unseen data. Finally, the GA method may be used to choose between a variety of possible constitutive models based on a transparent best fit approach. The model has been demonstrated by using datasets from the literature for DH–36 steel and Ti-6Al-4V. This includes data from different studies, in which there are both random and systematic variations. The framework developed here is made freely available and modifiable, and may be extended to include other constitutive models as required.

A One-Dimensional Dynamic Constitutive Modeling of Ethylene Vinyl Acetate (EVA) Foam.

Ethylene vinyl acetate copolymer (EVA) is good for impact protection and energy absorption, and belongs to rate sensitive-dependent materials. This study aimed to investigate the influence of increased strain rate and the presence of entrapped air on the enhancement of foam material strength. The compression deformation behavior of EVA foams containing a microporous structure was extensively investigated over different strain rates of 0.0017/s, 0.033/s, and 0.17/s, where each test was conducted at a constant compression velocity. A one-dimensional dynamic constitutive model was established to describe the large deformation response of EVA to different strain rates. The model included two components, the material action part and the air pressure part. Quasi-static and dynamic compression tests were used to determine the constitutive relations of three parameters, a1, a2, and the leaking rate δ·. The samples with EVA foams at different strain rates were fitted using ORIGIN software, and the constitutive model parameters were obtained. It was found that the ratio of the air leaking rate to the strain rate gradually decreases, causing air within the EVA to be trapped in the cells rather than escaping in a timely manner with increasing strain rates.

Room-to-low temperature thermo-mechanical behavior and corresponding constitutive model of liquid oxygen compatible epoxy composites

The room-to-low temperature (RT-LT) mechanical behavior of liquid oxygen-compatible epoxy composites (LOC-EP) is of great importance in the strength analysis of lightweight liquid oxygen tanks. This article first explores the tensile-compressive mechanical behaviors of LOC-EP from RT down to −183 °C. The results show that compared with RT, the tensile strength, compressive strength, and elastic modulus at −183 °C increase by 44%, 109%, and 160% respectively. Secondly, based on the theories of molecular chain freezing degree and yield surface extension, a ductile-brittle transition T of −60 °C and a completely brittle T of −90 °C are obtained sequentially. Moreover, a universal thermal-mechanical constitutive model for EP is derived, and the constitutive model parameters of LOC-EP from RT to −183 °C are fitted and calibrated using Matlab. Finally, the proposed constitutive model is introduced into Abaqus through a user subroutine. On the one hand, three-dimensional one-element analyses demonstrate that the simulation curves are highly consistent with the experimental and Matlab-fitted curves (errors less than 3%) with good convergence/accuracy. On the other hand, the fracture modes obtained from macroscopic simulations of tensile and compressive specimens are also coherent with the experimental fracture modes.

High-fidelity computational micromechanics of composite materials using image-based periodic representative volume element

This study presents numerical investigations into the progressive damages in unidirectional carbon fiber reinforced plastics (CFRP) using computational micromechanics with an image-based periodic representative volume element (RVE). This RVE modeling approach combines the methodologies of image-based RVE and artificial periodic RVE to reflect the actual fiber packing while retaining geometrical periodicity. For high-fidelity modeling, the RVE model is prepared with more than 200 carbon fibers extracted from X-ray computed tomography images. Both homogenization simulation for elastic properties and unidirectional loading simulations for plastic and fracture properties are carried out. The constitutive model parameters are identified and verified by comparing the experimental and predicted effective (spatially averaged) elastic and plastic properties, and ultimate strength. Then, with the identified parameters, the local damage initiation and propagation mechanism, and their influence on the macroscopic nonlinear stress–strain behaviors are discussed. Finally, the influences of fiber packing on the predicted accuracy of computational micromechanics are discussed by comparing the results between the proposed image-based RVE and simple RVEs with the square and hexagonal arrays.

Nonlinear finite element analysis of partially encased composite columns under non-uniform moments

This paper presents a numerical investigation to evaluate the behavior of partially encased composite (PEC) columns with compact sections of three different heights submitted to non-uniform moment distribution. A 3D finite element model developed using the software ABAQUS was calibrated based on results from previous experimental research. The influence of concrete constitutive model parameters, column slenderness, load eccentricities, and moment distribution along height was investigated. The parametric study showed that constant moment distribution (case 1) is the most critical compared to linear moment variation (cases 2 and 3). This pattern is a direct consequence of the larger displacements at the mid-height section that causes higher second-order moments in the case 1 column. Long columns activated more confinement when a single curvature bending moment was applied at a minor axis. An increase in slenderness decreased the load capacity for non-uniform bending moments through the major axis.

Parameter determination and verification of ZWT viscoelastic dynamic constitutive model of Al/Ep/W material considering strain rate effect

As a new type of energetic structural material, Al/Ep/W(Aluminum/epoxy/tungsten), whether as a fragment or projectile material, should comprehensively consider the impact energy release and structural strength, especially the structural strength is the premise to ensure the material integrity. The dynamic constitutive model of materials is the theoretical basis for describing the strength and dynamic behavior of materials. Therefore, it is great significance to determine the dynamic constitutive model parameters of Al/Ep/W materials considering strain rate effect, and to verify the reliability of the model. In this paper, Al/Ep/W material is prepared, and the stress/strain relationship curve of the material under high strain rate is obtained through Split Hopkinson Pressure Bar (SHPB) test. The ZWT viscoelastic constitutive model is selected based on the composition of the material and the distribution of the internal components, and the simplified ZWT constitutive model with damage under constant strain rate is derived, and the parameters of the constitutive model are fitted by the least square method. By using Kirchhoff stress and Green strain tensor theory, the incremental form of the constitutive model is derived, and the Abaqus user material subroutine is written and embedded in the finite element software. The accuracy of material VUMAT subroutine is verified by comparing the results of SHPB test and numerical simulation under high strain rate. Combined with the verified material model subroutine, the experiment and numerical simulation of Al/Ep/W cylindrical projectile impacting aluminum plate are conducted. The results show that the experimental and numerical simulation results are in good agreement. The proposed model can be used to evaluate the dynamic response characteristics of the new energetic material projectile to the lightweight aluminum armor protective structure.