Constitutive Model Parameters Research Articles

Predictive abilities of constitutive models for clay under monotonic and cyclic loading: element tests and centrifuge experiments

A critical investigation of three constitutive models for clay by means of analyses of a sophisticated laboratory testing program and of centrifuge tests on monopiles in clay subjected to (cyclic) lateral loading is presented. Constitutive models of varying complexity, namely the basic Modified Cam Clay model, the hypoplastic model with Intergranular Strain (known as Clay hypoplasticity model) and the more recently proposed anisotropic visco-ISA model, are considered. From the simulations of the centrifuge tests with monotonic loading it is concluded that all three constitutive models give satisfactory results if a proper calibration of constitutive model parameters and proper initialisation of state variables is ensured. In the case of cyclic loading, the AVISA model is found to perform superior to the hypoplastic model with Intergranular Strain.

Uncertainty quantification and global sensitivity analysis of bearing capacity of push-out specimen considering randomness in bond-slip behaviour

As an artificial composite material, the uncertainty in mechanical property of concrete significantly impacts the bond-slip behaviour of the shaped steel concrete structure. To investigate the effect of the uncertainty of concrete mechanical properties on the bearing capacity of push-out specimens, based on the data of a small number of push-out test with identical design parameters, the improved Bootstrap method is utilized to execute sample augmentation for the bond stress-slip curves, and the stochastic bond slip constitutive model is established after considering five parameters (K1, …, K5) in the deterministic bond-slip model as random variables. Simultaneously, considering the randomness in elastic modulus of concrete (Ec), uncertainty quantification (UQ) of the bearing capacities of the push-out specimens is conducted using the arbitrary polynomial chaos (aPC) method. Subsequently, the global sensitivity analysis of the ultimate and residual bearing capacities is accomplished through the aPC surrogate model. The results indicate that the probability distribution types of the parameters in the stochastic bond-slip constitutive model can be arbitrary when considering the randomness of concrete material, and the aPC method with at least a third-order expansion is recommended to execute UQ for the push-out test due to the strong nonlinearty between the bearing capacities and the random parameters. The ultimate bearing capacity is primarily affected by the parameter K2, followed by K4, K3, and K5. Whereas the residual bearing capacity is predominantly influenced by the parameter K4, followed by K5, the remaining parameters exhibit negligible influence. In contrast, K1 and Ec have the greatest influence on equivalent plastic strain of the concrete near the loading end of the push-out specimen.

Investigations on the Johnson-Cook Constitutive and Damage-Fracture Model Parameters of a Q345C Steel

Due to the rapid development of high-speed trains, the service safety of vehicle body materials and structures has become a focal point in transport and impact engineering. Numerical simulations on the collision resistance of vehicle materials and structures are crucial for the safety assessment and optimal structural design of high-speed trains but have not been fully investigated due to the lack of damage model parameters. This study focuses on the Johnson-Cook (J-C) constitutive and damage-fracture models of a typical vehicle material, Q345C steel. A series of mechanical tests are conducted on the Q345C steel, including the quasi-static and dynamic compression/tension tests, quasi-static tension tests at different temperatures, and fracture tests along different stress paths, using the material test system and the split Hopkinson pressure/tension bar. Then, the parameters of the Johnson-Cook constitutive and damage-fracture models are calibrated based on the experimental results. In terms of the damage parameters related to stress paths, a new method of combining experiments and simulations is proposed to obtain the real, local fracture strains of the Q345C steel samples. This method allows the measurements of equivalent plastic strain and stress triaxiality histories under nonlinear stress paths, which are hardly accessible from individual experiments, and facilitates the accurate calibration of stress-path-related damage parameters. In addition, a high-speed plate penetration test is used to validate the J-C parameters, which can be directly implemented in the commercial finite element software Abaqus. The projectile trajectories from the simulation and experiment agree well with each other, demonstrating the reliability of the model parameters for impact scenarios and the efficiency of the experimental procedures utilized for calibration.

A dislocation density-based crystal plasticity constitutive model: comparison of VPSC effective medium predictions with ρ-CP finite element predictions

This work presents a dislocation density-based crystal plasticity constitutive model for glide kinetics, strengthening and dislocation density evolution, implemented in the effective medium-based visco-plastic self consistent (VPSC) framework and the spatially resolved, ρ-CP crystal plasticity finite element framework. Additionally, a distribution of intragranular stresses is introduced in the VPSC framework, instead of the conventionally used mean value of grain stress for effective medium calculations. The ρ-CP model is first calibrated to predict the mechanical response of a bcc ferritic steel with an initial rolled texture. The same set of constitutive model parameters are then used in VPSC to predict the aggregate stress–strain response and total dislocation densities. For these VPSC simulations, the interaction parameter governing the interaction between the grain and the effective medium in the Eshelby inclusion formalism, and a scalar parameter representative of the distribution of intragranular stresses within a grain, are used to calibrate the VPSC predictions in order to match the predictions of the ρ-CP model. A parametric study is performed to understand the effect of these two parameters on the VPSC predictions. Further, simulations are also performed for a random untextured polycrystal to identify the corresponding VPSC simulation parameters for predicting a similar response as the ρ-CP model. The novelty of the work is in the same set of constitutive models and associated parameters have been implemented in VPSC and ρ-CP to predict similar aggregate stress–strain response and total dislocation densities. This finite element-calibrated effective medium crystal plasticity approach reduces the computational time by at least two orders of magnitude and represents an advance towards the development of multiscale crystal plasticity modeling tools.

Study on Plastic Constitutive Relation and Ductile Fracture Criterion of AM60B Magnesium Alloy.

It is currently a challenge to accurately predict the deformation and fracture behavior of metal parts in automobile crashes. Many studies have shown that the deformation and fracture behavior of materials are significantly affected by the stress state during automobile crashes with complex stress state characteristics. In order to further promote the application of die-cast magnesium alloys in automobiles, it is particularly important to study the material deformation and fracture behavior of die-cast magnesium alloys. In this paper, the mechanical properties of the AM60B die-cast magnesium alloy sheet under four stress states (shear, tension, R10 notch tension, and cupping) were designed and tested. Based on the von Mises isotropic constitutive model and Swift weighted Hockett-Sherby hardening model, the plastic constitutive model of die-cast magnesium alloy was established. Based on the plastic model and the fracture model (JC, MMC, and DIEM) considering the influence of three stress states, the deformation and fracture behavior of the AM60B die-cast magnesium alloy front-end members in three-point bending were predicted by experiments and finite element simulation. The experimental results show that the deformation mode and loading-displacement curve trend of the AM60B die-cast magnesium alloy front members are the same, the crack initiation point and crack initiation time are the same, and the crack shape is similar. The results show that the complex stress state constitutive model parameters and the DIEM fracture model obtained in this paper can accurately predict the deformation and fracture failure behavior of the AM60B die-cast magnesium alloy sheet.

A Case Study on Advanced CPT Data Interpretation: From Stratification to Soil Parameters

AbstractThe cone penetration test (CPT) is considered as one of the most reliable in-situ tests and has found numerous applications in the geotechnical engineering field. Traditional CPT interpretation includes, but are not limited to the identification of the soil stratification and the determination of soil parameters. This paper presents a case study concerning a test site located in Salzburg, Austria, in which we focus on the interpretation of CPTs from different perspectives. The manuscript is divided into three main sections dealing with three different aspects of CPT interpretation, namely stratification, ground variability and soil parameters. The first strategy introduces a machine learning based stratification identification strategy to detect soil layer boundaries from CPT measurements. A comparison with reference solutions demonstrates relative merits of this approach to classical filter algorithms based on empirical CPT classifications. The second strategy introduces an intuitive approach to evaluate the ground variability. This is achieved by calculating the level of fluctuation on the basis of CPT measurements and could be used as a data-driven decision-making tool for the improved design of CPT investigation layouts. The third strategy is embedded in an ongoing research project that aims to determine constitutive model parameters from in-situ tests using a graph-based methodology. In the present work, the developed automated parameter determination framework is applied to evaluate the soil parameters of one selected soil layer identified from the CPT interpretations. Potential lines of research in the context of CPT interpretation are explored throughout this work and may serve as valuable reference in future research.

Automatic parameter identification of a shape memory alloy model using characteristic experimental data points

Identifying material parameters of constitutive models can be a time consuming process. This is especially evident when the constitutive models have many parameters. In this work, an automatic identification procedure is described to determine the various parameters of a shape memory alloy model. The procedure requires some parameters as manual inputs (to be determined via trial and error) and determines some of the parameters directly from experimental data. In addition, the procedure calculates some of the parameters using Newton’s method based on characteristic data points so that the simulation curves pass through those points. As a result, the method essentially decouples the effects of the parameters on the simulation uniaxial test curves. The automatic identification procedure is applied for uniaxial tests dealing with transformation, tension–compression asymmetry, internal loops, plasticity and functional fatigue. The procedure is fast, flexible and reasonably accurate. However, the approach is currently limited to uniaxial tests, small strains and needs to be tailored to each model individually.

Numerical investigations on constitutive model parameters of HRB400 and HTRB600 steel bars based on tensile and fatigue tests

Abstract In recent years, HRB400 and HTRB600 steel bars have become the mainstream standard reinforcing steel used in concrete structures in China. However, significant controversy still exists regarding the selection of material constitutive models and the determination of model parameters for buckling, fatigue, hysteresis, and other material characteristics. In this article, an automated process of multi-parameter calculation of the constitutive model for reinforcing steel – simulation accuracy evaluation of the constitutive model – selection of the constitutive model of reinforcing steel is established based on the hybrid programming method using MATLAB and OpenSees software. First, tensile and low-cycle fatigue tests were carried out on HRB400 and HTRB600 steel bars. Second, based on the constitutive model in OpenSees software and the skeleton curve and characteristics such as yielding, fatigue, and hysteresis, the constitutive model parameters of HRB400 and HTRB600 steel bars are determined using indirect and direct fitting methods. Finally, the five similarity parameters of the simulated normalized cumulative hysteretic energy dissipation coefficient are compared with the test results. The results indicate that the simulation accuracy of the Reinforcing Steel model exceeds 72%, which is higher than other four models, making it the best choice for reinforcing steel in numerical simulation.

On the uncertainty quantification of the active uterine contraction during the second stage of labor simulation.

Uterine contractions in the myometrium occur at multiple scales, spanning both organ and cellular levels. This complex biological process plays an essential role in the fetus delivery during the second stage of labor. Several finite element models of active uterine contractions have already been developed to simulate the descent of the fetus through the birth canal. However, the developed models suffer severe reliability issues due to the uncertain parameters. In this context, the present study aimed to perform the uncertainty quantification (UQ) of the active uterine contraction simulation to advance our understanding of pregnancy mechanisms with more reliable indicators. A uterus model with and without fetus was developed integrating a transversely isotropic Mooney-Rivlin material with two distinct fiber orientation architectures. Different contraction patterns with complex boundary conditions were designed and applied. A global sensitivity study was performed to select the most valuable parameters for the uncertainty quantification (UQ) process using a copula-based Monte Carlo method. As results, four critical material parameters ( ) of the active uterine contraction model were identified and used for the UQ process. The stress distribution on the uterus during the fetus descent, considering first and second fiber orientation families, ranged from 0.144 to 1.234MPa and 0.044 to 1.619MPa, respectively. The simulation outcomes revealed also the segment-specific contraction pattern of the uterus tissue. The present study quantified, for the first time, the effect of uncertain parameters of the complex constitutive model of the active uterine contraction on the fetus descent process. As perspectives, a full maternal pelvis model will be coupled with reinforcement learning to automatically identify the delivery mechanism behind the cardinal movements of the fetus during the active expulsion process.

Structural parameters defining distribution of collagen fiber directions in human carotid arteries

Collagen fiber arrangement is decisive for constitutive description of anisotropic mechanical response of arterial wall. In this study, their orientation in human common carotid artery was investigated using polarized light microscopy and an automated algorithm giving more than 4·106 fiber angles per slice. In total 113 slices acquired from 18 arteries taken from 14 cadavers were used for fiber orientation in the circumferential-axial plane. All histograms were approximated with unimodal von Mises distribution to evaluate dominant direction of fibers and their concentration parameter. 10 specimens were analyzed also in circumferential-radial and axial-radial planes (2-4 slices per specimen in each plane); the portion of radially oriented fibers was found insignificant. In the circumferential-axial plane, most specimens showed a pronounced unimodal distribution with angle to circumferential direction μ = 0.7° ± 9.4° and concentration parameter b = 3.4 ± 1.9. Suitability of the unimodal fit was confirmed by high values of coefficient of determination (mean R2 = 0.97, median R2 = 0.99). Differences between media and adventitia layers were not found statistically significant. The results are directly applicable as structural parameters in the GOH constitutive model of arterial wall if the postulated two fiber families are unified into one with circumferential orientation.

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.

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.

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.