Multiaxial Constitutive Model Research Articles

Multiaxial stress-fractional plasticity model for anisotropically overconsolidated clay

Clays in the field can experience various consolidation histories, e.g., isotropic or anisotropic overconsolidation, before subjected to three-dimensional loads exerted by the neighbouring geotechnical infrastructures. Correct representation of the multiaxial strength and deformation behaivour of anisotropically overconsolidated clay is a prerequisite for engineering design. Accordingly, a multiaxial constitutive model is developed in this study, by employing the anisotropic stress-fractional plasticity two surfaces. The consolidation history is represented by using an inclined bounding surface, while the loading behaviour in multiaxial stress space is captured through the stress transformation of an inclined loading surface. The incorporation of such stress transformation method overcomes the difficulty in obtaining the fractional derivative of the Lode's angle. To capture the dilatancy behaviour of anisotropically overconsolidated clay, a multiaxial state-dependant nonassociated plastic flow rule is developed by only using the stress-fractional gradient of the loading surface, which significantly differs from the prior attempts using traditional plasticity. In addition, a multiaxial rotational hardening law for the bounding/loading surface is suggested to characterise the shearing-induced fabric destruction of anisotropically overconsolidated clay. Finally, test results of two different clays under various consolidation histories and stress paths are adopted to validate the developed model. It is found that the predicted strength and deformation behaviour of clay depends the Lode's angle and anisotropic consolidation path, which agrees with the corresponding test results. Specifically speaking, the hardening and softening behaviour of clay induced at seven different overconsolidation ratios ranging from 1 to 10 can be quantified, and the multiaxial strength behaviour of clay loaded from a wide range of Lode's angles ranging from 0° to 60° can be also quantified.

Discontinuous plastic flow in stainless steels subjected to combined loads at extremely low temperatures

In the present paper, the question of the mechanism of discontinuous plastic flow (DPF) occurring at extremely low temperatures (in the proximity of absolute zero), is for the first time raised in the context of kinematically controlled combined loads (independent control of displacement and rotation) and non-proportional loading paths. In order to identify the multiaxial stress state during DPF, a unique set-up for testing tubular samples under kinematically controlled traction and torsion in liquid helium (4.2 K) has been developed. The results of tests performed on grade 304 stainless steel thin-walled tubular samples subjected to combined loads (traction and torsion) in the proximity of absolute zero are for the first time reported. These novel results confirm the assumptions accepted when building the multiaxial constitutive model of discontinuous plastic flow, namely, the production of lattice barriers, the pile-ups of dislocations and the criterion of their collective failure, as well as the assumption that the serrations may be recorded by force and torque transducers independently. Thus, the numerically implemented model allows to reproduce the observed serrations, and to redistribute them between the loading directions.

Calibration of Concrete Damaged Plasticity Model parameters for shear walls

ABSTRACT Reinforced concrete structures are relatively complex to analyze, with nonlinear effects like cracking, crushing, steel yielding, aggregate interlock, dowel effect, concrete-rebar interaction and so on. The concrete damaged plasticity CDP model is a consolidated smeared-crack model which accounts for multiaxial behavior with good agreement to experimental results. One particular relevant application which benefits greatly from such feature is the shear wall, as shear stress significantly influences its overall behavior, therefore multiaxial constitutive models and three-dimensional finite elements usage consist in a fitting modeling approach. Reinforced concrete shear walls are structures especially useful for lateral force-resisting systems, as they provide ductility, stiffness and strength. Albeit CDP is widely applied, its parameters are not consensus in the literature, which represents a relevant research gap. The present work considers and compares CDP parameters from relevant literature, in order to calibrate those parameters for the case of reinforced concrete shear walls. To this purpose, four wall experiments related in the bibliography are modeled using solid finite elements for concrete and trusses for rebars using commercial package ABAQUS. All walls are flexure-controlled with aspect ratio greater than 2.0. By varying those parameters and comparing obtained force vs. displacement curves and interesting values attained, like yield lateral force and displacement, stiffness and maximum lateral force, it is settled a set of parameters with acceptable response focusing in the post-peak response based on the lower estimated error of displacement capacity. Those parameters agree reasonably with literature, although it is possible that obtained calibration is restricted to flexure controlled shear walls scope. It is possible that usage of trusses to represent reinforcement does not consider dowel effect, so a suggestion for future studies is to change trusses for elements with transverse stiffness, like beams or solids.

Deterministic ground motion simulations with shallow crust nonlinearity at Garner Valley in Southern California

AbstractWe present deterministic ground motion simulations that account for the cyclic multiaxial response of sediments in the shallow crust. We use the Garner Valley in Southern California as a test case. The multiaxial constitutive model is based on the bounding surface plasticity theory in terms of total stress and is implemented in a high‐performance computing finite‐element parallel code. A major advantage of this model is the small number of free parameters that need to be calibrated given a shear modulus reduction curve and the ultimate soil strength. This, in turn, makes the model suitable for regional‐scale simulations, where geotechnical data in the shallow crust are scarce. In this paper, we first describe a series of numerical experiments designed to verify the model implementation. This is followed by a series of idealized large‐scale simulations in a 35 26 4.5 km domain that encompasses the Garner Valley downhole array site, which is an instrumented and well‐characterized site in Southern California. Material properties were extracted from the Southern California Earthquake Center Community velocity model, CVM‐S4.26, considering its optional geotechnical layer, while the modulus reduction curves and soil strength were selected empirically to constrain the nonlinear soil model parameters. Our nonlinear simulations suggest that peak ground displacements within the valley increase relative to the linear case, while peak ground accelerations can increase or decrease, depending on the frequency content of the excitation. The comparisons of our simulations against hybrid three‐dimensional–one‐dimensional site response analyses suggest the inadequacy of the latter to capture the complexity of fully three‐dimensional simulations.

A multiaxial constitutive model for fibre-reinforced sand

Fibre orientation in fibre-reinforced sand (FRS) is highly anisotropic due to compaction during sample preparation or field construction. This makes the mechanical behaviour of FRS, such as strength and dilatancy, highly dependent on the strain increment direction. While constitutive models that are able to capture such anisotropic behaviour of FRS have been proposed for conventional triaxial compression and extension conditions only, this paper proposes for the first time a full anisotropic model for FRS formulated in the general multiaxial stress space. The new model is developed based on the assumption that the strain of FRS is dependent on the deformation of the sand skeleton. In turn, the fibre presence affects the void ratio and effective stress of the soil skeleton, which governs the elastic properties, dilatancy and plastic hardening of the FRS. The effect of anisotropic fibre orientation on the FRS behaviour is considered through an anisotropic variable which characterises the relative orientation between the loading direction tensor and fibre orientation tensor. The model does not require direct measurement of the stress–strain relationship of individual fibres. Although the model is for FRS under multiaxial loading conditions, the parameters associated with the fibre inclusion can be determined based on triaxial test results, provided that the orientation of fibres is known. The model has been used to predict the stress–strain relationship of fibre-reinforced Hostun RF (S28) sand under multiaxial loading conditions. Satisfactory agreement between the experimental data and model predictions is observed.

Multidirectional cyclic shearing of clays and sands: Evaluation of two bounding surface plasticity models

Seismic site response analysis (SSRA) is typically performed considering only one horizontal component of earthquake excitation. In many cases, however, two or three components are needed for the analysis to properly account for the true multidirectional nature of seismic loading. In this type of analysis, it is essential to use multiaxial constitutive models that can realistically describe the stress-strain response of soils. Development and validation of such constitutive models are essential steps toward this goal. Fortunately, a large quantity of experimental data from multidirectional cyclic shear tests is available and can provide physical basis for validating such models. This paper focuses on evaluation of two members of the SANICLAY and SANISAND families of constitutive models for simulating the response of clay and sand, respectively, when subjected to multidirectional cyclic shearing. The models have anisotropic elasto-plastic formulation, within the framework of critical state soil mechanics, and follow the bounding surface plasticity theory. They are calibrated and evaluated against experimental data on Gulf of Mexico clay and Monterey No. 0/30 sand in undrained multidirectional cyclic shear tests, including linear, circular/oval, and figure-8 loading paths. This study provides a basis for evaluation of the capabilities of these models in multidirectional shearing, thereby paving the way towards future applications in multidirectional SSRA.

Visco-plastic constitutive model considering non-proportional hardening at elevated temperature under multiaxial loading

ABSTRACTBased on the Chaboche unified visco-plastic constitutive model, a visco-plastic constitutive model which can take into account non-proportional hardening was proposed for nickel-base alloy at elevated temperature under multiaxial loading. In the proposed multiaxial visco-plastic constitutive model, the non-proportional hardening is considered as a change of kinematic hardening property. The kinematic hardening parameters which can evolve exponentially with the cumulative plastic strain and rotation factor resulted from loading path were proposed to take into account the non-proportional hardening at high temperature under non-proportional loading. Experimental verification showed that the proposed model can accurately predict the peak stresses and the hysteresis loop compared with the original model during the tension-torsion loading process for nickel-base alloy at elevated temperature under non-proportional loading.

Effect of grout properties on shear strength of column base connections: FEA and analytical approach

Concrete grout is used in most column base connections to facilitate the construction process and to ensure that full contact is achieved between the steel plate and the concrete pedestal. However, insignificant attention has been given to its use and performance while there is a lack of clear understanding towards its contribution to the shear strength of column base connections. A comprehensive finite element (FE) study is presented herein investigating the shear capacity of the column base connection on the grout thickness and strength. 3D FE models incorporate important behavioural aspects including the surface interaction and multi-axial constitutive models of the assemblages. The results of the investigation indicated that the introduction of grout improves the behaviour and strength of the column base connections significantly by developing a different load path system consisted of the grout strut, the friction between the base plate and grout, and the tension in the anchor rod due to second order effects. It is found that the current design codes of practice do not consider the positive influence of grout and lead to very conservative shear strengths. Furthermore, the paper proposes a mathematical equation to account for the lateral displacement which is overlooked in the current international regulations.

Thermodynamic-Based Elastoplasticity Multiaxial Constitutive Model for Concrete at Elevated Temperatures

AbstractIn the current study, a multiaxial plastic-damage constitutive model for concrete at different temperatures is developed. The model is implemented in three-dimensional finite element analys...

New multi-axial constitutive models for large elastic deformation behaviors of soft solids up to breaking

A hyperelastic model is proposed to characterize large elastic deformation behaviors of soft solids. Novelties in four respects are incorporated in this model, namely, (i) general compressible deformations may be treated and, accordingly, the usually-assumed incompressibility constraint and associated issues may be bypassed; (ii) applicability for all kinds of material samples may be automatically ensured, in the sense that any given test data for three deformation modes may be exactly fitted, including uniaxial, equi-biaxial and plane-strain extension; (iii) model parameters of direct physical meanings may be provided to characterize both strain-stiffening and softening effects; and (iv) breaking behavior may be simulated. Numerical results for model validation are in good agreement with Treloar’s classic data for rubbers and with extensive data for various kinds of polymer gels.

Prediction of microstructure and ductile damage of a high-speed railway axle steel during cross wedge rolling

Microstructure and ductile damage have a significant influence on the deformation behavior of high-speed railway axles during hot cross wedge rolling (CWR) and its final performance. In this study, based on the continuum damage mechanics, a multiaxial constitutive model coupling microstructure and ductile damage was established to predict the evolution of microstructure and ductile damage of 25CrMo4 during hot CWR processes. Material constants within the multiaxial constitutive model were determined by Genetic Algorithm (GA) optimization techniques from thermo-mechanical test data. The derived multiaxial constitutive model was embedded into the DEFORM-3D software through a user subroutine. FE simulation of CWR was performed to predict the microstructure evolution and ductile damage. CWR experiments were also carried out to validate the proposed model. The predicted grain size and ductile damage agree well with the experimental results. Good agreements indicate that the derived multiaxial constitutive model is reliable and can be used to predict the evolution of microstructure and ductile damage during CWR process.

Strain localization during discontinuous plastic flow at extremely low temperatures

• The paper deals with an extended, physically based, multiaxial constitutive model of discontinuous plastic flow, including new feature of strain localization at near 0 K temperatures in polycrystalline materials. • Another new feature defines the drop of stress being entirely determined by dislocations density before and after the serration. • Regular way of nucleation and free unconstrained glide of slip bands is observed within the sample, in the absence of phase transformation. • Contrary to former views, strong coupling of discontinuous plastic flow with fcc-bcc phase transformation in metastable materials is observed. The phenomenon of strain localization in the course of discontinuous plastic flow (DPF) at extremely low temperatures is investigated. DPF is observed mainly in fcc metals and alloys strained in cryogenic conditions, practically down to absolute zero. These materials undergo at low temperatures a process similar to dynamic strain ageing, manifested by the so called serrated yielding (DPF). DPF is attributed to the mechanism of local catastrophic failure of lattice barriers (including Lomer–Cottrell locks), under the stress fields related to the accumulating edge dislocations. Failure of LC locks leads to massive motion of released dislocations, accompanied by step-wise increase of the strain rate (macroscopic slip) and drastic drop of stress. Recent experiments indicate strong strain localization in the form of shear bands propagating along the sample. The plastic power dissipated in the shear band is partially converted to heat, which results in a local drastic increase of temperature promoted by the so-called thermodynamic instability (nearly adiabatic process). The Dirac-like temperature function is measured by two thermometers located in the gage length of the sample. Spatio-temporal correlation indicates smooth shear band propagation, as long as the process of phase transformation remains on hold. A physically based multiaxial constitutive model presented in the paper describes both DPF and strain localization, accompanied by temperature distribution represented by Green-like solution of heat diffusion equation. The model accounts for the thermodynamic background, including phonon mechanism of heat transport, accompanied by specific heat vanishing with the temperature approaching absolute zero. Experimental identification of parameters of the constitutive model is carried out. A projection of the model to the range where the phase transformation takes place is discussed.

Constitutive modeling of human saphenous veins at overloading pressures

In the present study, inflation tests with free axial extension of 15 human vena saphena magna were conducted ex vivo to obtain data suitable for multi-axial constitutive modeling at overloading conditions (pressures up to approximately 15kPa). Subsequently the data were fitted with a hyperelastic, nonlinear and anisotropic constitutive model based on the theory of the closed thick-walled tube. It was observed that initial highly deformable behavior (up to approximately 2.5kPa) in the pressure–circumferential stretch response is followed by progressive large strain stiffening. Contrary to that, samples were much stiffer in longitudinal direction, where the observed stretches were in the range 0.98–1.03 during the entire pressurization in most cases. The effect of possible residual stress was evaluated in a simulation of the intramural stress distribution with the opening angle prescribed to 0°, 10°, 20°, 30°, 40°, and 50°. The result suggests that the optimal opening angle making the stress distribution through the wall thickness uniform is about 40°. The material parameters presented here are suitable for use in mechanobiological simulations describing the adaptation of the autologous vein wall after bypass surgery.

A plastic-damage model for concrete in fire: Applications in structural fire engineering

The research aims at developing a new multiaxial constitutive model for concrete in the fire situation. In addition to validity at the material level, a crucial feature of a constitutive model is the applicability at the structural level; yet for concrete in fire there remains a serious lack of models combining reliability and robustness. The theoretical aspects and validation of the new model, which rely on a plastic-damage formulation, have been the subject of a former publication; they are briefly summarized here. This paper explores the capabilities of the concrete model for being used in a performance-based structural fire engineering framework. Several examples of numerical simulations by non-linear finite element method are discussed, with emphasis on practical applications that are demanding for the material model. In particular, it is shown that the simulations using the new concrete model succeed in capturing, at ambient temperature, the crack pattern in a plain concrete specimen and the influence of the loading path on reinforced concrete (RC) slabs. At high temperature, the presented applications include a RC slab subjected to furnace fire and a large-scale composite steel–concrete structure subjected to natural fire. In the numerical analyses, no parameter calibration was required on the particular concrete type, except for the uniaxial strengths and tensile crack energy which are to be defined case-by-case. The results illustrate the reliability and numerical robustness of the model. Also, they suggest that satisfactory prediction of structural behavior in fire can be obtained when no additional data is available on the specific properties of the particular concrete mix that is used in the project, as is often the case in practice, by using standard values of parameters.

Multiaxial constitutive model of discontinuous plastic flow at cryogenic temperatures

FCC metals and alloys are massively used in cryogenic applications down to the temperature of absolute zero, because of suitable physical and mechanical properties including high level ductility. Many of these materials undergo at low temperatures a process similar to dynamic strain ageing, reflected by the so-called discontinuous plastic flow (DPF, serrated yielding). The physically based multiaxial constitutive model presented in the paper constitutes a generalization of the previous uniaxial model that proved efficient in describing the plastic flow instabilities occurring at extremely low temperatures. The model takes into account thermodynamic background, including the phonon mechanism of heat transport and thermodynamic instability caused by specific heat vanishing with the temperature approaching absolute zero. The DPF is described by the mechanism of local catastrophic failure of lattice barriers (for instance Lomer-Cottrell locks) under the stress fields related to the accumulating edge dislocations. The failure of LC locks leads to massive motion of released dislocations accompanied by step-wise increase of the strain rate (macroscopic slip). In the present paper the plastic flow discontinuity associated with the proportional loading paths is studied. Identification of parameters of the constitutive model is based on the experimental data collected during several campaigns of tensile tests carried out on copper and stainless steel samples immersed in liquid helium (4.2K).

A multiaxial constitutive model for concrete in the fire situation: Theoretical formulation

This paper aims to develop a multiaxial concrete model for implementation in finite element software dedicated to the analysis of structures in fire. The need for proper concrete model remains a challenging task in structural fire engineering because of the complexity of the concrete mechanical behavior characterization and the severe requirements for the material models raised by the development of performance-based design. A fully three-dimensional model is developed based on the combination of elastoplasticity and damage theories. The state of damage in concrete, assumed isotropic, is modeled by means of a fourth order damage tensor to capture the unilateral effect. The concrete model comprises a limited number of parameters that can be identified by three simple tests at ambient temperature. At high temperatures, a generic transient creep model is included to take into account explicitly the effect of transient creep strain. The numerical implementation of the concrete model in a finite element software is presented and a series of numerical simulations are conducted for validation. The concrete behavior is accurately captured in a large range of temperature and stress states. A limitation appears when modeling the concrete post-peak behavior in highly confined stress states, due to the coupling assumption between damage and plasticity, but the considered levels of triaxial confinement are unusual stress states in structural concrete.

A Multiaxial Damage Statistic Constitutive Model for Concrete

In order to apply the uniaxial damage evolution equation that established with the variable of strain to the multiaxial damage quantitative analysis, this paper bases on the Hsieh-Tang-Chen four-parameter failure criterion and adopts the way of making the triaxial equivalent strain combining with the uniaxial damage evolution equation to analyze and deduce the uniaxial damage evolution equation of SRHSHPC, and which is expanded to multiaxial condition as well. A function considered triaxial stress state and a related correction value are suggested, then, improving the damage evolution equation from triaxial to multiaxial form, finally proposing the multiaxial damage statistic constitutive equation for concrete, taking numerical simulation with the complete decoupling method and the result shows that the model is effective.

Study on Multi-Axial Mechanical Properties of a Polyurethane Foam and Experimental Verification

In order to investigate the multi-axial mechanical properties of a kind of PU (polyurethane) foam, some experiments in different loading conditions including uni-axial tension, uni-axial compression, hydrostatic compression and three-point bending were conducted. It is shown that the hydrostatic component influences yield behavior of PU foam, the yield strength and degree of strain hardening in hydrostatic compression exceed those for uni-axial compression. In terms of the differential hardening constitutive model, the evolution of PU foam yield surface and plastic hardening laws were fitted from experimental data. A finite element method was applied to analyze the quasi-static responses of the PU foam sandwich beam subjected to three-point bending, and good agreement was observed between experimental load-displacement responses and computational predictions, which validated the multi-axial loading methods and stress-strain constitutive model parameters. Moreover, effects of two foam models applied to uni-axial loading and multi-axial loading conditions were analyzed and compared with three-point bending tests and simulations. It is found that the multi-axial constitutive model can bring more accurate prediction whose parameters are obtained from the tests above mentioned.

Length Effects in Tensile Strength in the Orthogonal Directions of Structural Composite Lumber

Abstract The natural variation of strength properties within brittle materials leads to the phenomenon of size effect which causes the expected strength of a material to decrease as the stressed volume increases. An important implication of size effect is that size adjustment parameters must be incorporated into multi-axial constitutive and failure models used in numerical simulations such as those made using the finite element method. These size adjustments are based on the sizes of the individual elements, rather than the size of the structural member. This experimental study seeks to determine whether such a size effect is present in the orthotropic principal material directions of parallel strand lumber (PSL) and laminated veneer lumber (LVL), and, if the effect is present, to quantify it. Tensile tests were performed on specimens of different test section lengths oriented in the longitudinal, transverse, and through-thickness (PSL only) directions and size effect adjustment parameters were estimated. Statistical results indicate the existence of size effect in LVL and PSL for the longitudinal and transverse directions.

A Damage-coupled Multi-axial Time-dependent Low Cycle Fatigue Failure Model for SS304 Stainless Steel at High Temperature

Based on the time-dependent strain cyclic characteristics and fatigue behaviors of SS304 stainless steel under multi-axial cyclic loading at 700 ◦C, and in the frame of unified visoco-plastic cyclic constitutive model and continuum damage mechanics theory, the damage-coupled multi-axial time-dependent constitutive model and fatigue failure model were proposed. In the model, the evolution equation of damage was introduced in and the time-dependent effects, e.g. holding time, loading rate, were taken into account. The model was applied to the simulation of whole-life cyclic deformation behaviors and prediction of LCF life for SS304 stainless steel in multiaxial time-dependent low cycle fatigue tests. It is shown that the simulated results agree well with experimental ones.