Elasto-viscoplastic Model Research Articles

The effect of initial texture on multiple necking formation in polycrystalline thin rings subjected to dynamic expansion

In this paper, we have investigated, using finite element calculations, the effect of initial texture on the formation of multiple necking patterns in ductile metallic rings subjected to rapid radial expansion. The mechanical behavior of the material has been modeled with the elasto-viscoplastic single crystal constitutive model developed by Marin (2006). The polycrystalline microstructure of the ring has been generated using random Voronoi seeds. Both 5000 grain and 15000 grain aggregates have been investigated, and for each polycrystalline aggregate three different spatial distributions of grains have been considered. The calculations have been performed within a wide range of strain rates varying from 1.66⋅104s−1 to 3.33⋅105s−1, and the rings have been modeled with four different initial textures: isotropic texture, 001∥Θ Goss texture, 001∥ R Goss texture and 111∥ Z fiber texture. The finite element results show that: (i) the spatial distribution of grains affects the location of the necks, (ii) the decrease of the grain size delays the formation of the necking pattern and increases the number of necks, (iii) the initial texture affects the number of necks, the location of the necks, and the necking time, (iv) the development of the necks is accompanied by a local increase of the slip activity. This work provides new insights into the effect of crystallographic microstructure on dynamic plastic localization and guidelines to tailor the initial texture in order to delay dynamic necking formation and, thus, to improve the energy absorption capacity of ductile metallic materials at high strain rates.

Predicting settlement of embankments built on PVD-improved soil using Bayesian back analysis and elasto-viscoplastic modelling

In this study, an implicit finite difference program, 1DFDM, based on the fully coupled one dimensional elasto-viscoplastic (1D EVP) model combining radial and vertical drainage is developed to perform consolidation analysis of embankments constructed on soft soils. Class A prediction (prior prediction) is performed by using 1DFDM for the embankment constructed on soft clay in Ballina, Australia. However, the prediction deviates significantly from the measurements, and the model parameters need to be calibrated. Bayesian back analysis is thus combined with 1DFDM in this study to do Class C prediction. Three updating schemes (using monitoring settlement only, using monitoring pore water pressure only, and using both monitoring settlement and pore water pressure) are employed to shed light on the effects of the monitoring data types on settlement prediction. The results show that the long-term settlement and pore water pressure predictions could be further improved if both the monitoring settlement and pore water pressure data are incorporated. The coupling effects in the constitutive model can reduce the fluctuations in the updated optimum parameters. A stable and physically reasonable parameter set could be obtained if enough monitoring data is incorporated into the Bayesian back analysis.

Finite Element Simulation of Radial Tire Building and Shaping Processes Using an Elasto-Viscoplastic Model

The comprehensive tire building and shaping processes are investigated through the finite element method (FEM) in this article. The mechanical properties of the uncured rubber from different tire components are investigated through cyclic loading-unloading experiments under different strain rates. Based on the experiments, an elasto-viscoplastic constitutive model is adopted to describe the mechanical behaviors of the uncured rubber. The distinct mechanical properties, including the stress level, hysteresis and residual strain, of the uncured rubber can all be well characterized. The whole tire building process (including component winding, rubber bladder inflation, component stitching and carcass band folding-back) and the shaping process are simulated using this constitutive model. The simulated green tire profile is in good agreement with the actual profile obtained through 3D scanning. The deformation and stress of the rubber components and the cord reinforcements during production can be obtained from the FE simulation, which is helpful for judging the rationality of the tire construction design. Finally, the influence of the parameter “drum width” is investigated, and the simulated result is found to be consistent with the experimental observations, which verifies the effectiveness of the simulation. The established simulation strategy provides some guiding significance for the improvement of tire design parameters and the elimination of tire production defects.

A two-particle approach for dry high density-ratio granular collapse

We report on the role of density ratio for granular column collapse experimentally and numerically by demonstrating the fundamental changes using a two-particle approach. The influence of the density ratio for the different profile arrangements on the velocity distribution, interface, and energy transition is described using the Moving Particle Semi-Implicit method (MPS). A constitutive equation utilizing the granular material strength is formulated using the elasto-viscoplastic model under the μ ( I ) rheology framework by replacing the frictional coefficient with the internal friction angle. The dense state of the granular materials results in a linear relationship between the length scale and inertia constant, which makes the shear strength the driving parameter. Experimental data are compared with numerical simulation for granular collapse with varying density profile configurations to validate the method. We found that the density ratio does not influence the velocity and free surface profile. The interface is maintained similarly to a single-phased granular flow except for erosive configurations where a penetrating regime is evident. The rate at which the granular kinetic energy transforms to the potential energy when the lower density material is on top and at the left of the higher granular materials is similar compared to other profile arrangements. The results demonstrated that the density ratio for different profile arrangements could significantly influence the deformation of the granular materials depending on the particle arrangements. The numerical investigation for the granular column collapse agrees well with experimental studies. Collapse mechanisms of varying density ratio configuration. • Flow dynamics and energy evolution in density ratio granular column collapse. • Replacement of the μ (I) rheology model parameters with the material strength parameters. • Effective phase-change for high-density ratio for single and two-phase granular flow. • Relationship between the inertia constant and wave front. • The meshfree particle method, MPS, shows excellent agreement with the experiment.

Numerical analysis of time-dependent negative skin friction on pile in soft soils

The generation of negative skin friction (NSF) induces the additional axial force on the pile, which exerts a detrimental load rather than a beneficial one. However, the effect of soil creep on the long-term development of NSF has remained poorly understood. The study uses numerical analysis to investigate this effect. First, an elasto-viscoplastic model with an enhanced time integration algorithm is successfully implemented into a finite element code. Next, the two-dimensional axisymmetric pile-soil interaction model is established and properly calibrated with a known field case. Finally, parametric studies are conducted to examine different degrees of creep effect on the variation in NSF and neutral plane (NP) within the primary and secondary consolidation periods. According to the findings, a high creep coefficient of the soil results in an increase in NSF and descending trend of the NP. The creep induced delay of NSF is observed attributed to the increase in excess pore pressure during the early stage of consolidation. The NP position varies drastically at the commencement of consolidation when taking creep into consideration. Lastly, the study proposes an exponential prediction model to reflect the time dependence of the location of the NP.

A unified elasto-viscoplastic peridynamics model for brittle and ductile fractures under high-velocity impact loading

Peridynamics (PD), as an alternative formulation of classical continuum mechanics, is a powerful method for predicting the spontaneous initiation and propagation of cracks. In this paper, a unified elasto-viscoplastic peridynamics model, named the Bodner-Partom theory-based Peridynamics (BPPD) model, is proposed to describe the whole deformation-damage-fracture process for both brittle and ductile materials under impact loadings. It defines the bond-wise elasto-viscoplastic deformation by incorporating the Bodner-Partom's (B-P) constitutive theory into the ordinary state-based PD framework. In BPPD model, the bond deterioration is introduced as an intrinsic variable coupled with the modified B-P theory and the bond fracture is realized by the critical bond stretch model. The proposed BPPD model permits the natural development of plastic deformation and material deterioration, which shares the same vision as PD theory. Equipped with the elastic short-range force contact model, the present study further investigates the modelling capacity of the BPPD model under various impact loadings. Simulations for brittle drop-ball test, Taylor impact test and ballistic penetration test show a good agreement between numerical results and experiment data. The proposed BPPD model can accurately capture the whole deformation processes of various impact fractures and thus contribute a new diversity to the development of PD theory and a new perspective to the understanding of material fracture mechanism.

Multi-fidelity data-driven modelling of rate-dependent behaviour of soft clays

ABSTRACT Conventional phenomenological elasto-viscoplastic models include numerous parameters that need to be calibrated by case-specific experiments. Data-driven modelling has recently emerged and provided an alternative to constitutive modelling. This study proposes a modelling framework based on multi-fidelity data to model the rate-dependent behaviour of soft clays. In this framework, low-fidelity (LF) data generated by an elasto-viscoplastic model and high-fidelity (HF) data from experimental tests are necessary. Stress–strain-strain rate correlations behind LF and HF data can be captured by long short-term memory and feedforward neural networks, respectively, such that final predictions can be given by a multi-fidelity residual neural network (MR-NN). Such a framework with the same LF data is applied in Hong Kong marine deposits and Merville clay to investigate its feasibility and generalisation ability. In addition, the effect of LF data on the performance of MR-NN is discussed to verify the robustness of the framework. All results demonstrate that rate-dependent undrained shear strength and pore-water pressure can be accurately modelled through the framework, showing adaptive non-linear modelling capability, less demand for experimental data, and superior robustness. These characteristics indicate a considerable potential in modelling the rate-dependent behaviour of clays.

Effective stress analysis of dynamically installed anchor installation in rate-dependent clay

Accurate prediction of the final embedment depth and installation-induced excess pore pressure of dynamically installed anchors (DIAs) are prerequisites for the design of subsequent anchor set-up during a waiting period and capacity under operational loadings. This paper presents a dynamic large deformation finite element approach within the effective stress framework and investigates the installation behaviour of DIAs in clay. An elasto-viscoplastic model is adopted to capture strain rate dependency of the undrained shear strength. Development of excess pore pressure for various impact velocities, anchor geometries, viscosity parameters are quantified. An expression is proposed for estimating the final embedment depth of DIAs in clay.

Peridynamics methodology for elasto-viscoplastic ductile fracture

This paper presents a novel peridynamics (PD) methodology and implementation approach for predicting the ductile fracture of elasto-viscoplastic materials. The proposed analysis model consists of three components: 1) an elasto-viscoplastic constitutive model based on modified Bodner-Partom (BP) constitutive theory; 2) bond damage prediction based on Wang’s unified damage theory; 3) crack growth prediction using the PD critical bond stretch criterion. The PD model for BP materials is realized under the ordinary state-based PD framework to define the bond-wise relationship between deformation state and force state. The use of a unified constitutive theory endows the present model with the characteristic of no yield criterion. In addition, the non-local nature of the PD framework allows discontinuities to naturally occur, thereby ensuring the present model can capture the initiation and propagation of ductile fracture. Simulations of the standard tension tests and mode-I compact tension tests were carried out to demonstrate the use of the PD model for BP materials in practical problems. Particle-wise indicators, representing the intensities of plasticity, damage and fracture, were extracted for post-processing. An in-depth analysis shows that the presented PD model for BP materials can effectively reproduce ductile fractures at the macro-scale, allowing a general PD description of ductile behavior, which brings a new outlook for the application of PD methods.

A simple bounding surface elasto-viscoplasticity model for marine clays under monotonic and cyclic loading

This paper develops a bounding surface elasto-viscoplasticity model to consider the viscous behaviors of saturated clays. Consisting of a bounding surface, a dynamic loading surface, and a static loading surface, the model is formulated by combining the elasto-viscoplasticity overstress theory with the bounding surface framework. An overstress function defined by the static and dynamic loading surfaces is adopted, allowing the existence of viscoplastic strains for stress states inside the bounding surface. Enhanced by a static loading surface relocation strategy, the model enables capturing the accumulation of viscoplastic deformations of cyclically loaded clays. A rotated bounding surface is adopted to consider the initial anisotropic condition of natural clays. Besides, the hardening parameter is assumed to be associated with the accumulated viscoplastic deviatoric strain to better simulate the clay cyclic behaviors. The model is implemented into ABAQUS finite element program by using the two-step Euler method with sub-stepping techniques. The model is quantitatively validated by comparing the simulation results of several element tests to the available experimental data. Performance of the developed model in reproducing the secondary compression behaviors at various over-consolidation ratios and the loading frequency dependency of undrained cyclic responses is also examined qualitatively.

A multi-material ALE model for investigating impact dynamics of pile-soil systems

The dynamic pile-soil interaction is one of the most important and challenging problem in geomechanics, especially when geometrical, material-related, and dynamic contact-related nonlinearities exist. Geometrical nonlinearity is a fundamental obstacle to the popular Lagrangian finite element methods (FEM) that have been utilized in other areas of geomechanics research. This paper introduces a Multi-Material Arbitrary Lagrangian-Eulerian (MM-ALE) model for predicting the pile-soil interaction and forces during lateral dynamic impact events. The study used the MM-ALE method in conjunction with an elasto-viscoplastic soil material model that included strain softening and an elasto-plastic steel material model that incorporated strain rate effects to examine pile response during lateral vehicle impacts. The model was validated using large-scale, dynamic impact test data for piles embedded in soil, thus confirming its capability to simulate the complex dynamic impact pile-soil interaction. The effects of impact velocity, embedment depth, and soil strength on impact forces, energy dissipation, and impulse response of a pile-soil system were subsequently investigated. It was determined that average impact force, Favg, and impact velocity, are proportional to one another as Favg∝v2 regardless of pile embedment depth. This relationship provides evidence for the existence of inertial or hydrodynamic drag forces in the pile-soil system during lateral impacts similar to a solid object passing through a fluid.

Analysis on Compressional Behavior of Cotton Fiber Assembly and Its Influencing Factors

ABSTRACT Cotton fiber is a kind of cellulosic fiber and is widely used in textile. To legitimately determine the parameters of compressive force properties of cotton fiber assembly, axial stress was set up through a uniaxial quasi-static loading experiment on cotton fiber assembly. The constitutive model was built for cotton fiber assembly with viscoelastic plastic theory to calculate its mechanical parameters. The results showed that the viscoelasto plastic model was established to characterize the mechanical response. The constitutive model of stress and time had been adopted at the compression and relaxation processes. The viscoelastic constitutive model can be used to describe the densifying process. Loading cycles, compression velocity, and humidity on the parameters were also investigated by analyzing the E 1, E 2, η 2, loading cycles, and humidity showed significant influence on mechanical parameters. The E 1, E 2, and η 2 values of Stage II were lower than others because the cotton fiber assembly of Stage II was an unsteady structure. The E 1 values were almost higher than the E 2 values, the E 1, E 2, and η 2 values of Stage III and recovery were much higher than others. The senior viscoelastic stage of cotton fiber assembly mainly showed elastic deformation from loose and disordered fiber structures.

A dual-scale elasto-viscoplastic self-consistent model for the cyclic behavior of polycrystalline materials considering combined nonlinear kinematic hardening

A dual-scale elasto-viscoplastic self-consistent model for the cyclic behavior of polycrystalline materials considering combined nonlinear kinematic hardening

Meso-scale computational modeling of the fracture of concrete with complex shaped aggregates under the self-restraint stress

Modelling irregularly shaped aggregates in concrete uses advanced algorithms to describe complex geometric profile of, e.g, crushed gravels. Consequently, discretization of the complex geometry and computational convergence of the resulting mesh scheme are the bottlenecks that prevent wider application of mesoscopic fracture simulation of concrete with more realistic aggregates. In this paper, a novel modelling framework with simple pre-processing and good computational convergence is proposed based on the diffuse meshing technique and the coupled elasto-viscoplastic damage model. The proposed model discretizes concrete using only regular elements that may have different material components such as aggregates, mortar matrix and aggregate/matrix interface. The accuracy of the proposed model is validated by comparing with the full three-phase model that meshes aggregate, mortar and their interfaces separately. The proposed model is applied then to investigate the failure mechanism of concrete under uniaxial compression and tension. Furthermore, the effect of using simplified aggregate meso-structure is studied by comparing the results of using the complex shaped aggregate models and the spherical shaped aggregate model. The results show that the morphology of aggregate has a no-negligible influence on post-peak mechanical behavior, the orientation of aggregate affects crack initiation and propagation, and self-restraint stresses reduce the strength of concrete.

Inelastic Deformation of Coronary Stents: Two-Level Model.

This study describes the internal structure of materials used to produce medical stents. A two-level elastoviscoplastic mathematical model, which sets the parameters and describes the processes at the grain level, was developed and numerically implemented. A separate study was conducted to identify the most dangerous deformation modes in the balloon-expandable stent placement using the finite-element method in COMSOL Multiphysics. As a result, the challenging strain state type required for setting the kinematic loading on a representative macrovolume in the two-level model was obtained. A yield surface for different deformation paths in the principal deformation space for stainless steel AISI 316L was obtained and the effect of grain size on the deformation behavior of this material was explored using the developed model.

Elongational behaviour of electrostatically stabilised and concentrated CNF and CNC hydrogels: Experiments and modelling

TEMPO-oxidized cellulose nanofibril (CNF) hydrogels or cellulose nanocrystal (CNC) hydrogels can now be obtained at high concentrations (>10 wt%) and used to fabricate biobased materials and structures. Thus, it is required to control and model their rheology in process-induced multiaxial flow conditions using 3D tensorial models. For that purpose, it is necessary to investigate their elongational rheology. Thus, concentrated TEMPO-oxidized CNF and CNC hydrogels were subjected to monotonic and cyclic lubricated compression tests. These tests revealed for the first time that the complex compression rheology of these two electrostatically stabilised hydrogels combines viscoelasticity and viscoplasticity. The effect of their nanofibre content and aspect ratio on their compression response was clearly emphasised and discussed. The ability of a non-linear elasto-viscoplastic model to reproduce the experiments was assessed. Even if some discrepancies were observed at low or high strain rates, the model was consistent with the experiments.

Machine learning aided modelling of thermomechanical fatigue of solder joints in electronic component assemblies

Printed board assemblies, i.e. components soldered on printed circuit boards (PCBs), are exposed to thermal cycles responsible for fatigue cracking of solder joints as a result of thermal expansion mismatch between the constituting elements. Advanced finite element simulations are performed using a traction–separation law to represent the cracking process and a temperature-dependent elasto-viscoplastic model for the joint response. Predictions are successfully assessed towards machine learning processed experimental data. In particular, the high sensitivity of thermal ageing reliability to geometric dimensions and solder joint thickness is properly captured. Additional parameters, related to the PCB substrate, are also studied, opening new avenues towards design optimization.

Yield strength of CeO2 measured from static compression in a radial diamond anvil cell

Cerium oxide (ceria, CeO2) is frequently used as a standard in applications such as synchrotron and x-ray free electron lasers for calibrating x-ray wavelengths and offers the potential for understanding the high pressure properties and deformation mechanisms in a wide range of similar face centered cubic (fcc) materials. In this study, the pressure dependence of the strength of ceria was investigated up to 38 GPa using angle dispersive x-ray diffraction in a radial geometry in a diamond anvil cell. In this experiment, the difference in the stress along the axis of compression and perpendicular to the direction of compression can be determined, giving a quantity known as the differential stress. It was found that the differential stress (t), a measure of the lower bound for yield strength, initially increases rapidly from 0.35 ± 0.06 GPa to 2.2 ± 0.4 GPa at pressures of 1.8 and 3.8 GPa, respectively. Above 4 GPa, t increases more slowly to 13.8 ± 2.6 GPa at a pressure of 38 GPa. The changes in the preferred orientation (texture) of CeO2 with pressure were also measured, allowing for the determination of active deformation mechanisms using an elasto-viscoplastic self-consistent model (EVPSC). It was found that as pressure increased, the [001] direction had a slight preferred orientation along the axis of compression. Our EVPSC model of experimental fiber (cylindrically symmetric) textures and lattice strains were most consistent with dominant slip activity along {111}⟨11¯0⟩.

Shear stress and intravascular pressure effects on vascular dynamics: two-phase blood flow in elastic microvessels accounting for the passive stresses.

We study the steady hemodynamics in physiological elastic microvessels proposing an advanced fluid-structure interaction model. The arteriolar tissue is modeled as a two-layer fiber-reinforced hyperelastic material representing its Media and Adventitia layers. The constitutive model employed (Holzapfel et al. in J Elast 61:1-48, 2000) is parametrized via available data on stress-strain experiments for arterioles. The model is completed by simulating the blood/plasma flow in the lumen, using the thixotropic elasto-viscoplastic model in its core, and the linear Phan-Thien and Tanner viscoelastic model in its annular part. The Cell-Free Layer (CFL) and the Fåhraeus and Fåhraeus-Lindqvist effects are considered via analytical expressions based on experimental data (Giannokostas et al. in Materials (Basel) 14:367, 2021b). The coupling between tissue deformation and blood flow is achieved through the experimentally verified pressure-shear hypothesis (Pries et al. Circ Res 77:1017-1023, 1995). Our calculations confirm that the increase in the reference inner radius produces larger expansion. Also, by increasing the intraluminal pressure, the thinning of the walls is more pronounced and it may reach 40% of the initial thickness. Comparing our predictions with those in rigid-wall microtubes, we conclude that apart from the vital importance of vasodilation, there is an up to 25% reduction in wall shear stress. The passive vasodilation contributes to the decrease in the tissue stress fields and affects the hemodynamic features such as the CFL thickness, reducing the plasma layer when blood flows in vessels with elastic walls, in quantitative agreement with previous experiments. Our calculations verify the correctness of the pressure-shear hypothesis but not that of the Laplace law.

Insight in thermomechanical constitutive modeling of shape memory polymers

Shape memory polymers (SMPs) are a new member of the smart materials family. SMPs have found wide applications or potential applications in almost all manmade structures and devices. In order to better design smart structures and devices using SMPs, thermomechanical constitutive modeling is essential. In this insight paper, we will focus on presenting several multi-length-scale and multi-physics modeling frameworks, including the thermodynamics consistent model, elasto-viscoplastic model, statistical mechanics model, and phase evaluation law model. The SMPs modeled will include amorphous one-way shape memory polymers, semicrystalline one-way shape memory polymers, semicrystalline two-way shape memory polymers, and functional and mechanical damage effects on SMPs. Finally, we will give some in-depth perspectives on future development in this area of study.