Elastic-viscoplastic Model Research Articles

A fractional elasto-viscoplastic model for describing creep behavior of soft soil

In order to solve the analytical solution of the general rate-dependent model and make the theoretical model better reflect the creep behavior of soil, the fractional calculus theory is applied to the EVP (elastic–viscoplastic) model based on the overstress theory. A fractional strain rate model is proposed to construct a constitutive equation of fractional strain rate. The analytical solution of the fractional creep model is solved by applying Laplace integral transformation, and the fractional creep equation under undrained conditions is discussed. Then, the undrained shear creep test results of isotropic consolidated Fukakusa clay and K0 consolidated Sackville clay are used to verify the validity of the time-based fractional creep equation and the sensitivity analysis of the analytical solution. The effectiveness of the fractional creep model for predicting the creep behavior of soil such as soft clay is revealed. The results show that the fractional EVP creep model is obviously better than the traditional integer EVP model. Moreover, when the fractional order is 1, the fractional strain rate model can be reduced to an integer strain rate model, but the fractional creep equation degenerates into a linear creep equation.

A numerical study of the effects of overload on fatigue crack growth in plastically compressible hardening and hardening-softening-hardening solids

Variation of cyclic loading effect on fatigue crack growth is investigated under plane strain and small scale yielding (SSY) conditions. The material is characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The influence of cyclic stress intensity factor range (), load ratio (R), number of cycles (N), plastic compressibility ( overload and material softening on near tip deformation was studied in detail. For comparison purpose, a few results pertaining to plastically incompressible solids are also considered. The crack tip opening displacement (CTOD), plastic crack growth, deformed crack tip shape, plastic zone shape and size near the crack tip appear to depend significantly on R, N, overload and material softening. The overload produces strong plastic deformation ahead of the crack tip and decreases the fatigue crack growth substantially. Highlights Variation of cyclic loading effect on fatigue crack growth is investigated for materials characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Both plastically compressible and incompressible solids are considered. The influence of cyclic stress intensity factor range (), load ratio (R), number of cycles (N), plastic compressibility ( overload and material softening on near tip deformation was studied in detail. The crack tip opening displacement, plastic crack growth, plastic zone shape and size near the crack tip appear to depend significantly on R, N, overload and material softening. The combination of softening or softening-hardening material response and plastic compressibility leads to major deviations in crack tip blunting and fatigue crack growth from those that prevail for a hardening material.

A review of isotache modeling and secondary consolidation behavior of soft clays

Secondary consolidation of soils has gained much importance as a major contributor in the long term settlements of soft clays. In the scenario where constructions on such problematic soils are increasing, accurate prediction of long term settlements is very challenging. This paper reviews the evolution of the secondary compression characteristics from the concept of Cα to the creep isotaches. The generation of the 3 D elastic viscoplastic model from the equivalent time (isotache) approach is also discussed in this paper. This model is an extension of Maxwell’s rheological model. With relevance to Indian soils, the secondary compression characteristics of Kuttanad and Cochin marine clay are also reported in this paper.

Viscoelastic-plastic constitutive model with non-constant parameters for brittle rock under high stress conditions

Under the long-term effect of high stress, the stability problem caused by the time-dependent deformation of brittle surrounding rock in deep engineering is becoming more and more prominent. The accurate description of the effectiveness of brittle rock is an important basis for the prediction of mechanical response and the stability evaluation of surrounding rock in deep engineering. To describe the accelerated time-dependent deformation behavior of brittle rock, a Newtonian body with non-constant parameters considering the effects of stress state is proposed. Combined with the improved Burgers model, a viscoelastic model with non-constant parameters of brittle rock is developed. The effects of time, delay coefficient, and stress level on the viscosity coefficient, as well as the influence of delay coefficient and initial viscosity coefficient on the accelerated time-dependent deformation, are examined. The results show that (1) the viscosity coefficient decreases with time and increases with the delay coefficient, while the attenuation rate increases; (2) the viscosity coefficient decreases with increasing stress level, and its attenuation rate increases with time; (3) with the increase of the delay coefficient, the nonlinear characteristics of the accelerated phase of the rock time-dependent deformation curve become more and more obvious; and (4) as the initial viscosity coefficient increases, the nonlinear characteristics of the accelerated phase of the time-dependent deformation curve become less and less obvious. The above laws fully reflect the evolutionary law of the nonlinear time-dependent deformation of rock. By comparing the results of the marble creep test with theoretical predictions, we found that when the stress limit is exceeded, the established model can well describe the initial attenuation, steady state, and accelerated characteristics of the rock time-dependent deformation curve, thus verifying the ability of the proposed model to describe the accelerated creep behavior, as well as the overall rationality of the model.

Study on Improved Nonlinear Viscoelastic-Plastic Creep Model Based on the Nishihara Model

The description of rock creep by existing rheological models mainly focuses on the first two stages of creep. However, the description of the accelerated creep stage is rare, which is contrary to the common study of soft rock failure in engineering applications. Therefore, the study of the accelerated creep stage is an important research direction at present. In this paper, a new model that can describe accelerated creep is proposed on the basis of the Nishihara model, and creep constitutive relation of the model is deduced via relevant laws. The parameters of the model are obtained by the whole rheological curves of the sandy mudstone of the diversion tunnel of a hydropower station and the strongly weathered sandstone in the bottom of the Xiangjiaba dam foundation. A fitting analysis of the theoretical results and experimental data indicates that the fitting results are highly consistent; the correlation coefficients are all above 0.98, which shows the rationality and correctness of the model. The nonlinear viscoelastic-plastic model proposed in this paper can accurately describe the accelerated creep stage of rock, and its applicability is obviously broader than that of the traditional Nishihara model. This nonlinear viscoelastic-plastic model can be used to not only predict the critical sliding of a rock mass in slope, tunnel and hydraulic engineering but also enrich the theory of rock rheology.

Development and performance of new simplified method for soft soil with creep under multi-staged loading

In this paper, a new simplified method (de-coupled method) is presented for calculating consolidation settlements of a soft soil layer with creep under multi-staged loadings. All equations of this new simplified method are derived for a general multi-staged loading case. Different stress-states of the soil layer are considered. At the same time, a fully coupled finite element computer program with an Elastic Visco-Plastic (EVP) model and Hypothesis A method are used to calculate the consolidation settlements of the same soil layer with the same conditions. Then, the settlement results using this new simplified method are presented and compared with results from the finite element (FE) simulations and the Hypothesis A method. Based on the comparison, it is demonstrated that the new simplified method is much better than the Hypothesis A method. In addition, this new simplified method is used in the Berthierville test site subjected to three-staged loading. The comparison of calculated results and measured data demonstrates that the new simplified method is easy to use by simple spread-sheet calculation and has a good accuracy for the situations analyzed in this study.

Two-level elastic-viscoplastic model: application to the analysis of the crystal anisotropy influence

Multilevel crystal plasticity models have been widely used to study the processes of inelastic deformation of polycrystalline materials over the last 15-20 years. Anisotropy of plastic strains in crystallites is usually taken into account at the mesoscale, while their elastic properties are often assumed to be isotropic. The objective of this work is to assess the differences in the stress-strain characteristics (especially, residual mesoscopic stresses) by taking into account the anisotropy of elastic properties of materials calculated for the isothermal deformation of polycrystals with various types of crystallitelattice symmetry within a representative macrovolume. For this purpose, the results obtained by the authors were compared with the data received for the material with isotropic elastic properties and obtained using the Voigt-Reuss-Hill averaging procedures. The results of the analysis for the stress-strain state of polycrystalline samples with FCC, BCC, and HCP lattices obtained in a simple sheartest(up to the accumulated strain of 50%) are presented. The statistical two-level model developed on the basis of the geometrically nonlinear elasto-viscoplasticity theoryis used to perform calculations. In such constitutive models, the main fundamental relation is the elastic law written in the rate relaxation form in terms of the measures of the stress rates and strain rates, being independent of the choice of a reference frame (or superimposed rigid motion). It is shown that the analysis of the anisotropy effect has a noticeable impacton the characteristic macrovolume stress-strain state only at the initial stage of deformation. Subsequently, for deformations exceeding 1-1.5%, the difference becomes insignificant. At the same time, the results of calculations of the residual mesoscopic stresses (i.e., the stresses after unloading a representative macrovolume), which have a significant effect on the strength characteristics of materials, taking into account the crystallite anisotropy, turned out to be significantly different from those obtained under the isotropy hypothesis.

A constitutive model for the flow stress behavior and microstructure evolution in aluminum alloys under hot working conditions – with application to AA6099

A constitutive model for aluminum alloys under hot working conditions is proposed. The elastic-viscoplastic model is implemented in a finite strain continuum mechanical framework. The model accounts for the interplay between dynamic recovery and recrystallization during hot working of aluminum alloys and central aspects of microstructure evolution such as grain/subgrain size and dislocation density. The proposed model is generic in the sense that it can be used for arbitrary aluminum alloys, but in order to demonstrate its capabilities, the model is calibrated to a newly developed AA6099 alloy in the present study. The model is thoroughly discussed and details on the numerical implementation as well as on the calibration of the model against experimental data are provided.

Meso-scale failure simulation of polymer bonded explosive with initial defects by the numerical manifold method

Polymer bonded explosive (PBX) is a composite consisting of the polymer binder and embedded explosive particles, along with a large number of the particle/binder interfaces as the third constituent. The particle volume fraction is often higher than 90%. In the present work, a visco-elastic constitutive model, an elastic visco-plastic constitutive model and a bilinear cohesive contact relationship model are implemented into the numerical manifold method (NMM) program, an open source code programmed with C language, to describe the deformations of the polymer binder, the explosive particles and the particle/binder interfaces, respectively. The fracturing of the polymer binder and explosive particles is described based on the maximum tensile stress and the Mohr-Coulomb criteria. Three categories of initial defects, including the initial interfacial debonding, initial voids in the polymer binder, and initial micro-cracks in the explosive particles, are considered in the PBX meso-structures under both uniaxial tensile and compressive conditions. The tension-compression asymmetry, the influence of the initial defects on the meso-structure failure modes/patterns and the macroscopic effective tensile/compressive strength of PBXs are investigated. The factors that cause the differences between the NMM results and other numerical or experimental results are analyzed and discussed. This work enables and proves the NMM to be an robust numerical tool for further simulation studies of the mechanical performances of PBXs, as well as other particle-filled composites, at the meso-scale.

Crystal plasticity modeling and neutron diffraction measurements of a magnesium AZ31B plate: Effects of plastic anisotropy and surrounding grains

This study used in-situ neutron diffraction measurements and Elastic ViscoPlastic Self-Consistent polycrystal plasticity model, which incorporates a Twinning and DeTwinning scheme (denoted by EVPSC-TDT), to examine the macro-and micro-mechanical behaviors of a rolled AZ31B plate subjected to uniaxial tension. Three specimens were specifically designed for minimum, maximum and intermediate twinning: (1) loading along the rolling direction, (2) loading along the plate normal, and (3) loading along the direction 45° with respect to the plate normal. Apart from the macroscopic stress strain response, the measured diffraction intensities and internal elastic strains were obtained to examine the activities of the deformation modes at the grain level. The diffraction intensity evolution signaled the volume fraction change of twinning, while the internal elastic strain evolution designated the stress partitioning among the grain orientations. The effect of the surrounding grains on the development of the internal elastic strain was investigated by identifying the corresponding deformation mechanisms. Notably, the corresponding modeling work revealed that the EVPSC-TDT model permitted the prediction of the strain hardening and anisotropic behavior along the directions with minimum, maximum and intermediate twinning at the macroscale, and the evolution of the diffraction intensities and internal strains at the microscale. The results provide a physical understanding of the effects of the load direction, texture and surrounding grains on the role of the deformation modes in hexagonal close-packed polycrystalline materials.

Study on the dependence of the force of shock interaction on the body size using a mechanorheological model

The issues of modeling processes and designs in various industries are crucial. Particular attention is paid to dynamic processes of movement, vibration and shock interaction of structural elements and mechanical systems. Using the viscoelastic plastic model, the influence of the size of a spherical body on the force of shock interaction was studied. With an increase in the diameter of a spherical body, the body mass and the radius of curvature increase. The impact of both factors and each separate factor was evaluated using mathematical models of shock interaction. With a simultaneous increase in the body mass and the radius of curvature due to an increase in the diameter of a spherical body, the force of shock interaction increases. It was identified that an increase in the body mass causes a more significant increase in the force of shock interaction. An increase in the radius of curvature causes a slight increase in the force of shock interaction. Simultaneous changes in two factors cause a more significant increase in the force of shock interaction. An increase in plasticity of the model decreases the force of shock interaction. Thus, the results of the study show that the force of shock interaction depends significantly on the size of an interacting body due to the influence of the body mass and the radius of curvature on the dynamics of movement and deformation of bodies.

Proposal of a mathematical model for describing magnetorheological fluid dynamic behavior

This study proposes a model for describing magnetorheological (MR) fluid dynamic behavior. Experimental research was conducted to validate the model that represents the dynamic behavior of the MR fluid. MR fluid composed of 35 % carbonyl iron and 65 % silicon oil was used. In the experimental setup, sinusoidal excitation was applied to MR fluid under various frequencies while applying various currents, and the experimental data, including displacement, velocity, time and force, were recorded. Proposed model was described and details of the model explained. Force was predicted from the model by using computer software and approximated to experimental force. The error between the predicted results from the model and the measured data was calculated. After the experiments and optimization, the proposed model was compared with extended Bingham and viscoelastic-plastic models. After the analysis, it was seen that the proposed model coincides with other models in the literature. This novel model is practical to use in many engineering applications.

Microcrack and microvoid dominated damage behaviors for polymer bonded explosives under different dynamic loading conditions

A damaged viscoelastic-plastic model incorporating with both microcrack and microvoid evolution laws has been developed and implemented in the hydrodynamic code DREXH, to predict overall mechanical behavior and gain insights into possible failure mode of polymer-bonded explosives (PBXs) under complicated dynamic loading conditions. Multiple stress-state loadings will motivate evolution modes of microcracks, i.e., friction-locked, shear with friction, pure shear, mixed shear and open, and normal open, or microvoids, i.e., void collapse, void distortion. The simulated results connected the asymmetry of PBXs under uniaxial tension and compression with the critical stresses for open-crack and shear-crack initiation. Under high-confinement compression, crack growth is inhibited due to friction-locked (stable) state while more voids become collapsed accompanying with a strong plastic flow, corresponding to the occurrence of brittle-to-ductile transition for PBXs. Under simple shear loading, growth of pure-shear crack contributes more on failure rather than void distortion for pressed PBXs. Effects of void distortion on failure become more important for PBXs containing higher-fraction ductile binder. The simulated results agree with experimental observations and contribute to deepening our understanding of underlying microcrack and microvoid mechanisms for dynamic mechanical failure behavior of PBXs.

Elastic Visco-Plastic Model for Binary Sand-Clay Mixtures with Applications to One-Dimensional Finite Strain Consolidation Analysis

AbstractThe pore water dissipation of sand–clay mixtures is significantly affected by the sand fraction due to nonuniform stress distribution. On the basis of the elastic visco-plastic modeling con...

Rheological model of viscoelastic–plastic geogrid-reinforced tailings

A non-linear, four-parameter viscoelastic–plastic model is proposed to characterise the mechanical properties of geogrids under long-term and low-stress load. In this study, a simplified rheological model of viscoelastic–plastic geogrid-reinforced tailings was established. The stress analysis of the whole reinforced tailings complex was divided into two stages. The time for the tailings to produce plastic deformation (plastic arrival time) was the cut-off point for the two stages. The first stage (E-VP model) corresponded to the elastic state of tailings during which the stress of geogrids decreased with time, causing the recombination of microstress in tailings until they reached the yield condition. The second stage (P-VP model) corresponded to the plastic state during which the stress of geogrids remained constant, whereas the overall strain of the reinforced complex increased as a result of the geogrid creep. The force of the reinforced complex changed rapidly from the first to the second stage. Owing to the small deformation in the first stage, the overall strain of the complex was mainly caused during the second stage. The plastic arrival time t p of the reinforced tailings complex was significantly influenced by the plastic strain ε p and viscosity coefficient η of geogrids and internal friction angle ϕ of tailings.

Experimental investigation and simulation on stress rupture behavior of a Ni-based DS superalloy affected by initial elastic-plastic multi-axial stress state

In this study, the stress rupture behavior of a Ni-based directionally solidified (DS) superalloy affected by initial elastic-plastic multiaxial stress state at 850 °C has been investigated. Smooth and three types of U-shape notched plate specimens have been adopted. The notch effect on stress rupture lives is exhibited as notch softening, and there is a positive correlation between the degree of notch softening and theoretical stress concentration factor. Scanning electron microscopy (SEM) observation is conducted to reveal failure mechanism. For both smooth and notched specimens, thickness dependence on crack initiation due to the changed crack tip stress state is exhibited. The initiation of microcracks is mainly caused by interfacial decohesion at the carbide/matrix interface, non-uniform deformation field at eutectic/matrix interface and stress concentration around cavities. The plastic fiber zone of smooth plate is located in the intermediate region, which is occurred throughout a wide region near notch root of notched specimen. Finally, a finite element analysis (FEA) is performed based on the transverses elastic viscoplastic constitutive model with the Kachanov-Rabotnov damage rule. The simulation results show that the effect of notch softening is due to the fact that the redistributed tensile stress is higher than the value of net section stress in a very wide region.

Development of a Decoupled Multiscale Analysis Method for Woven Composites

In this study, development of a decoupled multiscale analysis method for woven composites is conducted. To this end, an elastic-viscoplastic macroscopic constitutive model which is able to express strong anisotropy of composites is introduced, and the material parameters in the constitutive model are determined based on the results of triple-scale homogenization analysis. Moreover, the constitutive model is implemented in the finite element analysis code LS-DYNA. The developed method is applied to 3-point bending analysis of plain-woven carbon fiber-reinforced plastic (CFRP) composites with various types of laminates configurations. It is shown that the present method can analyze their different behavior depending on the laminate configuration with greatly reduced computational costs.

A finite strain elastic-viscoplastic model of Gum Metal

A hyperelastic-viscoplastic model of Gum Metal is presented. The model is formulated in the large strain framework. The free energy function is postulated consisting of the hyperelastic and viscoplastic components. Original extension of the Neo-Hooke model with a power law component is proposed for hyperelasticity, which enables to describe a relatively large non-linear elastic regime observed for the alloy. Viscoplastic strain follows the Perzyna-type law with an overstress function. The model is implemented into the finite element method and used to simulate the Gum Metal response in multiple tension loading-unloading cycles. The results are compared with experimental outcomes. Good accordance of the simulation results and the available experimental data is obtained.

TIME EFFECT OF PILE-SOIL INTERACTION AND ITS ELASTIC-VISCOPLASTIC CONSTITUTIVE MODEL

Pile-soil interaction is considered to be one of the most important problems in the study of the mechanical behaviour of pile foundation. In this paper, the lateral friction resistance and pile-soil relative displacement of bridge piles in deep soft soils are monitored for an extended period by using concrete strain gauges that are embedded in the test pile. Field test results show that both the pile lateral frictional resistance and pile-soil relative displacement increase along with time, while the pile-soil interaction demonstrates a time effect. Therefore, an elastic-viscoplastic constitutive model must be established to better simulate the time-dependent mechanical behaviour of the pile-soil contact. Based on the Goodman model, we developed an elastic-viscoplastic interface constitutive model of the pile-soil interface into the FRIC subroutine through ABAQUS software, which is one of the most commonly used finite element analysis softwares in the world, to simulate a well-recorded pile test in deep soft soils. The calculated pile lateral frictional resistance and pile-soil relative displacement are close to the measured values, and the ability of the interface model to describe the changes in the shear stress-strain of the pile-soil interface along with time is validated.

Modelling Semi-Solid Behaviour and Brittle Temperature Range

In this paper, a new elastic viscoplastic micromechanical modelling is proposed to represent the semi-solid behaviour and predict the ductile-brittle transition of the C38LTT near the solidus. It is based on a viscoplastic modelling previously presented in [1]. The originality of the new model comes from three main enhancements: the transition between the solid state and the semi-solid state was included meaning that the material properties were taken temperature-dependent, the elastic properties was taken into account similarly as [2] and the evolution of the internal variable describing the degree of agglomeration of the solid phase was enhanced. The model was implemented in the commercial software FORGE©. Tensile tests representing the experimental thermal conditions and obtained using a GLEEBLE© machine were simulated. The comparison of the predicted and experimental results shows that, for the first time to our knowledge, the three steps of the load-displacement response and ductile-brittle transition were successfully described.