Elasto-viscoplastic Model Research Articles

Physical modeling experiments to study periodic activation of faults in seismic zones

Our study aimed to find a mechanism that controls preparation and subsequent full seismic activation of large faults that may act as sources of strong earthquakes. A large fault was physically modeled to investigate the dynamics of its deformation. The experiments were conducted on elastoviscoplastic and elastic models of the lithosphere. A digital camera was used to capture images in the course of the modeling experiments. The digital image correlation method (DIC) detected the moments of impulse activation and displacements along the entire fault or its major segment. Between the activation moments, the fault structure consists of segments, including active ones. Activation is directional and involves a few large segments of the fault, then numerous small ruptures, and the latter are gradually degenerating. The long-term deformation dynamics of the fault is represented by a regular sequence of its full activations. In most cases, each moment of activation correlates with a minimum dip angle of the repeatability curve (β) and a maximum value of information entropy (Si). We analysed in detail the deformation dynamics of the fault and in its wings between two full activation that occurred in a regular pattern, including the phases of regression and progression of the deformation process. The analysis revealed two similar scenarios in the evolution of the active segments and plastic micro slip faults within the active segments. In some intervals of time, deformation takes place considerably differently on the segments and the plastic micro slip faults. Such differences suggest that in the studies attempting to statistically predict and assess a large and potentially seismically hazardous fault zone, this zone should be considered spatially subdivided into a central narrow subzone (including the main fault plane) and two wide subzones framing the fault wings. According to our physical modeling results, the central subzone can be up to10 km wide, and the total width of all the subzones can amount to100 km or more. This study contributes to the development of the concepts of geodynamics of large faults in the seismic zones of the lithosphere and investigates one of the possible mechanisms preparing strong earthquakes in the seismic zones.

Computational modeling of multiphase viscoelastic and elastoviscoplastic flows

SummaryIn this paper, a three‐dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time three‐dimensional simulations of inertial and turbulent EVP fluids with a large number particles and droplets. This is achieved by combining fast and highly scalable methods such as an FFT‐based pressure solver, with the evolution equation for non‐Newtonian (including EVP) stresses. In this flexible computational framework, the fluid can be modeled by either Oldroyd‐B, neo‐Hookean, FENE‐P, or Saramito EVP models, and the additional equations for the non‐Newtonian stresses are fully coupled with the flow. The rigid particles are discretized on a moving Lagrangian grid, whereas the flow equations are solved on a fixed Eulerian grid. The solid particles are represented by an immersed boundary method with a computationally efficient direct forcing method, allowing simulations of a large numbers of particles. The immersed boundary force is computed at the particle surface and then included in the momentum equations as a body force. The droplets and soft particles on the other hand are simulated in a fully Eulerian framework, the former with a level‐set method to capture the moving interface and the latter with an indicator function. The solver is first validated for various benchmark single‐phase and two‐phase EVP flow problems through comparison with data from the literature. Finally, we present new results on the dynamics of a buoyancy‐driven drop in an EVP fluid.

A viscoelastoplastic stiffening model for plant fibre unidirectional reinforced composite behaviour under monotonic and cyclic tensile loading

At room conditions and standard strain rate (ε˙∼10−4s−1), unidirectional (UD) plant-based reinforced organic polymers often exhibit nonlinear mechanical behaviour in tension. A viscoelastoplastic model (VEP model) for the simulation of UD plant fibre composite mechanical behaviour in tension, previously validated from twisted flax yarn epoxy composite under room conditions and standard strain rate, is calibrated with new data obtained from flax fibre epoxy composite under repeated progressive loading and a wide range of strain rates (ε˙∼10−3 to 10−7s−1). The VEP model does not reproduce well the experimental observations. There seems to be a lack of stiffening in this phenomenological model.We propose an improved VEP model, developed within the frameworks of thermodynamics and limited to uniaxial tension and infinitesimal strains. An internal variable s representing the stiffening is added to create a VEP-stiffening model. This internal variable represents the coupled effects of reorienting cellulose microfibrils in kink band areas, spiral spring-like extension of cellulose microfibrils, and shear-stress-induced crystallization of the amorphous cellulose of flax fibres. The stiffening phenomenon was considered viscous, without a threshold, and was related to the tension energy in the direction of the fibres. Three viscosity coefficients drive the three phenomena: η (elastic), K (plastic), and Ks (stiffening). In the chosen formalism, this leads to two thermodynamic potentials φVEPs and ΩVEPs in which the stiffening phenomenon is strongly coupled with all the others.This VEP-stiffening model of the UD flax fibre epoxy composite correlates well with experimental observations. The paper also explores the evolution of the three viscous phenomena (elastic, plastic, and stiffening) by simulation of different loading conditions: monotonic, cyclic, and creep.This VEP-stiffening model can easily enrich existing multiaxial models of UD behaviour in the fibre direction. Implemented in a finite element model, it could be used at different length scales to numerically explore the origin of the mechanical behaviour of plant-based reinforced polymers.

An elasto-viscoplastic model to describe the ratcheting behavior of articular cartilage.

In the present work, a constitutive model for articular cartilage is proposed in finite elasto-viscoplasticity. For simplification, articular cartilage is supposed to be a typical composite composed of a soft basis and a fiber assembly. The stress tensor and free energy function are hence accordingly divided into two components. The high nonlinear stress-strain response is assumed to be mainly related to the fiber assembly and described by an exponential-type hypoelastic relation. Ratcheting is considered according to the viscoplasticity, the evolution rule of which is deduced from the dissipative inequality by the co-directionality hypotheses. Then, the capability of the proposed model is validated by comparing its predictions with related experimental observations. Results show that the ratcheting behavior and stress-strain hysteresis loops are reasonably captured by the proposed model.

Identifying poromechanism and spatially varying parameters of aquifer compaction in Choushui River alluvial fan, Taiwan

Subsidence occurs in many alluvial depositional environments, causing substantial socio-economic losses. Thick aquifers with interbedding or lens-structured clay can contribute significantly to compaction. The poromechanism of aquifer compaction is usually complicated, and its spatial variation is poorly understood, inhibiting our ability to fully explain the region-wide nature of groundwater-exploitation-induced land subsidence. In this study, we explore the poromechanism of aquifer deformation in the Choushui River alluvial fan, Taiwan. Groundwater level and multi-layer compaction data were collected for analyses. Elastic, plastic, and viscous characteristics all appear in the deformation data to various extents. A visco-elasto-plastic (VEP) model composed of a visco-elastic set and a visco-plastic set in series, which are associated with different viscous dampers, is proposed to model the deformation. Compared with existing models, the proposed model is superior in terms of simulating compaction as well as its applicability and versatility. The proposed VEP model is applied to observation wells in the proximal, middle, and distal fans of the Choushui River alluvial fan to explore the spatial variation in the poromechanical properties. The results show that the Young's modulus of the elastic spring increases with depth and with the distance from the distal fan to the proximal fan. The Young's modulus of the plastic element decreases with depth. The system response factor of the visco-plastic set decreases with depth and with the distance from the distal fan to the proximal fan. Aquifer recovery incapability increases with depth. Both the trend and dynamic fluctuations in compaction for the Choushui River alluvial fan are well captured by the proposed VEP model, which is essential for assessing long-term land and water resource management and evaluating potential short-term threats to infrastructure caused by seasonal subsidence.

A hydromechanical approach for anisotropic elasto-viscoplastic geomaterials: Application to underground excavations in sedimentary rocks

To better describe excavation operations in deep geological formations, several aspects should be considered, especially the material anisotropy, time-dependent behavior, and hydromechanical coupling. In the present paper, a hydromechanical model based on the framework of continuous porous media was proposed. The mechanical elasto-viscoplastic constitutive model accounted for the material elastic and non-elastic anisotropies, using a transformation between the real transversely isotropic material and a fictitious isotropic material. Considering the hydraulic behavior, the permeability was expressed as a function of the volumetric viscoplastic strain. The model was applied to a case study of two tunnel excavations in an anisotropic rock under an initial anisotropic stress state. The results of the numerical simulations using a finite element code were in good agreement with the field convergence and permeability data.

Micromechanical Modeling of the Elasto-Viscoplastic Behavior and Incompatibility Stresses of β-Ti Alloys.

Near β titanium alloys can now compete with quasi-α or α/β titanium alloys for airframe forging applications. The body-centered cubic β-phase can represent up to 40% of the volume. However, the way that its elastic anisotropy impacts the mechanical behavior remains an open question. In the present work, an advanced elasto-viscoplastic self-consistent model is used to investigate the tensile behavior at different applied strain rates of a fully β-phase Ti alloy taken as a model material. The model considers crystalline anisotropic elasticity and plasticity. It is first shown that two sets of elastic constants taken from the literature can be used to well reproduce the experimental elasto-viscoplastic transition, but lead to scattered mechanical behaviors at the grain scale. Incompatibility stresses and strains are found to increase in magnitude with the elastic anisotropy factor. The highest local stresses are obtained toward the end of the elastic regime for grains oriented with their <111> direction parallel to the tensile axis. Finally, as a major result, it is shown that the elastic anisotropy of the β-phase can affect the distribution of slip activities. In contrast with the isotropic elastic case, it is predicted that {112} <111> slip systems become predominant at the onset of plastic deformation when elastic anisotropy is considered in the micromechanical model.

Dynamic modelling of retrogressive landslides with emphasis on the role of clay sensitivity

SummaryThis paper presents a detailed numerical study of the retrogressive failure of landslides in sensitive clays. The dynamic modelling of the landslides is carried out using a novel continuum approach, the particle finite element method, complemented with an elastoviscoplastic constitutive model. The multiwedge failure mode in the collapse is captured successfully, and the multiple retrogressive failures that have been widely observed in landslides in sensitive clays are reproduced with the failure mechanism, the kinematics, and the deposition being discussed in detail. Special attention has been paid to the role of the clay sensitivity on each retrogressive failure as well as on the final retrogression distance and the final run‐out distance via parametric studies. Moreover, the effects of the viscosity of sensitive clays on the failure are also investigated for different clay sensitivities.

Heterogeneous [formula omitted] microstructures in nickel-base superalloys and their influence on tensile and creep performance

Mechanical properties of nickel-base superalloys can be greatly influenced by spatial variation of γ′ microstructure, calling for models at mesoscale to study additional complexity in the underlying microstructure/property relationship. We combine a FFT-based elasto-viscoplasticity (FFT-EVP) model with a phase-field (PF) model to study plastic deformation of γ/γ′ superalloys. The model is applied to Haynes 282 (H282), where the low volume fraction (<20%) of dispersed spherical γ′ particles results in a dislocation-particle interaction of either Orowan looping at tensile conditions or climb-bypass at creep conditions. The incorporation of these mechanisms is achieved through the framework of a dislocation density based constitutive model in FFT-EVP, together with the introduction of a location-dependent inter-particle spacing based on the k-nearest neighbor algorithm. Features of non-uniform γ′ microstructures, including γ′ volume fraction variation and non-uniform γ′ distribution due to element microsegregation observed in welded H282 samples, are modeled using the PF method and then passed to FFT-EVP to explore their influence on the tensile and creep properties in a parametric manner. It is found that if the particle distribution is uniform, γ′ volume fraction variation can exhibit a nonlinear effect on both the tensile strength and creep rate; for a given overall γ′ volume fraction, the degree of particle distribution non-uniformity can also exhibit nonlinear influence on the tensile strength and creep rate. It is also shown that the location-dependent inter-particle spacing serves as a better microstructure descriptor than the conventional analytical expression of the average inter-particle spacing in terms of establishing a homogenized but microstructure-sensitive constitutive microstructure-property relationship for fast-acting engineering applications.

Yielding characterization of waxy gels by energy dissipation

The rheological behaviors of yield stress fluids are commonly interpreted from the energy perspective, yet this perspective has rarely been applied for waxy gel. In this study, we calculated the energy dissipated into the waxy gel caused by viscous strain during the deformation process with the aid of a well-tested elasto-viscoplastic thixotropic model. The energy dissipation shows a power-law dependence on the strain regardless of the stress ramping rate. The energy dissipation has been shown to be useful to characterize the ductility of waxy gel, that is, the larger the energy is dissipated during fracture, the more ductile the waxy gel is. When the waxy gel is induced to the same strain by different stress ramping rate, the energy dissipation during the deformation process shows little dependence on the stress ramping rate. However, if during the loading process the stress is increased to the same value by different ramping rate, a higher stress ramping rate causes lower energy dissipation. These findings are helpful to elucidate the widely observed experimental observation for waxy gels that the measured yield stress depends on the stress ramping rate whereas the measured yield strain shows little dependence.

Elastoviscoplastic flows in porous media

We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier–Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution [1]. In this model, the material behaves as a viscoelastic solid when unyielded, and as a viscoelastic Oldroyd-B fluid for stresses higher than the yield stress. The porous media is made of a symmetric array of cylinders, and we solve the flow in one periodic cell. We find that the solution is time-dependent even at low Reynolds numbers as we observe oscillations in time of the unyielded region especially at high Bingham numbers. The volume of the unyielded region slightly decreases with the Reynolds number and strongly increases with the Bingham number; up to 70% of the total volume is unyielded for the highest Bingham numbers considered here. The flow is mainly shear dominated in the yielded region, while shear and elongational flow are equally distributed in the unyielded region. We compute the relation between the pressure drop and the flow rate in the porous medium and present an empirical closure as function of the Bingham and Reynolds numbers. The apparent permeability, normalized with the case of Newtonian fluids, is shown to be greater than 1 at low Bingham numbers, corresponding to lower pressure drops due to the flow elasticity, and smaller than 1 for high Bingham numbers, indicating larger dissipation in the flow owing to the presence of the yielded regions. Finally we investigate the effect of the Weissenberg number on the distribution of the unyielded regions and on the pressure gradient.

Multiscale Material Modeling and Simulation of the Mechanical Behavior of Dual Phase Steels Under Different Strain Rates: Parametric Study and Optimization

Recent studies on developing dual phase (DP) steels showed that the combination of strength/ductility could be significantly improved when changing the volume fraction and grain size of phases in the microstructure depending on microstructure properties. Consequently, DP steel manufacturers are interested in predicting microstructure properties as well as optimizing microstructure design at different strain rate conditions. In this work, a microstructure-based approach using a multiscale material and structure model was developed. The approach examined the mechanical behavior of DP steels using virtual tensile tests with a full micro-macro multiscale material model to identify specific mechanical properties. Microstructures with varied ferrite grain sizes, martensite volume fractions, and carbon content in DP steels were also studied. The influence of these microscopic parameters at different strain rates on the mechanical properties of DP steels was examined numerically using a full micro-macro multiscale finite element method. An elasto-viscoplastic constitutive model and a response surface methodology (RSM) were used to determine the optimum microstructure parameters for a required combination of strength/ductility at different strain rates. The results from the numerical simulations were compared with experimental results found in the literature. The developed methodology proved to be a powerful tool for studying the effect and interaction of key strain rate sensitivity and microstructure parameters on mechanical behavior and thus can be used to identify optimum microstructural conditions at different strain rates.

Key Factors Influencing the Energy Absorption of Dual-Phase Steels: Multiscale Material Model Approach and Microstructural Optimization

The increase in use of dual-phase (DP) steel grades by vehicle manufacturers to enhance crash resistance and reduce body car weight requires the development of a clear understanding of the effect of various microstructural parameters on the energy absorption in these materials. Accordingly, DP steelmakers are interested in predicting the effect of various microscopic factors as well as optimizing microstructural properties for application in crash-relevant components of vehicle bodies. This study presents a microstructure-based approach using a multiscale material and structure model. In this approach, Digimat and LS-DYNA software were coupled and employed to provide a full micro–macro multiscale material model, which is then used to simulate tensile tests. Microstructures with varied ferrite grain sizes, martensite volume fractions, and carbon content in DP steels were studied. The impact of these microstructural features at different strain rates on energy absorption characteristics of DP steels is investigated numerically using an elasto-viscoplastic constitutive model. The model is implemented in a multiscale finite-element framework. A comprehensive statistical parametric study using response surface methodology is performed to determine the optimum microstructural features for a required tensile toughness at different strain rates. The simulation results are validated using experimental data found in the literature. The developed methodology proved to be effective for investigating the influence and interaction of key microscopic properties on the energy absorption characteristics of DP steels. Furthermore, it is shown that this method can be used to identify optimum microstructural conditions at different strain-rate conditions.

Analysis of the cyclic tensile behaviour of an elasto-viscoplastic polyvinylidene fluoride (PVDF)

The present paper aims to perform an experimental and theoretical study regarding the inelastic deformation progressive accumulation observed in a polyvinylidene fluoride (PVDF) specimen machined from flexible pipe internal pressure sheaths under cyclic load-unload tensile tests and in monotonic tensile tests. Experiments show that the elastic mechanical behaviour is not rate-dependent because the Young's modulus does not suffer a considerable variation with change in the strain rate. However, the strain hardening induced by the plastic deformation is strongly rate-dependent. Hence, the mechanical behaviour of this polymer is not elasto-plastic or viscoelastic, but elasto-viscoplastic. Also, the kinematic hardening strongly increases with growth of accumulated inelastic strain, making it much more significant than the isotropic hardening. This paper proposes an elasto-viscoplastic mechanical model capable of describing the cyclic and monotonic inelastic behaviour for an arbitrary loading history. The kinenatic hardening observed for this PVDF makes it possible to identify experimentally all material parameters that arise in the model by performing load-unload tests using flat specimens, eliminating buckling problems and the need to control eventual misalignment in the universal test machine grips. Good agreement was noted when comparing the theoretical results with experiments.

A coupled hydro-mechanical creep damage model for clayey rock and its application to nuclear waste repository

In this paper we propose a new nonlinear elasto-viscoplastic damage model, based on a modified Mohr-Coulomb criterion, to study the creep and seepage in clayey rock during construction of a high-level radioactive waste repository through laboratory experiments and field tests. First, three types of damage evolution equations are constructed by using the relationship between the damage variable and the strain. Then, a self-healing model is investigated for the clayey rock by considering the damage, confining pressure, pore water, and duration of saturated state. By introducing the damage, permeability evolution and self-healing as the key factors, a fully coupled hydro-mechanical model for clayey rock is developed with the commercial software ABAQUS. The hydro-mechanical behaviour in the surrounding rock is simulated with the proposed model considering the actual construction of the repository. The numerical results show that the construction quality has a significant effect on the stability of the rock formation, and that the extent of the horizontal gallery disturbed by shield tunnelling is less than that of the test drift disturbed by using jackhammers method. The creep damage of the surrounding rock increases rapidly at the early stage and tends to stabilize gradually after 15 years, and the damage in the middle part of the surrounding rock is larger than that in the bottom and top parts. In addition, due to the self-healing effect of clayey rock, around three years later, the permeability of the excavation disturbed zone (EDZ) is close to that of the original clayey rock with an order of magnitude 10−19 m2. The present model can also be used to predict the long-term stability of tunnels.

Thermomechanical fatigue behaviour of ferritic stainless steel grades for high temperatures applications

Nowadays high temperatures resistant materials are needed to resist to high temperature applications (up to 1000°C), such as automotive exhaust gas manifolds. Some developed stainless steel grades, including ferritic grades or austenitic refractory grades, can be used in this temperature range and both in continuous or cyclic thermal conditions. In order to predict the thermomechanical fatigue damage of stainless steel parts submitted to cyclic thermal loading and constrained bonding conditions, the elastoviscoplastic model by Chaboche is determined for a wide range of temperatures, of strain amplitudes and strain rate levels thanks to isothermal traction-compression tests. The validation procedure is performed afterward by comparison with stabilized behavior under non isothermal conditions on a dedicated thermal fatigue test performed on V-shape specimens. Results of simulation show very good fitting with the experimental curves which would lead to a more accurate fatigue life prediction. A damage model was derived from Taira’s thermal low-cycle fatigue model to include dwell-time period at high temperature and creep-oxidation effect. In this paper the example of K44X, a dedicated grade for high temperatures applications, is presented.

Study of hot cracking potential in a 6-ton steel ingot casting

A new hot cracking potential (HCP) criterion, for the appearance of hot tearing in steel ingot castings, is proposed. The maximum value of the first principal stress, divided by the dynamic yield strength in the brittle temperature range (BTR), was used to identify the HCP. Experiments were carried out on a 6-ton P91 steel ingot in which severe hot tearing was detected in the upper centerline. Another ingot, with a better heat preservation riser, and without hot tearing, was used for comparison. Samples were obtained from the area of the ingot body with hot tearing, and their morphologies were inspected by a X-ray high energy industrial computed tomography. The carbon and sulfur distributions around the hot tearing were characterized by an infrared spectrometry carbon and sulfur analyzer. High temperature mechanical properties were obtained by a Gleeble thermal simulation machine, under different strain rates. Then, thermo-mechanical simulations using an elasto-viscoplastic finite-element model were conducted to analyze the stress and strain evolution during ingot solidification. The results showed that the hot tearing area, which was rich in both carbon and sulfur, was under excessive tensile stress in the BTR, bearing the highest HCP.

A new fatigue model including thermal ageing for low copper aluminum-silicon alloys

Numerical simulation is more and more used in automotive industry to reduce design time and cost. Moreover, for high performance engines, the development of cylinder heads requires well known and adapted materials to ensure their reliability.The estimation of adapted fatigue criteria based on few experiments is thus an important challenge: to obtain more predictive model on more complex mechanical phenomena.This paper describes the methodology adopted by Renault to estimate fatigue life of a new aluminum-silicon alloy.A low copper aluminum-silicon alloy has been developed for a new generation of cylinder heads. Those kinds of alloys provide a good compromise between the two main failure modes encountered for cylinder heads: high cycle fatigue of water jacket and low cycle fatigue of fire deck.However, those materials are subjected to thermal ageing that can affect mechanical behavior, such as yield stress and hardening, but also fatigue mechanisms at higher temperatures.This article presents first the selected constitutive equations that introduce thermal ageing effect in a cyclic elasto-viscoplastic model. The low cycle fatigue criterion is then calibrated on the relevant database, which includes isothermal and non-isothermal tests.The fatigue criterion is a specific version of a classical model previously developed at Onera. The critical variables for the fatigue part are the stress amplitude and the mean stress, both of them being normalized by an ultimate stress which depends on temperature and ageing state.Finally, the constitutive and damage models have been applied on 3D cylinder head numerical analysis. The paper proposes a brief comparison of those results with more classical simulations made on cylinder heads and highlights the perspectives offered by this new aluminum-silicon alloy.

Unified viscoplasticity modelling and its application to fatigue-creep behaviour of gas turbine rotor

This paper presents an elasto-viscoplastic finite element modelling framework including the associated UMAT codes to investigate the high-temperature behaviour of a gas turbine rotor steel. The model used in the FE study is an improved and unified Chaboche–Lemaitre model which combines a power flow rule with non-linear anisothermal evolution of isotropic and kinematic hardening. The computational methodology is a three-dimensional framework following an implicit formulation and based on a radial return mapping algorithm. The UMAT is calibrated and validated across isothermal hold-time cyclic tests. The model is applied to a classical industrial gas turbine rotor to study the spatial heterogeneities and critical high stress areas within the rotor structure. The effect of thermal transients and geometry singularities on the development of residual stresses is underlined. Finally, the potential improvements and extensions of such FE viscoplastic analysis are discussed.

Numerical analysis of Ballina test embankment on a soft structured clay foundation

This paper focuses on numerical modeling of the responses of Ballina test embankment by an improved EVP-SANICLAY constitutive model with a novel rotational hardening (RH) law. The modified RH law guarantees the uniqueness of the critical state line, prevents excessive rotation of yield surface and is particularly simple that makes it very useful for practical applications. To consider strain-rate dependency of the soil behavior, Perzyna’s overstress theory is employed. Using the newly released data at Ballina test embankment site, the values of model parameters and state variables are calibrated and evaluated for Class C predictions, and their differences with the previously determined parameter values for Class A predictions are highlighted and discussed. The elasto-viscoplastic anisotropic constitutive model is implemented in PLAXIS software to carry out the simulations of the case study embankment. The numerical modeling results, in terms of time-dependent variations of deformations and pore water pressures, both during and after the embankment construction, are compared with the physical measurements at the test site. The results of Class C analyses show that the model is capable of capturing the temporal changes in surface settlement and lateral deformations with good accuracy, with the latter being particularly challenging when modeling the behavior of soft clays. Simulation of pore water pressure variations however proved more difficult. To highlight the advantages of the proposed EVP-SANICLAY model, the simulations are also compared with those using the classical Mohr-Coulomb and modified Cam-clay models, and the results are presented and discussed in detail.