Constitutive Model Parameters Research Articles

Extracting general knowledge of model parameters for clays out of numerous laboratory tests

This paper is concerned with the process of determining the material parameters of advanced constitutive models for clays. Provided results are applicable already in the early stages of geotechnical survey when no detailed data from laboratory tests of soils expected at construction site are known. A worldwide database of laboratory tests obtained during four year operation of web calibration application ExCalibre was used for this purpose. This application allows automatic calibration of three advanced constitutive soil models based on detailed data from triaxial and edometric tests. The paper describes the process of determining the confidence intervals of each material parameter of modified Cam-clay and hypoplastic clay models for low (CL) and high (CH) plasticity clay according to unified soil classification system (USCS) and tabulates their typical ranges. The purpose of presented work was to contribute to the use of advanced constitutive models among practical engineers.

Uncertainty quantification and propagation in the microstructure-sensitive prediction of the stress-strain response of woven ceramic matrix composites

Hierarchical multiscale modeling of heterogeneous materials has traditionally relied upon a deterministic estimation of constitutive properties when making microstructure-sensitive predictions of effective response at each subsequent length-scale. Such an approach is wholly unsuitable for a variety of material classes, such as ceramic matrix composites, which exhibit large variability at multiple length-scales. This work demonstrates a framework for approaching two open problems towards improved microstructure-sensitive predictions, namely, (i) probabilistically calibrating complex constitutive models at the mesoscale to sparsely observed macroscale experimental data, and (ii) propagating this stochastic constituent behavior at the mesoscale towards low-cost homogenized predictions for unseen microstructures. The proposed stochastic scale-bridging framework displays a continuity of information flow where no portion of the experimental data is neglected out of convenience, facilitating the greatest information gain from oftentimes costly experiments. In this paper, suitable protocols were developed to address the challenges described above. The protocols were subsequently demonstrated on ceramic matrix composite’s uniaxial tensile stress–strain response, where constituent behavior at the mesoscale was described using continuum damage mechanics, and predictions encapsulating constitutive model parameter uncertainty were made for novel microstructures. The methodology presented in this work is broadly applicable to various material classes and constitutive models with high-dimensional parameter sets.

Creep monitoring and parameters inversion methods for rock salt in extremely deep formation

When underground salt caverns are used for natural gas storage, the pressure difference between the inside and outside of the cavern will cause continuous creep deformation of the surrounding rock. Understanding the creep characteristics and constitutive model parameters of rock salt in actual formations is of great significance for guiding the construction and safe operation of gas storage facilities. In this paper, a creep contraction calculation model for slender cylindrical rock salt caverns was established firstly, based on the theory of complex variables and viscoelasticity. This model can calculate the radial displacement of the surrounding rock at any moment on the cross-section of the rock salt wellbore. Subsequently, two indirect monitoring methods for deep rock salt creep using the open hole section of the well were proposed based on this model, which involves using the cavern pressure change after wellhead closure and the liquid overflow rate after wellhead opening to indirectly reflect the deformation of underground rock salt. These two sets of field experiments can be used together to determine the values of the constitutive model parameters of rock salt creep under actual stress conditions. This theoretical framework was applied in the Ningjin Salt Cavern Gas Storage Project in China. Pressure monitoring was conducted for 150 days, and wellbore fluid overflow was measured for 45 h in a rock salt well at a depth close to 3000 m. The calculated results showed good agreement with the field monitoring data, and the parameters of the Burgers creep model for rock salt under actual conditions were determined. This demonstrates the strong feasibility of the monitoring method and the validity of the computational model. Finally, using the obtained creep parameters, a quantitative analysis of the creep contraction of the wellbore was performed considering factors such as internal pressure, in situ stress, and Poisson's ratio of the rock salt.

A Novel Approach for Optimization of Soft Material Constitutive Model Parameters Based on a Genetic Algorithm and Drucker's Stability Criterion.

The growing interest in soft materials to develop flexible devices involves the need to create accurate methodologies to determine parameter values of constitutive models to improve their modeling. In this work, a novel approach for the optimization of constitutive model parameters is presented, which consists of using a genetic algorithm (GA) to obtain a set of solutions from data of uniaxial tensile tests, which are later used to simulate the mechanical test using finite element analysis (FEA) software to find an optimal solution considering Drucker's stability criterion. This approach was applied to the elastomer Ecoflex 00-30 considering the Warner and Yeoh models and Rivlin's phenomenological theory. The correlation between the experimental and the predicted data by the models was determined using the root mean squared error (RMSE), where the found parameter sets provided a close fit to the experimental data with RMSE values of 0.022 (ANSYS) and 0.024 (ABAQUS) for Warner's model, while for Yeoh's model were 0.014 (ANSYS) and 0.012 (ABAQUS). It was found that the best parameter values accurately follow the experimental material behavior using FEA. The proposed GA not only optimizes the material parameters but also has a high reproducibility level with average RMSE values of 0.024 for Warner's model and 0.009 for Yeoh's model, fulfilling Drucker's stability criterion.

On the stress dependency of sand production coefficient in hydro-dynamical sanding criteria

Solids production is a complex physical process which is controlled by several factors including mechanical failure from in-situ stresses and hydrodynamic erosion from fluid flow. Hydrodynamic models for the prediction of sand production involve sanding criteria based on filtration theories. Such models contain a constitutive model parameter, the coefficient λ, with dimensions of inverse length which is calibrated by sand erosion tests, but its nature and its dependencies have not been clarified to date. The aim of this work is an attempt to refine the hydrodynamic models by investigating the dependence of the sand production coefficient λ on the external stress conditions and on the plastic zone Λ that is developed on hollow cylinders tests and propose an expression describing its importance in the sand production prediction modelling. The aim of the work is obtained through simulations with finite elements by utilizing the well-established Arbitrary Lagrangian-Eulerian (ALE) analysis considering the poro-mechanical coupling of the fluid-solid system for simulating hollow cylinder tests. Best fitting experimental data estimated values for the sand production coefficient for various values of external stress are obtained through back analysis. The dependence of λ on the external stress turns out to be fairly smooth and a three-parameter model is proposed to describe that dependence: a scale parameter, an exponent, and a stress parameter defining the magnitude of stress at which erosion onset is predicted. It turns out that the stress parameter is associated with the minimum stress required for plastic yielding to occur, which was also estimated theoretically. This finding is in agreement with the physical assumption underlying the simulations that erosion onsets and progresses after the material reaches a critical plastic strain as a consequence of material plastic yielding. A power law model describing the dependence of λ on the plastic zone depth is also proposed and discussed.

Research on PTFE/Al reactive jet formation of shaped charge

During the PTFE/Al reactive shaped charge jet formation, the burst wave generated by the explosion of the explosive is sufficient to achieve the ignition conditions of the reactive materials (RMS). As a result, the RMS will react, resulting in an energy loss from the reactive jet. In order to research the forming features of PTFE/Al reactive jet and the energy loss during the jet formation, a PTFE/Al reactive liner with a diameter of 74 mm was prepared and an X-ray pulses photography experiment was performed on the jet formation. And the parameters of Johnson-Cook constitutive model of RMS were obtained through quasi-static experiments and Hopkinson pressure bar experiments. The jet formation were simulated, and the AUTODYN secondary development technology was used. The results show that the secondary development technology can intuitively show the reaction of the active material during the jet formation. The PTFE/Al reactive jet is less cohesive, its jet diameter is thicker, and the morphology is divergent. The reactive materials reacted during the PTFE/Al reactive shaped charge jet formation. And during the reactive jet formation, the inner layer of the liner collided. Therefore, most of the chemical reactions occur inside the reactive jet.

Optimize characteristic value of SPT for seismic design of offshore wind turbines in liquefiable soils by stochastic models

Dynamic numerical analyses on an offshore wind turbine (OWT) supported by a suction bucket foundation were performed to investigate the effects of soil spatial variability on the ground liquefaction and tilts of OWT, and to provide suggestions on selecting a representative percentile of the random distributions of a clean sand equivalent SPT blow count, (N1)60cs, for deterministic models. The material parameters of an elastoplastic constitutive model (Cyclic Mobility model) in the numerical model were derived from the (N1)60cs (spatial variability). Monte Carlo simulations were used to describe the seismic responses of the laterally loaded suction bucket foundation in spatially variable soil. Simulation results for deterministic models (uniform properties of soil) were compared to results for random models (spatially variable properties of soil). Tilts of OWT and liquefaction potential index of ground are chosen as criteria, and those obtained from the random models and deterministic models were compared to identify the representative (N1)60cs, based on the principle that the deterministic models produce reasonable consistency with the upper limit of the random model responses. The effects of site conditions, seismic conditions, and other factors were evaluated, and it is found that the coefficient of variation (COV), (N1)60cs, acceleration, and frequency have significant influence.

Determination of material parameters in constitutive models using adaptive neural network machine learning

A challenge in the constitutive modeling of time dependent, non-linear solids is the identification of potentially large numbers of material parameters. Here we present an efficient method to determine these parameters using a machine learning algorithm based on Singular Value Decomposition (SVD) and an adaptive neural network (NN). SVD compresses training data and provides outputs for the NN. The trained network rapidly computes the material responses for a large set of material parameters. These responses are then compared with experimental data to determine the optimal parameters. We test our algorithm by performing uniaxial cyclic and relaxation tests on three hydrogels with very different time dependent behaviors: a chemically and physically crosslinked polyampholyte (c-PA) gel; a pure physically crosslinked PA (p-PA) gel, and a Poly(vinylalcohol) (PVA) hydrogel with both chemical and physical crosslinks.

Interpretation of piezocone tests in normally- and over-consolidated clay using a spherical cavity expansion solution

This paper presents the derivation of closed-form expressions for the interpretation of piezocone tests in clay on the basis of an undrained cavity expansion solution. The cavity expansion solution employs the modified Unified Hardening model to describe the undrained behaviour of normally- and over-consolidated clays upon shearing. The derived expressions correlate the measured tip resistance and pore pressure with the undrained shear strength and the over-consolidation ratio, using a cone factor that, unlike empirical formulas, is calculated directly from the constitutive model parameters and the cone geometry. The cavity expansion solution is validated via comparison of its results against published studies, and accordingly the accuracy of the proposed expressions is benchmarked against field data. We show that, despite the simplifications introduced in the derivation, the calibrated expressions are capable of reproducing the field data with reasonable accuracy.

FEM investigation of full-scale tests on DSSI, including gravel-rubber mixtures as geotechnical seismic isolation

Soil-rubber mixtures underneath foundations are an eco-sustainable and low-cost Geotechnical Seismic Isolation (GSI) solution. Using rubber grains from end-of-life tyres in the mixtures can provide a modern recycling system that reduces the stockpile of scrap tyres worldwide. In recent years, gravel-rubber mixtures (GRMs) properties have been investigated, finding good behaviour in static and dynamic conditions. Laboratory tests on GRMs advantages as GSI in the form of a layer underlying the foundation of a structure are available in the literature. Nevertheless, only one experimental campaign on a full-scale prototype structure resting on GRMs with 0% and 30% rubber content per weight was performed (SOFIA-SERA Research Programme).This paper presents 3D advanced nonlinear FEM analyses to reproduce and furnish new results about the above-mentioned full-scale test. The calibration of the parameters of the different constitutive models used for modelling the foundation soil and the GRMs was supported by an extensive geotechnical characterization. The developed FEM model was validated by the results from the above-mentioned full-scale test in terms of accelerations and velocities. Then, the dynamic behaviour of the GRMs was studied, also considering the shear strains versus the shear stresses and the horizontal and vertical displacements, quantities not investigated experimentally. Finally, the GRMs static behaviour was also investigated, considering the GRMs axial strains and the GRMs and foundation vertical displacements.The paper highlights the fundamental role of both experimental tests and numerical modelling, as invaluable tools for coupled analyses of the seismic behaviour of soil-structure systems, including innovative materials, such as GRMs, and the main advantages of using GRMs as GSI.

A numerical model for non-linear shear behavior of high damping rubber bearings

The dynamic behavior of isolated structures is strongly controlled by the force–deformation constitutive behavior of the isolators. Among the different types of existing isolation devices, High Damping Rubber Bearings (HDRBs) are commonly used in practice, which behavior is highly non-linear and difficult to model analytically. Consequently, this article proposes a simple, but sufficiently accurate, mathematical model for simulating the non-linear shear behavior of HDRBs under large deformations, and an estimation procedure for its parameter values using the geometrical features and mechanical characteristics of the device. First, we briefly describe the phenomena observed in the experimental test data, as well as other phenomena not observed within the range of experimental deformations. Then, the mathematical formulation is presented, which is based on the consideration of two components connected in parallel, a hyperelastic spring and a dissipative component. The governing equation for the former is derived from the expanded formulation of the Mooney–Rivlin model for isotropic hyperelastic materials, and the latter from a Bouc-Wen model with hardening. A novel model is included to account for stiffness degradation, including scragging and Mullins effects, which is developed from experimental data of 924 tested devices. The proposed model fits well the experimental test results of HDRBs with different geometric features and material properties. Based on the evolution laws for the different variables, the model can be successfully used in structural dynamic analysis. To facilitate model calibration, a statistical estimation procedure is proposed to reduce the 17 force–deformation constitutive model parameters of the isolator to 9 unknown parameters, which are computed from the geometric features of the device and mechanical characteristics of the rubber material. This makes the calibration of the force–deformation constitutive model parameters feasible. The estimation procedure successfully predicts the behavior of an average device within a batch of HDRBs, showing good agreement with two different experimental datasets.

Physical Regime Sensitivity

This work presents a novel sensitivity approach that quantifies sensitivity to regimes of a model’s state variables rather than constitutive model parameters. This Physical Regime Sensitivity (PRS) determines which regimes of a model’s independent variables have the biggest influence on an experiment or application. PRS analysis is demonstrated on a strength model used in the simulation of a copper Taylor cylinder. In a series of simulations, the strength model was perturbed sequentially in local regimes of plastic strain, plastic strain rate, temperature and pressure, and then the prediction of cylinder shape was compared to unperturbed calculations. Results show, for example, that the deformed length of the cylinder was most sensitive to strength at a strain rate of 1.0 × 104/sec., but the deformed footprint radius was most sensitive to strength at a strain rate of about 4.0 × 104/sec. Compared to current histogram approaches, PRS can be used to design or interpret integrated experiments by identifying not just which regimes are accessed somewhere in the experiment but the causality question of which regimes actually affect the measured data. PRS should allow one to focus experimental and modeling efforts where they are most needed and to better interpret experiments.

Determination of Johnson-Cook constitutive model coefficients considering initial gap between contact faces in SHPB test

When a material is deformed at high speed, it is well known that the flow stress is highly dependent on the strain rate and temperature. So, many studies of the stress-strain relationship at high strain rate condition have been conducted using the Split Hopkinson Pressure Bar (SHPB) test. Studies about the effects of friction, eccentricity, declination, and joints were also conducted. However, no study has been conducted about the effects of gaps formed by surface roughness of the contact faces. In this study, effect of initial gap between specimen and bars was investigated by SHPB test. The process of compressing initial gaps formed by rough places on contact surfaces was described as the initial gap compression effect. The proposed effect on measured stress-strain relation was confirmed experimentally and numerically by adjusting the surface roughness. Considering the initial gap compression effect, an equivalent gap compensation method was proposed for efficient finite element analysis. A methodology for determining Johnson-Cook (JC) coefficients using the optimization-based inverse method and the proposed equivalent gap model was presented. Also, the friction coefficients were measured to increase the accuracy of the determined coefficient. As a result, it was shown that accurate JC coefficients could be determined using the proposed methodology; the determined JC coefficients were considered to be reliable for various strain rates. Also, stress-strain relations obtained with and without initial gap compensation were compared to show the necessity of gap compensation. Consequently, it was revealed that consideration of the initial gap compression effect is essential for accurately determining plastic constitutive model parameters.

A new framework for the assessment of model probabilities of the different crystal plasticity models for lamellar grains in Titanium alloys

This paper presents a novel framework for assessing the relative accuracy of the different slip transfer criterion in modeling the constitutive response of the lamellar morphology grains in Titanium alloys. The main steps involved in the proposed framework include: (i) rigorous statistical evaluation of the salient morphological characteristics of the lamellar grains using image processing techniques, (ii) modeling the effects of dislocation slip transfer as additive penalties to the critical resolved shear strengths of the different slip systems in each phase, (iii) consideration of multiple geometric slip transfer criteria for the numerical evaluation of the different penalty terms, and (iv) the Bayesian calibration of the material parameters in the constitutive descriptions using spherical nanoindentation experimental data on a polycrystalline Ti-6Al-4V sample. Step (iv) described above involves the construction and refinement of a Gaussian process (GP) surrogate model for the indentation measurements, which is trained on crystal plasticity finite element simulations incorporating the constitutive descriptions selected in Steps (ii) and (iii). The GP surrogates are then combined with Markov Chain Monte Carlo sampling techniques to calibrate the parameters in the various constitutive models studied in this work. Additionally, we have computed the posterior model probabilities for all the constitutive models considered and identified the most plausible slip transfer criterion. This specific constitutive model is then utilized to present a homogenized crystal plasticity model for the lamellar morphology. The proposed framework presents a robust scale-bridging protocol for incorporating the uncertain information obtained from lower scales.

Establishment of constitutive model and dynamic parameter analysis of rubber conveyor belt

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Damage softening constitutive model of HTPB propellant for biaxial loading

In order to establish the damage constitutive model of composite solid propellant, it is assumed that the micro element strength in HTPB propellants follows Weibull distribution. Using the twin-shear unified strength theory, a damage distribution variable is established, and a constitutive model characterizing the damage deformation process of HTPB propellants is established. Based on the biaxial loading experimental data of HTPB propellant at room temperature (298.15 K) and three loading rates (0.40 s−1, 4.00 s−1, and 14.29 s−1), the model parameters were fitted, and the relationship between the parameters in the damage constitutive model and strain rate was given. The model was validated using experimental results at room temperature (298.15 K) and three other loading rates (1.00 s−1, 2.00 s −1, and 8.00 s−1). The results show that the damage constitutive model can well describe the stress strain relationship of HTPB propellant under biaxial loading, although the model prediction effect of the nonlinear transition region of the stress strain curves is poor. Finally, it is concluded that the constitutive model established in this paper reflects the softening characteristics of HTPB propellants and the phenomenon that the strength of HTPB propellants is affected by the stress state. The damage constitutive model can provide a reference for the damage analysis of composite solid propellants under complex loading conditions.

The effects of leaflet material properties on the simulated function of regurgitant mitral valves

Advances in three-dimensional imaging provide the ability to construct and analyze finite element (FE) models to evaluate the biomechanical behavior and function of atrioventricular valves. However, while obtaining patient-specific valve geometry is now possible, non-invasive measurement of patient-specific leaflet material properties remains nearly impossible. Both valve geometry and tissue properties play a significant role in governing valve dynamics, leading to the central question of whether clinically relevant insights can be attained from FE analysis of atrioventricular valves without precise knowledge of tissue properties. As such we investigated (1) the influence of tissue extensibility and (2) the effects of constitutive model parameters and leaflet thickness on simulated valve function and mechanics. We compared metrics of valve function (e.g., leaflet coaptation and regurgitant orifice area) and mechanics (e.g., stress and strain) across one normal and three regurgitant mitral valve (MV) models with common mechanisms of regurgitation (annular dilation, leaflet prolapse, leaflet tethering) of both moderate and severe degree. We developed a novel fully-automated approach to accurately quantify regurgitant orifice areas of complex valve geometries. We found that the relative ordering of the mechanical and functional metrics was maintained across a group of valves using material properties up to 15% softer than the representative adult mitral constitutive model. Our findings suggest that FE simulations can be used to qualitatively compare how differences and alterations in valve structure affect relative atrioventricular valve function even in populations where material properties are not precisely known.

Cyclic plasticity and ULCF behavior of steel butt-joints considering different welding methods

In order to reveal the influence of welding method on the cyclic plasticity and ultra-low cycle fatigue (ULCF) behavior of low-alloy butt-joints, three different welding methods, namely, shielded metal arc welding (SMAW), gas metal arc welding (GMAW), and submerged arc welding (SAW), were considered. Dog-bone flat-plate specimens with the welds were cut off from the plates for cyclic tests. The load-carrying capacity, energy dissipation property, and ULCF performance of the specimens were discussed. According to the experimental results, GMAW and SAW lead to the highest and lowest peak loads, respectively. The various welding methods have a slight influence on the equivalent viscos damping (EVD) coefficient of the specimens. Compared with those of the base metal (BM) specimen, ductility of the welded specimens is degraded by 34.62–61.54%, yield strength is deteriorated by 2.86–13.20%, ULCF life is decreased by 71.33%-92.31%. Metallurgical and scanning electron microscope (SEM) analysis were further conducted to reveal the mechanism behind the significantly compromised ULCF behavior of the welded specimens. In-depth numerical analysis was also conducted to reproduce the experimental processes. In the finite element (FE) analysis, inverse calibration technique was applied to determine the Voce-Chaboche (VC) combined hardening constitutive model parameters, and then cyclic void growth model (CVGM) was adopted for fracture simulation.

Poro-viscoelastic material parameter identification of brain tissue-mimicking hydrogels.

Understanding and characterizing the mechanical and structural properties of brain tissue is essential for developing and calibrating reliable material models. Based on the Theory of Porous Media, a novel nonlinear poro-viscoelastic computational model was recently proposed to describe the mechanical response of the tissue under different loading conditions. The model contains parameters related to the time-dependent behavior arising from both the viscoelastic relaxation of the solid matrix and its interaction with the fluid phase. This study focuses on the characterization of these parameters through indentation experiments on a tailor-made polyvinyl alcohol-based hydrogel mimicking brain tissue. The material behavior is adjusted to ex vivo porcine brain tissue. An inverse parameter identification scheme using a trust region reflective algorithm is introduced and applied to match experimental data obtained from the indentation with the proposed computational model. By minimizing the error between experimental values and finite element simulation results, the optimal constitutive model parameters of the brain tissue-mimicking hydrogel are extracted. Finally, the model is validated using the derived material parameters in a finite element simulation.

Experimental study and model on the low‐cycle fatigue behavior of thermoplastic vulcanizates

AbstractThermoplastic vulcanizates (TPVs) is composed of crosslinked rubber and plastic and have recently been used to replace traditional rubber. To investigate their constitutive behavior throughout the fatigue life, a series of tensile fatigue tests were carried out. The experimental results show significant fatigue softening of TPV, which can be regarded as the joint action of fatigue damage and fatigue creep. After many cycles, the viscous flow can also be restored; thus, the fatigue creep was eliminated by the cyclic‐pause‐cyclic experiment. The cyclic curves were obtained when the fatigue damage was the only effect. Based on a visco‐hyperelastic constitutive model, the evolution rate of the constitutive model parameters during fatigue damage was obtained using the network alteration theory. Considering fatigue damage and fatigue creep effect together, a fatigue‐softening constitutive model is proposed. The model can predict the constitutive behavior of TPVs over their entire fatigue life.