Elastic-viscoplastic Model Research Articles

Artificial ground freezing applications using an advanced elastic-viscoplastic model for frozen granular soils

Despite its increasing use and ongoing technical advance, artificial ground freezing (AGF) is still considered an expensive technique compared to conventional construction methods. The main reason for this is a conservative AGF design, which results from (semi-)analytical and elastic approaches that oversimplify the complex mechanical behavior of frozen soils. In contrast, advanced constitutive models for frozen soils offer a unique opportunity for efficient optimization of the AGF design. For this purpose, they must be implemented in finite element analysis (FEA) codes, extensively tested, and validated for AGF boundary value problems. This study presents the testing of a recently proposed elastic-viscoplastic model for frozen granular soils in both a shear and creep failure boundary value problem. The model can capture the rate-dependent ultimate shear strength for different temperatures observed in shear failure experiments from the literature. The simulation of a conventional tunnel excavation supported by a frozen soil body reflects the model's capability to accurately reproduce the frozen soil deformations experimentally measured during the excavation and the following creep phase. In addition, the tunnel boundary value problem is also simulated with an enhanced elastic model for frozen soils. Here, the comparison of both model responses highlights the geotechnical, economic, and safety AGF design potential of the proposed advanced model in relation to the simplified approaches commonly used hitherto.

Low strain rate yield characteristics and failure modes of solid composite propellant

Solid motor propellant grain is in low strain rate creep state under long-term storage condition. To analyze the yield characteristics and failure modes of HTPB (hydroxyl-terminated polybutadiene) propellant under different strain rate conditions, the constant speed tensile test of 2.38 × 10−5 s−1～2.38 × 10−2 s−1, 12-week long-term relaxation test and 4-week long-term creep test were carried out. The dynamic yield function of elastic-viscoplastic model was proposed, and the function parameters were fitted and verified by experimental data. The results show that the mechanical properties of the propellant show obvious rate dependence under lower strain rate, and the breaking strength and maximum elongation decrease significantly with the decrease of strain rate. The propellant starts to yield after strain reaching 15.0%, and the meso-structure enters an unstable state. The matrix and particle interface dewetting gradually becomes serious, developing into large particle shedding and matrix tearing, and finally causing macroscopic failure. The dynamic yield function can well describe the relationship between the dynamic yield strength, viscoplastic strain rate and static yield strength. The static yield strength of the propellant was analyzed and obtained as 0.06 MPa. The obtained yield strain and static yield strength can support the establishment of structural integrity failure criteria for long-term storage solid rocket motor.

Mesomechanical Aspects of the Strain-Rate Sensitivity of Armco-Iron Pulled in Tension

The phenomenon of the strain-rate sensitivity of metallic materials has been a topic of interest since the first mechanical tests at different strain rates were performed. The problem of its theoretical description appeared simultaneously. Despite the significant number of studies covering this issue, it is necessary to rule out a few drawbacks of previously reported models, which is the goal of this work. Herein, an extension of the elastic–viscoplastic model to a generalized state of stress is proposed while aiming to describe the strain rate sensitivity of Armco-iron samples that were pulled in tension within the framework of the finite-difference method. A mathematical model was formulated using equivalent stress and strain, which alleviated the complexity of the relaxation-type constitutive equations. The critical resolved shear stress (CRSS) function describes S-type instability with a single equation. The plastic strain rate was calculated based on the well-known Orowan equation, which is related to dislocation dynamics. In addition, the model took the material’s microstructure into account based on the design of a representative volume element (RVE) using the step-by-step packing (SSP) method. The results of the modeling were compared with the available experimental data and were found to satisfactorily correlate with them. The results suggest that the misfit error between the model and experimental data did not exceed 10% in the range of strain rates under study, which is a reliable outcome.

Investigation of high rate mechanical flow followed by ignition for high-energy propellant under dynamic extrusion loading

Investigating the ignition response of nitrate ester plasticized polyether (NEPE) propellant under dynamic extrusion loading is of great significant at least for two cases. Firstly, it helps to understand the mechanism and conditions of unwanted ignition inside charged propellant under accident stimulus. Secondly, evaluates the risk of a shell crevice in a solid rocket motor (SRM) under a falling or overturning scene. In the present study, an innovative visual crevice extrusion experiment is designed using a drop-weight apparatus. The dynamic responses of NEPE propellant during extrusion loading, including compaction and compression, rapid shear flow into the crevice, stress concentration, and ignition reaction, have been firstly observed using a high-performance high-speed camera. The ignition reaction is observed in the triangular region of the NEPE propellant sample above the crevice when the drop weight velocity was 1.90 m/s. Based on the user material subroutine interface UMAT provided by finite element software LS-DYNA, a viscoelastic-plastic model and dual ignition criterion related to plastic shear dissipation are developed and applied to the local ignition response analysis under crevice extrusion conditions. The stress concentration occurs in the crevice location of the propellant sample, the shear stress is relatively large, the effective plastic work is relatively large, and the ignition reaction is easy to occur. When the sample thickness decreases from 5 mm to 2.5 mm, the shear stress increases from 22.3 MPa to 28.6 MPa, the critical value of effective plastic work required for ignition is shortened from 1280 μs to 730 μs, and the triangular area is easily triggering an ignition reaction. The propellant sample with a small thickness is more likely to stress concentration, resulting in large shear stress and effective work, triggering an ignition reaction.

A thermal elastic visco-plastic model for soft clayey soils

It is frequently observed that the stress–strain behaviour of soft clayey soils is affected by temperature changes. Development and verification of a reliable constitutive model with consideration of variable temperature conditions are necessary. Due to the significant rheological and other nonlinear properties of clayey soils, the coupled effects of temperature, time dependency, structuration, nonlinear creep, and anisotropy should be considered in the constitutive model. In this study, a new three-dimensional (3D) thermal elastic visco-plastic model is established and verified for the time-dependent stress–strain behaviour of clayey soils considering temperature changes. The model is developed based on the existing elastic visco-plastic models with the equivalent time concept, the overstress theory, and the critical state model. The thermal elastic line and virgin heating line are introduced and generalized to construct constitutive equations for both thermal elastic and thermal visco-plastic behaviour of clayey soils in general stress conditions. After establishing the 3D basic model, further refinement is introduced to consider the nonlinear creep behaviour and structuration for natural and reconstituted clayey soils. Finally, the model is successfully validated by a series of laboratory test data on different clayey soils under variable temperature paths with reasonably good accuracy.

Triaxial creep tests and the visco-elastic-plastic constitutive model of hydrate formations

To study the creep properties of hydrate formations, triaxial mechanical tests and triaxial creep tests were conducted on hydrate-bearing samples. In addition, a visco-elastic-plastic constitutive model suitable for hydrate formation was established. Research results show that the higher the hydrate saturation, the stronger the cementation between skeletal particles. and the shear and crushing of the hydrate crystal during the loading process will increase the friction between the particles. As the hydrate saturation increases from 0 to 0.618, the cohesion of the samples increases from 0.4 MPa to 1.3 MPa; the angle of internal friction increases from 34.33° to 37.3°; and the long-term strength level increases from 0.5752 to 0.5866. When shear stress is lower than the long-term strength, the samples show attenuated creep characteristics, and the samples exhibit accelerated creep and constant visco-plastic deformation when higher than the long-term strength. Under identical shear stress, lower hydrate saturation corresponds to greater creep deformation of the samples. When the shear stress levels are close to strength, higher hydrate saturation corresponds to a faster accelerated creep rate. By connecting the elastic element, Kelvin element, and nonlinear viscous element in series, a viscoelastic model to describe the entire attenuated creep process of the hydrate-bearing samples is obtained. By linking the attenuated creep model with the nonlinear Newtonian element in series, a visco-elastic‒plastic model to describe the accelerated creep process of the samples is established. Compared with the test results, the calculation results of the models show a maximum error of only 7.12%.

On the cyclic torsion behavior of extruded AZ61A magnesium alloy tube

This work investigated the cyclic torsional behaviors of extruded AZ61A Mg alloy tubes through experiments and simulations. To capture the Bauschinger effect, the elastic viscoplastic self-consistent model with the twinning and detwinning scheme, together with a torsion-specific finite element approach was improved by adding a back-stress. A unique Swift effect with the “butterfly” shape was observed and reasonably reproduced by our model. Furthermore, the relative activities of deformation mechanisms, internal stress distributions, and twin volume fraction distributions under cyclic torsion were discussed. The findings could be beneficial to the design, manufacturing, and service of Mg alloys, particularly under cyclic torsion.

A novel parametric model for nonlinear hysteretic behaviours with strain-stiffening of magnetorheological gel composite

Magnetorheological (MR) gels are a new class of MR composite materials that can effectively address the issue of particle agglomeration in MR fluids, enhancing the controllability of materials in engineering applications. In this study, a novel parametric model was developed to track the nonlinear hysteretic behaviours with strain-stiffening of the MR gel. The model parameters were identified using the measurement data pertaining to five current levels (0A, 0.2A, 0.5A, 0.8A, and 1A) under a strain amplitude of 10% and a frequency of 0.1 Hz. The fruit fly optimisation algorithm (FOA) was used to determine the optimal solution for the model parameters. The model parameters were generalised with respect to the loading current, and the reliability of the generalised model was verified. The results of the study demonstrate that the proposed model outperforms two classical models, the Bouc–Wen model and viscoelastic–plastic model, in capturing the nonlinear and strain-stiffening behaviour of MR gels, particularly for higher current excitations. This study has potential applications in predicting the nonlinear hysteresis behaviour of automotive dampers, and provides a theoretical basis for the semi-active control of suspensions.

Study on the nonlinear time-dependent deformation characteristics and viscoelastic-plastic model of shale under direct shear loading path

Study on the nonlinear time-dependent deformation characteristics and viscoelastic-plastic model of shale under direct shear loading path

An elastic-viscoplastic model for time-dependent behavior of unsaturated soils

Modeling the time-dependent behavior of unsaturated soil is a topic that is poorly addressed by the current literature. This paper presents a novel elastic-viscoplastic constitutive model for reproducing the time-dependent behavior of unsaturated soil. The model is established using the theoretical framework of the Unified Hardening (UH) model and the Barcelona Basic Model (BBM) combined with Perzyna's overstress theory. A unified hardening parameter is introduced to modify the elastic-viscoplastic constitutive model to consider the effect of the loading history. A new expression for the secondary consolidation coefficient considering the effect of suction is presented, and the state variables related to the void ratio of unsaturated soil considering the time effect are derived. Combined with the one-dimensional viscoplastic hardening parameter, the viscoplastic scalar multiplier in overstress theory is presented, and a three-dimensional elastic-viscoplastic constitutive model is then constructed. With 17 parameters, the proposed model can describe the effects of time and suction on the shear, dilatancy, and compression behaviors of unsaturated soil with various initial void ratios and stresses. Comparisons between the model predictions and experimental data are employed to validate the capability of the proposed model in terms of reproducing the time-dependent behavior of unsaturated soil or soft rock.

A New One-Dimensional Thermal Elastic-Viscoplastic Model for the Thermal Creep of Saturated Clayey Soils

A New One-Dimensional Thermal Elastic-Viscoplastic Model for the Thermal Creep of Saturated Clayey Soils

An elastic–viscoplastic model with non-affine deformation and rotation of a distribution of embedded fibres

A large deformation continuum model for an elastically isotropic visco-plastic matrix reinforced by a distribution of fibres has been formulated. The fibre distribution is a symmetric positive-definite tensor with unit trace that is determined by an evolution equation. This evolution equation includes a competition between tendencies for affine evolution of the distribution and non-affine evolution causing the distribution to align with the elastic distortional deformation tensor or to become isotropic. Two elastic deformation measures are introduced associated with the fibre distribution. Specifically, non-affine measures of elastic distribution stretch and non-coaxiality of the distribution cause anisotropic stress response. The resulting model describes a number of effects relevant to growth and remodelling of biological tissues as well as to additive manufacturing of artificial materials. For example, the equations model the smooth transition from isotropic to anisotropic response seen in many biological tissues.

An Egg-Shaped Elastic Viscoplastic Model for Clay: Experimental Investigation and Constitutive Modelling

This paper presents the experimental investigation carried out for evaluation of the rheological behaviours of Hangzhou soft clay, and proposes a three-dimensional elastic viscoplastic model to describe the rheological characteristics under triaxial condition. Firstly, the time-dependent behaviours of Hangzhou soft clay, such as creep and strain rate effects, were observed and discussed based on the analysis of rheological tests. Subsequently, a constitutive model was formulated under the framework of Perzyna's overstress theory and incorporates other developments, including: 1) A smooth and continuous egg-shaped yield surface, whose shape can change from an ellipse to a teardrop shape, thus providing greater flexibility for better modelling; 2) An equivalent time concept, which enables the model to describe the time-dependent behaviours under different loading paths. By varying the shape parameter, the newly established model can be degenerated into modified Cam-clay (MCC) model or Yin-Graham elastic viscoplastic model. Finally, the model was solved numerically using the fourth-order convergent iterative method combined with the Runge-Kutta method. Comparison of simulation results and experimental data shows that the newly proposed model has an ability to predict creep characteristics and strain rate effects of soft clay.

One-dimensional elastic viscoplastic finite strain consolidation model for soft clay with uncertainty

One-dimensional elastic viscoplastic finite strain consolidation model for soft clay with uncertainty

Mechanical Properties of Gas Storage Sandstone under Uniaxial Cyclic Loading and Unloading Condition

In order to study the mechanical properties and damage evolution of the gas storage surrounding rock under the periodic injection-production process, the uniaxial cyclic loading and unloading tests of sandstone were carried out by TFD-2000 microcomputer servo-controlled rock triaxial testing machine. Results shown that the compressive strength of gas storage sandstone specimens were gradually decreases with increasing of the stress amplitude after 200 cycles. The stress-strain curve under uniaxial cyclic loading and unloading condition formed hysteresis loops, and the hysteresis loop presented sparse-dense-sparse when the stress amplitude was relative higher. The residual strains can be divided into three stages of decay deformation stage, stable deformation stage and accelerated deformation stage when the stress amplitude is 8~32 MPa, this phenomenon is very similar to the creep behavior of rocks. The energy evolution of sandstone under cyclic loading and unloading was analyzed and the damage evolution low of which was also discussed in detail, the damage variable defined by energy dissipative ratio accumulation can well reflect the damage development of sandstone under uniaxial cyclic loading and unloading. A nonlinear visco-plastic body was proposed by considering the accelerate stage of curves of the axial residual strains, and used the nonlinear visco-plastic body to replace the visco-plastic body of the traditional Nishihara model, a nonlinear viscoelastic-plastic model for cyclic loads was established and the applicability of the model is verified. The research results provide certain reference value for the construction and maintenance of gas storage.

The strain rate sensitive and anisotropic behavior of rare-earth magnesium alloy ZEK100 sheet

To overcome the limitation in formability at room temperature, manufacturers have developed magnesium alloys with remarkable properties by adding rare-earth elements. The rare-earth magnesium alloys behave differently from the conventional alloys, especially with respect to their coupled anisotropic and strain rate sensitive behavior. In the current work, such behavior of the rare-earth Mg alloy ZEK100 sheet at room temperature is investigated with the aid of the elastic viscoplastic self-consistent polycrystal plasticity model. Different strain rate sensitivities (SRSs) for various deformation modes are employed by the model to simulate the strain rate sensitive behaviors under different loading directions and loading rates. Good agreement between the experiments and simulations reveals the importance and necessity of using different SRSs for each deformation mode in hexagonal close-packed metals. Furthermore, the relative activities of each deformation mode and the texture evolution during different loadings are discussed. The anisotropic and strain rate sensitive behavior is ascribed to the various operating deformation modes with different SRSs during loading along different directions.

Viscoelastic–plastic response of tunnels based on a novel damage creep constitutive model

Geomaterial rheology plays an important role in engineering stability and can be used to understand the deformation behavior of rocks. This study proposes a novel damage constitutive model to describe the rheological properties of rocks, which includes a Maxwell body, a Kelvin body, and a new damage-plastic element. A series of uniaxial rock creep tests were performed, and the experimental results can verify the proposed viscoelastic–plastic model. A closed-form analytical solution of surrounding rock creep in a circular tunnel is derived using the proposed model, and parametric studies are examined to determine the influence of parameters on the surrounding rock deformation. Dengjiashan tunnel in Sichuan, China is employed to verify the analytical solution. The results show that the proposed viscoelastic–plastic model well describes the entire rock creep process. The geological strength index has a significant influence on the surrounding rock deformation. The analytical results agree well with the experimental and monitoring data. The proposed analytical solution can therefore be applied to predict the creep deformation of surrounding rocks due to tunnel excavation.

Этапы подготовки к прерывистому скольжению на предварительно вырезанных разломах в лабораторных моделях и проверка этапов в природе

This study is focused on analog modeling of the stick-slip process along an existing large fault in an elastic-viscoplastic model subjected to loading at a constant strain rate. Based on our model results and data from (Ma et al., 2012, 2014), we distinguish stable, meta-stable, and meta-instable stages of the stick-slip process (the latter includes the early and late sub-stages). Our experiments show that the fault is periodically reactivated by segmentation. We analysed this mechanism from one fault reactivation to another, and identified regressive and progressive trends of segmentation. The regressive segmentation takes place during the stable and meta-stable stages of the stick-slip process. Under regressive segmentation the number of active segments and their lengths are reduced. The progressive segmentation is initiated at the early meta-instable sub-stage of the stick-slip process. Its activity is desplayed by an increase in the number of active segments to a certain critical density, while their pattern becomes more chaotic. In the late sub-stage, number of segments decreases as they rapidly grow and join with each other to form larger active segments, up to full reactivation of the entire fault. For comparison with the model results, we interpret rock deformation monitoring records before the Bystroe earthquake. Our analysis confirms specific features of the anomalous rock deformation that are similar to the strain features observed along the model fault during the meta-instable stage. There are evidence to suggest that meta-instability of a fault is a potential candidate to short-term precursor of earthquakes.

Viscous Behavior and Constitutive Modeling of Peaty Soil in Kunming, China

The Kunming peaty soil exhibits distinct physical and mechanical properties from the inorganic clay due to the special soil-forming process and material composition. To better understand the viscous behavior of peaty soil, a series of laboratory tests, including four types of oedometer tests (one- and multistage loading creep tests, constant rate of strain tests, and constant rate of stress) and constant rate of strain undrained triaxial compression tests, are conducted on the Kunming peaty soil. The experimental results demonstrate that the Kunming peaty soil shows significant secondary compression during oedometer creep tests. Meanwhile, the variations of the measured preconsolidation pressure and undrained shear strength with the strain rate are essentially linear in log-log plot for the examined range of strain rate. Based on the generalized power law overstress viscoplastic theory, it is confirmed that the rate-sensitivity and time-dependency of the Kunming peaty soil can be uniformly described using the sensitivity parameter involved in the theory, regardless of the applied loading conditions. The average value of 0.06 for the sensitivity parameter is generally greater than those for inorganic clay, indicating that the Kunming peaty soil exhibits more significant viscous behavior. Finally, by using the yield surface of the modified Cam–clay model, an overstress elastic-viscoplastic model is established and numerically implemented. The numerical model with a unique sensitivity parameter can well predict the rate-sensitive and time-dependent response of Kunming peaty soil under different loading conditions.

Creep Properties of Mudstone Interlayer in Bedded Salt Rock Energy Storage Based on Multistage Creep Test: A Case Study of Huai’an Salt Mine, Jiangsu Province

Salt rock is internationally recognized as an excellent medium for energy storage. However, most of the domestic salt mines are lacustrine laminated formations with mudstone interlayers, which have different creep characteristics to pure salt rocks. Therefore, in this paper, uniaxial compression creep tests were carried out on a mudstone interlayer in Huai’an, Jiangsu, China, and the multistage creep mechanical behavior of the mudstone interlayer was investigated using acoustic emission (AE) technology. The results show that at low stress levels, the axial deformation of the interlayer is greater than the lateral deformation. As the increase of the stress level, the lateral deformation becomes more significant, and the corresponding axial and lateral steady-state creep rates both exhibit nonlinear acceleration with the increase of the loading stress. In the initial loading stage of each stress level, the mudstone interlayer releases a large number of AE signals. After the creep stabilization, the AE signals decreased obviously, and a large number of AE signals were released at the last stress level. Based on the creep test data, an improved fractional viscoelastic-plastic model was fitted to it and compared with the Nishihara model. The applicability of the model was also tested, and the model was found to be a good description of the mudstone interlayer after oil erosion. The research results reflected the creep law of the mudstone interlayer to a certain extent and are expected to serve as a reference to studies on the long-term stability of the surrounding rock of a bedded salt rock energy storage.