Viscoelastic-plastic Constitutive Model Research Articles

Experimental and numerical simulation investigation on dynamic fracture behavior of polymer bonded explosives under different high-g impact conditions

Impact tests of a projectile body penetrating a concrete target plate were carried out. In order to prolong the deformation stage without radial constraint of the PBX in the high-g impact environment and facilitate the study of the deformation and fracture of the PBX, the charging mode with a large gap was adopted. The different high-g environments of the PBX were realized by changing the weight of the steel pillar after the PBX. The mechanical response and damage failure modes of PBX with two different initial densities under different high-g impact conditions were investigated. Based on the viscoelastic-plastic constitutive model, a new constitutive model was developed by adding fracture. Then, the constitutive model established in this paper was used to simulate the impact tests in different deceleration environments using LS-DYNA large finite element software. By comparing with the experimental results, the results of the model were shown to be reliable and accurate. Through this model, the dynamic mechanical property curve and the fracture process of the PBX during the penetration process under high-g conditions, which could not be measured and observed in the test, were obtained. The crack propagation path and critical stress of the PBX under different high-g conditions were evaluated. The study is of great significance to analyze the dynamic failure mode of the PBX under high-g conditions.

Understanding the inelastic response of collagen fibrils: A viscoelastic-plastic constitutive model.

Collagen fibrils, which are the lowest level fibrillar unit of organization of collagen, are thus of primary interest towards understanding the mechanical behavior of load-bearing soft tissues. The deformation of collagen fibrils shows unique mechanical features; namely, their high energy dissipation is even superior compared to most engineering materials. Additionally, there are indications that cyclic loading can further improve the toughness of collagen fibrils. Recent experiments from Liu at al. (2018) focused on the response of type I collagen fibrils to uniaxial cyclic loading, revealing some interesting results regarding their rate-dependent and inelastic response. In this work, we aim to develop a model that allows interpreting the complex nonlinear and inelastic response of collagen fibrils under cyclic loading. We propose a constitutive model that accounts for viscoelastic deformations through a decoupled strain-energy density function (into an elastic and a viscous parts), and for plastic deformations through plastic evolution laws. The stress-stretch response results obtained using this constitutive law showed good agreement with experimental data over complex loading paths. Ultimately we use the model to gain more insights on how cyclic loading and rate effects control the interplay between viscoelastic and plastic deformation in collagen fibrils, and to extrapolate the results from experimental data, analyzing how complex cyclic load influences energy dissipation and deformation mechanisms. STATEMENT OF SIGNIFICANCE: In this work, we develop a viscoelastic-plastic constitutive model for collagen fibrils with the aim of analyzing the effects of inelasticity and energy dissipation in this material, and more specifically the competition between viscoelasticity and plasticity in the context of cyclic loading and overload. Experimental and theoretical approaches so far have not fully clarified the interplay between viscous and plastic deformations during cyclic loading of collagen fibrils. Here, we aim to interpret the complex nonlinear response of collagen fibrils and, ultimately, suggest predictive capabilities that can inform tissue-level response and injury. To validate our model, we compare our results against the stress-stretch data obtained from experiments of cyclic loaded single fibrils performed by Liu etal. (2018).

Fractional viscoelastic-plastic constitutive model for frozen soil based on microcosmic damage mechanism

Frozen soil is a kind of composite geotechnical material with significant creep properties. To develop a creep constitutive model that can consider the composite properties and internal microcosmic damage mechanism of frozen soil, it is first conceptualized as a binary medium material containing both bonded elements and frictional elements, and the creep breakage mechanism of frozen soil is analyzed. Then, the relationship between micro-strain and macro-strain is established based on the homogenization theory. The creep constitutive relations of bonded elements and frictional elements are established, respectively, based on the creep breakage mechanism and the fractional calculus theory. In addition, the breakage ratio is defined as a function of creep time. Finally, a new fractional constitutive model with a composite structure is established. The three-dimensional model is also derived to facilitate its extensive application. Reasonable agreement is achieved comparing the model prediction results with the creep experimental results, and the proposed model can accurately capture the creep deformation characteristics of each phase. The results of the parameter sensitivity analysis further demonstrate the applicability of the definition of composite structure for the frozen soil.

Evaluation of a nonlinear viscoelastic-plastic constitutive model in numerical simulation of thermoplastic polymers for stent application

Abstract To simulate the specific material properties of thermoplastic polymers a suitable constitutive model is essential. The parallel rheological framework (PRF) model was calibrated and evaluated in this study as potential constitutive model for polymer stent application. Tensile as well as recovery tests with different loading rates were performed using PLLA specimens. In order to calibrate the constitutive model, the conducted material tests were simulated accordingly. The parameters of the model were iteratively varied to obtain good accordance of the simulation with the material tests. In contrast to elastic plastic material models, viscoelastic material behavior can be represented with the nonlinear viscoelastic-plastic PRF model. The generated and possibly further refined model can be used for the simulation of polymer stents.

Viscoelastic-plastic constitutive model for the creep and stress relaxation characteristics of a geogrid

Viscoelastic-plastic constitutive model for the creep and stress relaxation characteristics of a geogrid

Viscoelastic–plastic constitutive model with damage of frozen soil under impact loading and freeze–thaw loading

This study aims to provide an understanding of the damage evolution and dynamic mechanical behavior of frozen soil under freezethaw (F-T) loading and impact loading.We used the split Hopkinson pressure bar (SHPB) device to evaluate the dynamic mechanical properties of frozen soil at different numbers and temperatures of F-T cycles. Our results indicate that the F-T process has a strong influence on the dynamic mechanical behavior of frozen soil. The peak stress of the frozen soil gradually weakens with an increase in the number of F-T cycles until the cycle number reaches the critical value for the steady state of the soil specimen (approximately 37 cycles). We observed a decrease in the peak stress of the frozen soil with a decrease in freezing temperature. We defined the F-T damage using wave impedance, which characterizes the microstructural properties of frozen soil, coupled it with the impact damage that satisfies the twoparameter Weibull distribution, and obtained the total damage of the frozen soil under F-T loading and impact loading. By combining the discretized ZhuWangTang (ZWT) model with the plastic theory that satisfies the DruckerPrager (D-P) yield criterion, which is based on the improved hardening criterion with strain rate terms, we constructed a viscoelasticplastic constitutive model with damage in frozen soil under F-T loading and impact loading. The results predicted by this model agree with the experimental data, validating its feasibility.

Viscoelastic–Plastic Constitutive Model Considering the Damage Characteristics of Concrete in the Process of Nonlinear Creep

Under long-term load, the creep deformation of concrete materials has a serious impact on the structural safety of hydraulic structures, especially under the action of ultra-high stress levels, the concrete materials will undergo nonlinear creep, which is extremely easy to cause structural damage. In this study, the uniaxial nonlinear creep test of concrete specimens was used to establish the damage index based on the wave velocity value of ultrasonic flaw detection, and the creep and damage degree curve of the concrete specimen were obtained. The ideal elastic element, the Kelvin body, and the nonlinear viscoplastic element are connected in series, and a new viscoelastic–plastic model considering the creep characteristics of concrete is proposed. Based on the principle of least squares, the Levenberg–Marquardt (LM) algorithm is used to inverse the parameters of the nonlinear creep test. In addition, the model is verified by the measured data of linear creep. At the same time, the sensitivity of each model parameter is analyzed. The research shows that the LM algorithm can give the fitting parameters of the model better and faster, and the fitting values of the model are similar to the experimental results. The sensitivity analysis of the parameters shows that the proposed model has good stability and good adaptability. The model has a more accurate description of the various stages of creep, and may be conveniently applied to concrete creep calculations in actual projects.

A Viscoelastic-Plastic Constitutive Model of Creep in Clay Based on Improved Nonlinear Elements

A Triaxial creep experiment was performed with Chengdu clay. The results demonstrate that the deformation of clay includes instantaneous elastic strain, attenuated creep deformation, steady creep deformation, and accelerated creep deformation. In view of the nonlinear properties of creep, an improved nonlinear viscous element describing attenuating creep and an improved fractional order viscous element describing accelerating creep are established, and a one-dimensional nonlinear fractional order five-element creep model is developed with the two improved elements. The model can theoretically describe the entire process of creep. The nonlinear fractional order five-element model and the traditional five-element model were employed to verify the creep test. Compared with the traditional five-element creep model, the nonlinear fractional order creep model more faithfully reproduces the experimental data and more accurately describes the deformation trend in each stage, especially the accelerated creep stage.

Research on viscoelastic-plastic damage characteristics of cement asphalt composite binder

In order to study the viscoelastic-plastic damage of cement asphalt composite binder (simplified as CACB) and the relationship between plastic damage and viscoelastic damage, a viscoelastic-plastic constitutive model (VE-P model) was constructed, and the viscoelastic-plastic damage process of CACB was analyzed. Effects of material composition and microstructure on viscoelastic-plastic damage were studied. During creep test, with the increase of stress ratio, the proportion of plastic strain and unrecoverable strain increases, and the ability of CACB to resist deformation and deformation recovery decreases. Stress ratio has different effects on elastic damage, viscous damage, delayed elastic damage and plastic damage. Temperature has little effect on elastic damage and delayed elastic damage, but has a greater effect on plastic damage. With the increase of initial plastic damage, the damage of elasticity, viscosity and delayed elasticity intensified. When A/C = 0.8, CACB can form a more reasonable microstructure, the mechanical properties of CACB are least affected by damage, and its mechanical properties are more stable. The research results in this paper provide a theoretical basis for CACB’s material design and performance evaluation.

Nonlinear Creep Behavior and Viscoelastic-Plastic Constitutive Model of Rock-Concrete Composite Mass

The joint force deformation of rock-concrete composite structures is different from that of simple rock specimens or concrete specimens, such as the tunnel surrounding rock-lining concrete, dam foundations, and concrete. In order to study the creep mechanical properties of rock-concrete composite structures under long-duration load, the TFD-2000 microcomputer servo triaxial creep testing machine is used to carry out step loading creep tests on rock-concrete composite specimens (hereinafter referred to as composite specimens) under different confining pressures (including the confining pressures σ3 = 0 MPa). The creep test results show that, under the same confining pressure, when axial deviatoric stress is applied step-by-step according to 10%, 20%, 30%, 40%, 50%, and so forth of the UCS (σ3 = 0 MPa) and TCS (triaxial compressive strength) of the composite specimens, the failure stress that the specimen can bear is closely related to the confining pressure. When the confining pressures are 0 MPa, 7 MPa, 15 MPa, and 22 MPa, respectively, the failure stresses that the composite specimens can bear are 60% (corresponds to 0 MPa), 50%, 30%, and 20% of the TCS under the current confining pressures, respectively. Under the same confining pressure, the initial creep rate of the composite specimen on each step shows a U-shaped change trend. Meanwhile, the instantaneous creep rate and failure creep rate of the specimen increase as the confining pressure increases. When the failure creep rate is excluded, the initial creep rate of other stepped loads at the same confining pressure level decreases step-by-step. The improved Nishihara model can better describe the whole creep process of rock-concrete composite specimens, especially in the accelerating creep step. The testing data and research results in this paper can serve as references for further research on mechanical properties of rock-concrete composite structures.

A macro–micro viscoelastic-plastic constitutive model for saturated frozen soil

A macro–micro creep constitutive model of viscoelastic-plastic deformation characteristics for three-phase saturated frozen soils is derived in this paper based on micromechanics, considering the influences of ice content and temperature. First, creep tests of saturated frozen soils are performed, and the mechanism of creep deformation is discussed from a micro perspective. Then, the micro-scale and macro-scale information are connected by establishing a relationship between the macroscopic strain energy rate and strain energy rate of the ice particles, soil matrix, and unfrozen water. The viscoelastic stress tensor for the three phases of materials is derived using the visoelastic correspondence principle and the micromechanics method. Thus, the macro-micro viscoelastic constitutive model for saturated frozen soils is obtained. Based on this analysis, the viscoelastic-plastic constitutive model is further considered for the viscoplastic properties of the soil matrix and ice particles. In addition, the corresponding relationship between viscoplastic and viscoelastic is established based on the “equivalent” method. Therefore, the macro-micro creep constitutive model of viscoelastic-plastic deformation characteristics for three-phase saturated frozen soils is finally derived. The model parameters are determined based on the creep tests of frozen soils and the model is verified using creep test results for saturated frozen soil. It is also determined that the proposed model can illustrate the influence of temperature and ice content on the creep of saturated frozen soils.

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.

A Viscoelastic-Plastic Constitutive Model of Shape Memory Polymer

ABSTRACTIt is of practical significance to develop a constitutive model which is able to predict the thermomechanical behaviors of the shape memory effect occurring in a shape memory polymer (SMP) accurately. The mechanism of shape memory effect of SMP is explained based on the assumption that SMP is composed by two phases, reversible phase and stationary phase. Especially the different flow elements are respectively added to the reversible phase and stationary phase in order to express the plastic behavior of SMP. There are two springs in series, one dashpot and one flow element in the reversible phase. There are two springs in parallel, one dashpot and one flow element in the stationary phase. A constitutive equation is developed to express the thermo-mechanical behaviors of shape memory effect in the SMP based on viscous-elastic mechanics and plastic theory. An internal variable, frozen ratio, is defined to follow the shape memory process in SMP, and the material properties are described as the functions of frozen ratio based on phase transition theorem. The developed constitutive model, which includes above constitutive equation and material parameter functions, is used to numerically simulate the thermo-mechanical behaviors of SMP under various load cycles. Results show that the developed constitutive model can not only predict the shape memory process of SMP accurately, but also express the rate-dependent behaviors of SMP effectively.

A Uniform Viscoelastic-Plastic Constitutive Model for MD-PMMA at a Wide Temperature Range

The deformation characteristics of MD-PMMA vary greatly at different temperatures. In the paper, whether a uniform model could be used to describe these complex characteristics was discussed. Tensile properties of MD-PMMA at the temperatures of -50˚C, -25˚C, 20˚C, 60˚C, 90˚C were experimentally investigated. The entire deformation processes of PMMA were divided into four stages: elastic stage, viscoelastic stage, yielding stage and post-yielding stage. Strain softening and strain hardening phenomenon occurred in the yielding and post-yielding stage, it was the results of the competition between loading rate and plastic strain rate. A nonlinear model of activation dashpot was constructed, in the model, the evolution rate of plastic deformation was defined by Eyring’s theory, and the actual stress was the difference between external applied stress and internal resistance stress caused by plastic strain. The above activation dashpot serially connected with the standard linear model (SLM) to identify elastic and viscoelastic characteristics. A two iterations integral algorithm was proposed to simplify the inter-coupling between the internal stress and the plastic strain, and the unknown parameters in the model could be easily fitted by the experimental data. This uniform viscoelastic-plastic model was demonstrated that could predict different deformation behaviors at a wide temperature range.

An internal-state-variable based viscoelastic-plastic model for polymers

In this study, a new viscoelastic-plastic constitutive model which has been formulated by utilizing the formalism of stress-like internal state variables is introduced. The developed constitutive equation allows for a good description of the inelastic material response of polymeric materials over a wide range of strain rates. An algorithm for numerical integration of the model equations has been derived. The FE implementation of the constitutive equation is widely discussed and the results of solving several exemplary problems are presented.

A viscoelastic-plastic constitutive model for uniaxial ratcheting behaviors of polycarbonate

In this paper, a modified viscoelastic–plastic constitutive model has been proposed on the framework of Anand's work to describe the uniaxial ratcheting behavior of polycarbonate (PC) under tension–tension cyclic loading. The experimental observation illustrates that the previously accumulated deformation has an assignable influence on the subsequent material response during the ratcheting process of PC. Thus, the deformation resistance in the viscoelastic micromechanism is assumed to be evolving with the local accumulated inelastic strain rather than keeping unchanged in the original Anand's model. The proposed model is validated firstly by the monotonic tension and creep experiment results of PC. Then, its capability to describe the uniaxial ratcheting behaviors is compared with Anand model. Finally, the modified model is adopted to study the effect of mean stress, stress amplitude, loading rate, and peak holding time on the ratcheting behaviors of PC. It is shown that the proposed model can predict reasonably the uniaxial tension–tension ratcheting behavior of polymer. POLYM. ENG. SCI., 55:2559–2565, 2015. © 2015 Society of Plastics Engineers

Visco-Elastic-Plastic Constitutive Model for A7N01-T6 Alloy Welding and Analytical Solutions with Finite Element Codes

This paper has established a viscoelasticplastic constitutive model for A7N01T6 alloy welding, which is temperature and deformation history dependent. The model uses elasticmixed hardening plastic and creep equation to describe the strain hardening at low temperatures and strain softening at high temperatures, respectively. Then it is applied for finite element numerical simulation of the welding process. By comparison with the conventional temperature dependent elasticperfectly plastic model, the overall longitudinal residual compressive plastic strain and the maximum deformation of welding sheet are larger. This is because that the plastic strain is mostly produced in high temperature range. Strain softening has great influence on the evolution of plastic strain. The compressive plastic strain during heating is larger than the tensile plastic strain during cooling. Strain hardening effect on welding residual strain and stress is almost negligible. Using the established constitutive model, welding residual stress and strain are in good agreement with the theoretical results.

A Study of Experimental Method for Mechanical Properties of Solid Propellant under Hydrostatic Compressive Loading

Mechanical behavior of solid propellant material under multi-axial loads has attracted much attention in engineering application. According to the properties of solid propellant material, a kind of triaxial compressive device for solid propellant material was designed by utilizing the operating principle of the soil triaxial compressive device. The structural features and operating principle were expounded, and some notes should be paid attention during tests, and mechanical properties of a kind of double-base propellant material under hydrostatic loading were investigated, and some very meaningful data and conclusions were obtained. The results show that the yield strength and compressive strength of double-base propellant material under hydrostatic loading have obtained more remarkable enhancement than those without the hydrostatic pressure effect. The experimental device and the test results may lay the foundation for further research into a viscoelastic-plastic constitutive model of solid propellant material.

Time-dependent mechanical response of a composite PFSA membrane

The mechanical response of a composite fuel cell membrane, made from layers of reinforced and unreinforced PFSA material, is investigated via both experimental and numerical means. First, the time-dependent mechanical properties for the reinforced layers are measured for a range of environmental and loading conditions. A three-network, viscoelastic-plastic constitutive model is developed to characterize the mechanical response of this reinforced membrane material. This constitutive model is then used in finite element simulations of a fuel cell unit (consisting of composite membrane, electrodes, gas diffusion layer and bipolar plates) where the effect of relative humidity (RH) cycling on the stress response of the composite membrane is investigated. Using numerical simulations, various layering configurations for the composite membrane and different load cases are studied. The investigation provides insight into the stress response of the membrane and suggests possible configurations that may improve the effective membrane life.

Effect of time-dependent material properties on the mechanical behavior of PFSA membranes subjected to humidity cycling

A viscoelastic-plastic constitutive model is developed to characterize the time-dependent mechanical response of perfluorosulphonic acid (PFSA) membranes. This model is then used in finite element simulations of a representative fuel cell unit, (consisting of electrodes, gas diffusion layer and bipolar plates) subjected to standardized relative humidity (RH) cycling test conditions. The effects of hold times at constant RH, the feed rate of humidified air and sorption rate of water into the membrane on the stress response are investigated. While the longer hold times at high and low humidity lead to considerable redistribution of the stresses, the lower feed and sorption rates were found to reduce the overall stress levels in the membrane. The redistribution and reduction in stress magnitudes along with inelastic deformation during hydration eventually lead to development of residual tensile stresses after dehydration. Simulations indicate that these tensile stresses can be on the order of 9–10 MPa which may lead to mechanical degradation of the membrane. The simulation results show that time-dependent properties can have a significant effect on the in-plane stress response of the membrane.