Validity Of Constitutive Model Research Articles

Constitutive models for confined elastomeric layers: Effects of nonlinearity and compressibility

Elastomers tend to undergo large deformations accompanied by small volumetric changes. For elastomeric layers sandwiched between rigid plates, large deformations can be significantly limited by the constraints imposed by the plates. Further, those constraints can be enhanced by material’s inability to undergo large volumetric changes. From this perspective, it is appropriate to examine the validity of constitutive models, in which an elastomer is treated as incompressible, for analysis of the confined layers. Here, this issue is addressed by considering the mechanical response of sandwiched elastomeric layers using three constitutive models. The first one, referred to as compressible neo-Hookean, is regarded as exact. The other two models are regarded as approximations. Of those two, the first one neglects nonlinearity and the second one neglects compressibility. Accordingly, the modeling errors associated with the former are treated as measures of importance of nonlinearity, and the modeling errors associated with the latter are treated as measures of importance of compressibility. The modeling errors are evaluated using the force–displacement curve and the mean stress at the layer center as the quantities of interest. Numerical results are presented for rubber and polydimethylsiloxane (PDMS), characterized by Poisson’s ratios ν=0.4999 and ν=0.49, respectively. It is shown that, even when the forces applied to the plates are large, considering nonlinearity is important for thick but not for thin layers. In contrast, considering compressibility is important for thin layers. The need for considering compressibility is further assessed by introducing a competition parameter, which reinforces the notion that compressibility is important for modeling PDMS layers and thin rubber layers.

Numerical inspection of Miner’s rule and drained cyclic preloading effects on fine-grained soils

The prediction of soil cyclic behaviour is relevant for several geotechnical applications. In order to obtain accurate predictions of settlements and pore water pressure build-up on boundary value simulations, robust constitutive models which are able to realistically reproduce the soil mechanical behaviour under monotonic and cyclic loading are necessary. To have confidence on their predictions, their capabilities and limitations should be very well known. In this article, the prediction capabilities and limitations of two advanced constitutive models for fine-grained soils, namely: CAM and AHP+ISA were inspected considering undrained cyclic triaxial tests with more complex and realistic nature than ”conventional” undrained cyclic tests usually considered in the literature for the calibration and validation of constitutive models but not representative of many real loading scenarios. In particular, the influence of drained cyclic preloadings and packages of cycles with different deviatoric stress amplitudes in different sequences (inspection of Miner’s rule) was evaluated. For that purpose, simulation results with the models were qualitatively as well as quantitatively compared against several experimental results under monotonic and cyclic loading on Malaysian kaolin reported by Duque et al. (2022a).

An experimental study of the mechanical behavior of rolled AZ31B magnesium alloy under combined axial-torsion loading

The mechanical behavior and microstructure at fracture of a rolled AZ31B magnesium alloy were experimentally investigated using tubular specimens subjected to combined axial-torsion loading with different ratios of the axial and shear stress components. The stress state influences the stress-strain responses. The equivalent stress-equivalent plastic strain curves under tension-torsion loading show a sigmoidal shape and the peak value of the equivalent strain hardening rate increases as the ratio of the axial stress to the shear stress increases. Under compression-torsion, the equivalent stress-equivalent plastic strain curves show a concave-down shape, and the equivalent strain hardening rate decreases at faster rates as the ratio of the axial stress to the shear stress increases. Among all the loading conditions investigated, pure tension and pure compression result in the highest strength, and torsion combined with a slight tension has the lowest strength. The trend of ductility is inversely proportional to the strength with respect to the influence of the combined axial-torsion loading. Detailed twinning structures reveal that extensive tension twins are induced under tension-torsion loading paths. Conversely, a combination of tension and compression twins is observed under compression-torsion loading due to the high Schmid factors of the compression twins resulted from the grains with favorable orientations. The significant effect of the stress state on the post-fracture texture is explained in terms of the twin variant favorability which is dominated by the crystal orientation relative to the orientation of the applied principal stresses. The experimental results are critical for the development and validation of constitutive models for magnesium alloys under multiaxial loading.

Methodology of structured development and validation of multiphysical constitutive models using the example of crushed salt compaction under 3D THM load conditions

Abstract. The conceptual plans for the final underground disposal of radioactive waste in rock salt formations are based on extensive backfilling with crushed salt of the residual cavities left after waste deposition. It is therefore of particular importance for the historical and prognostic analysis of the load-bearing behavior and impermeability of a final repository in rock salt to demonstrate that compaction of the crushed salt backfill, which progresses over time, is suitable to seal the breaches in the geological barrier created during the underground excavation of the cavity in the long term such that safe containment of the waste is ensured. Relevant investigations on the thermal-hydraulic-mechanical (THM) behavior of crushed salt revealed that the constitutive models for the description of crushed salt compaction, which have regularly been based on the evaluation of oedometer tests, are not suitable for a sufficiently realistic representation of the essentially three-dimensional stress-strain behavior of crushed salt depending on the external load in space and time. Evidence for the above statement lies in particular in the fact that even when standardized mixtures of crushed salt are used, a computational reanalysis of compaction tests using a standardized set of parameters has hitherto been unsuccessful when different loading scenarios were specified for these laboratory tests. This means that deformations and porosities measured in the context of one individual laboratory tests can currently only be reanalyzed in sufficient quantity, irrespective of the choice of constitutive model, if the model parameters are determined in relation to this test. As a result, it must be stated that, on the one hand, the compaction behavior of crushed salt in space and time is not yet definitively understood, while, on the other hand, to ensure reliable, robust and sufficiently realistic statements to be made on compaction behavior, and thus to prove the safe containment of radioactive waste in rock salt, the availability of extensive systematically and sufficiently validated constitutive models is indispensable. This presentation introduces a methodological approach for the systematic and structured development and validation of multiphysical constitutive models, an approach that has meanwhile been successfully tested many times. The practical application of this methodology will be presented here using the example of a constitutive model that takes into account the triaxial stress-strain behavior of crushed salt. The individual development and validation steps are documented for the crushed salt model, EXPO-COM, newly developed at the Chair for Waste Disposal Technologies and Geomechanics. Validation of the constitutive model is performed by means of a back-analysis of triaxial long-term crushed salt compaction tests as follows: Test TK-031 of the German Federal Institute for Geosciences and Natural Resources (Bundesanstalt für Geowissenschaften und Rohstoffe, BGR) for isotropic load conditions Tests V1 (dry), V2 (w=0.1 %), and V3 (wet) of the German Society for Plant and Reactor Safety (Gesellschaft für Anlagen- und Reaktorsicherheit gGmbH, GRS) for different stresses and temperature levels as well as humidity Test TUC_V2 of the Clausthal University of Technology (TUC) for isotropic and deviatoric stress conditions. The TUC_V2 test characterizes, in the context of the methodology for the structured development and validation of multiphysical constitutive models, an innovative test method geared towards constitutive model development, in which the loading boundary conditions specified in the test guarantee the isolated analysis of individual factors influencing compaction behavior (Fig. 1). A description of the tests and test techniques that are still required for the full development and validation of the EXPO-COM constitutive model planned as part of the KOMPASS II research project is given together with a description of methodological guidelines relating to requirements on reliability, functionality, practicability, and validity ranges of the EXPO-COM constitutive model (Fig. 2). As a result of the subsequently possible comparison of experimentally validated and not yet validated dependencies or process variables, a validation status is defined for the constitutive model EXPO-COM. This validation status shows which factors influencing the THM-coupled material behavior of crushed salt are currently sufficiently realistically taken into account, and which influencing factors cannot yet be validated by the constitutive model. The main objectives of the tests to be carried out as part of the KOMPASS II research project include: Continued validation based on the systematized database to be created in KOMPASS II. Testing of the constitutive model in the context of numerical analyses of the predictive quality and numerical stability of the constitutive model for in situ relevant stress boundary conditions, prediction times and material properties.

Superplastic deformation mechanical behavior and constitutive modelling of a near-α titanium alloy TNW700 sheet

TNW700 is a newly developed near-α high temperature titanium alloy and has great application potential in the aerospace industry owing to excellent creep strength and short-term service temperature up to 700 °C. The superplastic tensile deformation behavior and constitutive model of TNW700 alloy in the temperature range of 900–975 °C and strain rate range of 0.0005–0.01s−1 were investigated. Results indicated that TNW700 alloy exhibits significant work hardening behavior, which may be related to dynamic growth of β grains, dislocation evolution, and silicide precipitates. In addition, work hardening coefficient (n) as well as the critical strain between flow hardening and softening increases with decreasing strain rate, and first increases and then decreases with increasing deformation temperature. TNW700 alloy exhibits excellent superplasticity at 900 °C–950 °C corresponding to strain rate sensitivity exponent (m) greater than 0.3, and expresses poor superplasticity at 975 °C with lower m value. The m value decreases monotonously with strain owing to decrease of grain boundary sliding contribution caused by dynamic grain growth of β grains. The deformation activation energy increases with decreasing strain rate due to the change of deformation mechanism. A phenomenological constitutive model considering strain hardening, strain rate hardening and temperature softening was proposed and material constants were calibrated by true stress-strain data. The constitutive model was implemented into Abaqus code by UHARD subroutine to simulate the superplastic forming of cone parts, and thickness distribution and bulging heights under different forming time were used to verify the validity of constitutive model.

Particle breakage evolution of coral sand using triaxial compression tests

Particle breakage continuously changes the grading of granular materials and has a significant effect on their mechanical behaviors. Revealing the evolution pattern of particle breakage is valuable for development and validation of constitutive models for crushable materials. A series of parallel triaxial compression tests along the same loading paths but stopped at different axial strains were conducted on two coral sands with different particle sizes under drained and undrained conditions. The tested specimens were carefully sieved to investigate the intermediate accumulation of particle breakage during the loading process. The test results showed that under both drained and undrained conditions, particle breakage increases continuously with increasing axial strain but exhibits different accumulating patterns, and higher confining pressures lead to greater particle breakage. Based on the test results, the correlations between particle breakage and the stress state as well as the input energy were examined. The results demonstrated that either the stress state or input energy alone is inadequate for describing the intermediate process of particle breakage evolution. Then, based on experimental observation, a path-dependent model was proposed for particle breakage evolution, which was formulated in an incremental form and reasonably considers the effects of the past breakage history and current stress state on the breakage rate. The path-dependent model successfully reproduced the development of particle breakage during undrained triaxial compression using the parameters calibrated from the drained tests, preliminarily demonstrating its effectiveness for different stress paths.

Creep constitutive model considering the overstress theory with an associative viscoplastic flow rule

Abstract Tunnel excavation in squeezing ground is very challenging due to the difficulty in making reliable predictions at the preliminary design stage. Tunnel response in squeezing ground is made possible by employing creep constitutive models. However, literature outlines the limitations of the conventional creep constitutive models in estimating delayed deformations due to the squeezing mechanism. Hence this paper presents, a fractional-order derivative viscoelastic viscoplastic (FDVP) constitutive model capable of estimating delayed deformations characterized by squeezing. The FDVP constitutive equations are derived as an extension to the Burgers model and adjusted Perzyna overstress function with an associated viscoplastic flow rule. The constitutive model validation and verification are conducted by using the experimental data obtained from literature and monitored tunnel convergence data, respectively. Thereafter, the constitutive equations are implemented in FLAC3D and applied to simulate deformations responsible for squeezing within a tunnel employing in-built constitutive models for verification purposes. The constitutive model shows very good agreement with experimental data and yields close results with monitored tunnel convergence data. The model can be successfully used in numerical code for tunnel stability analysis in squeezing ground.

The effects of base motion variability and soil heterogeneity on lateral spreading of mildly sloping ground

Centrifuge modeling has been used to observe some key characteristics of liquefiable soils during seismic motions. If carefully conducted, the results of centrifuge tests can be used for validation of constitutive models and numerical modeling tools. However, a thorough evaluation of numerical models requires knowledge of the soil properties and the uncertainties associated with these properties. Moreover, the base excitations achieved in centrifuge tests often vary from the target base excitation, and a fair evaluation of the quality of blind prediction of a centrifuge test requires an account of the uncertainties associated with the achieved base motion. This paper presents an analysis of the effects of the inherent variability present in the soil density and base motion on the lateral spreading of mildly sloping ground. The analysis combines fully-coupled non-linear finite element modeling with Monte Carlo simulation. The stochastic analysis is based on the variabilities observed in the density of the soil specimens and in the achieved base motions of the centrifuge tests conducted for the Liquefaction Experiments and Analysis Projects (LEAP): LEAP-GWU-2015 and LEAP-UCD-2017. The two-surface plasticity model for sand is used to model the soil response. The model is calibrated against element tests performed on Ottawa-F65 sand to determine its liquefaction strength. The finite element model is pre-validated through deterministic simulation of the centrifuge experiments conducted during the LEAP project. The sources of variability are identified and their magnitudes are quantified based on the results obtained from the LEAP centrifuge experiments. First, the effects of the soil spatial variability are presented. Then, the effects of the base motion variability are discussed. Finally the combined effects of the variability in the soil density and base motion are evaluated. The results obtained from the stochastic analysis are compared with the variability in the soil response observed in the centrifuge experiments. The results obtained from this study show that by carefully modeling the different sources of variability, the stochastic analysis was able to model the observed variability in the lateral displacement of the centrifuge experiments. The results obtained confirm the observation that the lateral displacement of liquefiable soil is more sensitive to the base excitation variability than the variability in the soil density.

Validation of constitutive models for experimental stress-strain relationship of high-strength steel sheets under uniaxial tension

The constitutive relationship between stress and strain is one of the important issues in numerical simulation of metal forming. For steel, there are two kinds of constitutive models wildly used. One is power law like Ludwik and Swift. The other is saturation models like Voce and Hockett-Sherby. It is necessary to determine the most appropriate model and parameters for newly developed high strength steels. In order to describe the ultra-high strength dual phase and quenching and partitioning steels, uniaxial tensile tests with the aid of digital image correlation techniques were performed to analyse the strain field over the whole gauge section as well as the element close to the necking point. Through experimental data analysis and numerical fitting, the validity of different models have been confirmed. It shows that equation of Hockett-Sherby model has the best fitting accuracy and high strength steels require a model with more parameters. The extrapolated weighting coefficient of combined Swift and Hockett-Sherby models is characterized, which is proved to improve the accuracy of the numerical simulation of forming of ultra-high strength steels based on the conventional tensile tests.

A model‐based strategy for safety assessment of a robot arm interacting with humans

AbstractImpact and the resulting contact forces can be determined by dynamic simulation once a validated model for the robot and of the contact area of the human is available. Methods for the identification of relevant geometric and dynamic parameters of the robot model are well established. While the experimental validation of constitutive models for human body contact is still topic of ongoing research, which gave rise to the ISO/TS 15066 guidelines, adequate models are already available for computational simulation of human‐robot contact scenarios. However, dynamical simulations cannot be applied to exhaustively explore and assess all possible contact scenarios with the robot workspace. In this paper, first the model used for impact simulation is described and simulation as well experimental results are reported for contact at a predefined location. Then, the ability of the presented model to predict the measured contact force is discussed.

Constitutive modeling and strain hardening of CoCrFeNiAlx high-entropy alloys

The mechanical behaviors of CoCrFeNiAlx (x = 0, 0.3) high-entropy alloys are investigated under quasi-static loading. Evolution of phases and microstructures is analyzed by using the x-ray diffraction, scanning electron microscope and transmission electron microscopy. A constitutive model based on the crystal plasticity theory is presented and an explicit algorithm is constructed for calculation. A dislocation-density-based description of hardening model is used to describe the strain hardening behaviors. Constitutive model validation is performed by comparing numerical results with experimental data. Evolution of dislocation density with various slip systems during plastic deformation is established to reveal the effect of Al addition on the CoCrFeNi based HEAs.

In vivo stress relaxation of human scalp

ObjectiveConduct a first in vivo study on the large deformation stress relaxation behavior of the human scalp. MethodsThis study was conducted during Mohs micrographic surgery of the scalp of 14 patients aged 59–90 with wounds initially ranging from 9 to 41 mm wide. The initial wound diameter was measured under zero applied force. Then, the force required to close each wound using a single size 1 nylon suture and a SUTUREGARD suture retention device was measured, after which the suture was then locked in the retention device at fixed displacement. At time points of 300 s, 600 s, and 1800 s, the suture retention device was released, and the wound opening was again recorded at zero force, and the force required to close the wound was recorded. ResultsThe average wound closure force relaxed by 44% and 65% after 300 s and 1800 s, respectively. Average wound width decreased 30% and 42%, after 300 s and 1800 s, respectively, due to creep deformation. Furthermore, all wounds relaxed to be below 15 N of closure force after 600 s, which is considered the maximum clinically acceptable force. A relaxation time of ∼270 s and a threshold force for creep of ∼5 N was found. SignificanceResults of this study provide the first quantitative clinical guidance for efficient scalp closure of large wounds by creep deformation and stress relaxation. Furthermore, the methodology developed here can be used as a basis for future in vivo studies of the stress relaxation and creep deformation of human scalp, which in turn can provide data for the development and validation of constitutive models for scalp deformation.

A numerical study of isotropic and anisotropic constitutive models with relevance to healthy and unhealthy cerebral arterial tissues

This paper presents an analysis of hyperelastic constitutive models for continuous bodies both from a modeling and numerical point of view. Contributions are made within the context of finite element numerical simulations. Numerical results with relevance to flows in the cardiovascular system are outlined in the case of a sophisticated fluid–structure interaction problem, in specific complex geometries of anatomically accurate cerebral arteries in diseased state. In this regard, the work carefully outlines the numerical validation of constitutive models for healthy and unhealthy cerebral arterial tissues by means of simulations of static inflation tests on an idealized specimen of anterior cerebral artery (ACA). The healthy tissue is described by means of isotropic and anisotropic models that, are fitted with respect to experimental data describing the mechanical behavior of the ACA; the numerical results are presented highlighting the most important numerical aspects influencing the correct and efficient simulation of the mechanics of continuous bodies such as, for instance, the arterial wall. We further consider numerical simulations of unhealthy conditions of the tissue by taking into account different levels of weakening of its mechanical properties. Taking the cerebral cardiovascular system as a challenging test problem, we focus on the study of the effects of the imposed mechanical levels of degradation on kinematic quantities of interest by simulating static inflation tests for the different models. This work does not aim to propose a new mathematical model for the mechanical damage occurring at the onset of cardiovascular diseases such as cerebral aneurysms. The modeling and numerical techniques presented may be applied to a wide range of problems, equally challenging to that of the cardiovascular system with complex structural models and fluid–structure coupling.

Utilização da técnica de birrefringência em reômetro multipasse para a diferenciação de grades de poliestireno cristal

O entendimento de como as propriedades reológicas afetam o comportamento dos polímeros nas operações de processamento, por meio de diferentes técnicas experimentais, é de fundamental importância para ser possível prever e avaliar a estrutura final destes materiais. Neste contexto, o objetivo deste trabalho é aplicar a técnica de birrefringência para diferenciar dois grades de poliestireno cristal. Foram realizados experimentos em um reômetro multipasse que permitiram a aquisição de imagens de birrefringência, que representam o campo de tensão do escoamento, e obteve-se a queda de pressão durante os experimentos. Ao se compararem os padrões de birrefringência dos dois poliestirenos foi possível distinguir os materiais e verificar que o escoamento da amostra de maior massa molar é mais complexo, com maior birrefringência e tensão mais elevada. Os resultados obtidos, além de contribuírem para a caracterização reológica, podem ser empregados no estudo comparativo de modelos constitutivos e desenvolvimento de códigos computacionais.

The mechanical behaviour of poly(vinyl butyral) at different strain magnitudes and strain rates

The mechanical behaviour of poly(vinyl butyral) (PVB) at small ( 200%) is investigated experimentally over a range of strain rates to provide data for the development and validation of constitutive models. The small-strain response is investigated using dynamic mechanical analysis at frequencies from 1 to 100 Hz and temperatures from −80 to 70 °C. It is found that a generalised Maxwell model adequately describes the material behaviour in the small-strain regime. The large-strain response is investigated using a high-speed servo hydraulic test machine at strain rates from 0.2 to 400 s−1. It is found that the PVB response is characterised by a time-dependent steep initial rise in stress followed by a hyperelastic type response until failure. No current material model completely captures this time-dependent behaviour at large strains.

Static Performance Analysis on Combined Truss with Steel Tube and Concrete-Filled Steel Tube Based on Total Strain Crack Constitutive Model

Based on the total strain crack constitutive model and the available testing data, finite element model on three trusses were established by the finite element procedure MIDAS/FEA and the analysis were executed in order to verify the validity of constitutive model and study the static performance of combined truss. The results show that the finite element model based on total strain crack constitutive can reflect the static performance of combined truss and can carry the affective parameters analysis, which can offer theory evidence for engineering application of combined truss. The failure of three trusses were due to joint failure, however the failure modes were different and changed by the concrete filled in chord. The bearing capacity of three trusses was controlled by the jionts and the strength and stiffness of jionts were increased by the concrete filled in the chord, therefore the bearing capacity of trusses was increased while the deformation was decreased. In combined truss with steel tube and concrete filled steel tube, the concrete-filled steel tube joints can improve the bearing capacity and the steel tube joint can satisfy the requirements of plastic deformation, which have obvious advantages in the engineering application.

Using Hertzian Indentation to Understand the Strength and Ballistic Resistance of Silicon Carbide

This article presents an initial evaluation of the usefulness of spherical or Hertzian indentation for the determination and/or validation of constitutive models and for a potential link to ballistic resistance (interface defeat). Recent advancements in producing more confident elevated stress levels in Hertzian indentation make the usefulness of this test much more feasible. There are very few experimental techniques that can produce the high stresses, strains, and pressures produced in Hertzian indentation tests. Additionally, they are also relatively simple, repeatable, timely, and inexpensive. There is still the disadvantage that the stresses, strains, and pressures are not explicit outputs of the experiments requiring the constitutive response to be inferred by performing computations and comparing the computed force–deflection results to the experiment. Preliminary results indicate that Hertzian indentation can be used to help define the constitutive response but it is still uncertain if it can be used to rank a ceramic's ability to produce interface defeat.

019 高速炉機器設計のための非弾性解析に基づく評価手法の開発 : (3)構成モデルの妥当性検証(GS3-1 一般セッション)

019 高速炉機器設計のための非弾性解析に基づく評価手法の開発 : (3)構成モデルの妥当性検証(GS3-1 一般セッション)

A new approach for analyzing circular tunnel in strain-softening rock masses

Although it is relatively a simple problem to study circular tunnels excavated in isotropic rock masses under hydrostatic stress fields, the results of stresses and displacements around circular opening can be insightful for ground support design and stability evaluation. Moreover, the solutions are useful in the validation of constitutive models and numerical codes. In the several decades past, many scholars studied this kind of problem in the Mohr–Coulomb (M–C) media, the Hoek–Brown (H–B) media and the generalized H–B media and considered the elastic–perfectly plastic, elastic–brittle–plastic and strainsoftening models with associated flow and non-associated flow rules. According to the existing literature surveys, most [1–13] of the researches are about elastic–perfectly plastic and elastic– brittle–plastic models because closed-form solutions (or numerical solution) can be easily obtained under certain assumptions. However, Hoek and Brown [14] suggest that the average quality rock masses behave in a strain-softening mode in the field of underground rock engineering. Therefore, it is of practical importance to study the mechanical behavior of normal rock masses with strain-softening behavior. By means of the classical theory of plasticity, materials with perfectly brittle–plastic and perfectly plastic constitutive model can be easily described and simulated in numerical methods such as the finite element method [15,16], etc. But it is more difficult to model the strain-softening material due to the negative slope in the stress–strain coordinates. Even for the above-mentioned excavation of circular tunnel in strain-softening materials, fewer attempts have been made [17–23] thus far. The reason is that the relationship among the stresses, plastic strain and the strength

Instrumented anvil-on-rod tests for constitutive model validation and determination of strain-rate sensitivity of ultrafine-grained copper

Anvil-on-rod impact tests were performed on as-received (cold-rolled) OFHC copper rods and copper processed by 2- or 8-passes of equal channel angular pressing (ECAP). The average grain size ranged from ∼30 μm for the as-received sample to ∼440 nm for the 8-pass sample. The dynamic deformation states of the samples were captured by high-speed digital photography and velocity interferometry was used to record the sample back (free) surface velocity. Computer simulations utilizing AUTODYN-2D hydrocode with the Johnson–Cook constitutive model were used to generate free surface velocity traces and transient deformation profiles for comparison with the experimental data. The comparison of experimental results with AUTODYN simulations provided a means for extracting the strain-rate sensitivity of copper as a function of grain size. Strain-rate sensitivity was found to increase as grain size decreased.