Unloading Modulus Research Articles

Experimental study on the deformation behavior of soils under one-dimensional unloading

Soils are usually subjected to one-dimensional unloading due to the excavation, groundwater recharge, and other activities. This paper investigates the deformation behavior of soils under one-dimensional unloading. A series of oedometer tests with loading–unloading cycles were conducted on silty sand, silt, silty clay, and muddy silty clay samples extracted from southern Jiangsu, China. The influence of effective vertical stress before unloading on rebound deformation of soils was investigated. Test results show that the unloading deformation of soils increases nonlinearly with the increasing unloading ratio. When the unloading ratio reaches 0.8, only 30% of the total rebound deformation occurs. The rebound ratio increases with the increasing effective vertical stress before unloading. A power function was proposed to describe the relationship between one-dimensional unloading modulus and unloading ratio with two parameters named initial one-dimensional unloading modulus and decrease rate of the one-dimensional unloading modulus. The initial unloading modulus increased linearly with the increase of effective vertical stress before unloading, and a power function could be used to describe the relationship between the decrease rate and effective vertical stress. Formulas were also proposed to predict the initial unloading modulus and decrease rate of the one-dimensional unloading modulus based on piezocone test measurements.

SLM-printed lattice structures with tapered vertical struts: Design, simulation and experimentation

This study, designed new lattice structures using vertical struts that taper off. The degree of tapering was controlled using a parameter called “α”. To fabricate these structures, 3D-printing technology known as SLM (selected laser melting) was used. These lattice structures were also simulated using finite element analysis (FEA) and tested experimentally. The used material was 316L stainless steel. Stress–strain curves provided insights into their deformation behavior, revealing a noteworthy occurrence: the unloading modulus exceeded the loading modulus. The mechanical properties of these absolute and density-normalized lattice structures, demonstrated improvement with higher values of the shape parameter α. Yield stress increased by 31 %, loading modulus by 21 %, and energy absorption by 33 %. Specific yield stress improved by 24 %, and specific energy absorption increased by 27 %. While simulation and experimental results exhibited a correlation, they differed significantly in modulus estimation, with simulations overestimating it by more than 30 %.

Distinctive mechanism and model for whole-life ratcheting of cement-stabilized aggregates in tensile fatigue tests

In light of the limited research on the fatigue damage and plastic strain evolution of cement-stabilized aggregates (CSA) despite their widespread application, this study aims at modeling the ratcheting of CSA, which provides better characterization of fatigue by counting plastic strain accumulation. Uniaxial and indirect tensile fatigue tests were conducted to obtain the plastic strain accumulation and stress-strain curves. A bar system was constructed to describe the ratcheting mechanism of CSA, which considers the non-homogeneity of CSA's components and composes parallel bars with a distribution of plastic-damage properties. The ratcheting rate variation was attributed to the strength distribution of the bars. Then, to prevent complex and hard-to-implement parameter fitting, a predigested ratcheting model was proposed, which focuses only on the secant modulus and simplifies the generation of ratcheting to the difference between reloading and unloading secant modulus. The test results revealed a three-stages characteristic in the ratcheting evolution of CSA. The non-coincidence of reloading and unloading curves was deemed the intuitive cause of the ratcheting. The numerical implementation of the proposed mechanism indicated that the strength and modulus discrepancies between weak and strong bars can lead to ratcheting. By comparing with the experimental results, the effectiveness of the proposed model was verified in describing the ratcheting evolution of CSA and to characterizing the non-linearity of the accumulation curves. Moreover, the parameter fitting process requires the results of the current fatigue test instead of parallel tests or other loading tests, successfully eliminating calibration difficulties resulted from significant property discrepancies among CSA specimens.

The Mechanical Behavior and Constitutive Model Study of Coarse-Grained Soil under Cyclic Loading–Unloading in Large-Scale Plane Strain Conditions

To address loading and unloading issues in civil and hydraulic engineering projects that employ coarse-grained soil as fill material under plane strain conditions during construction and operation, cyclic loading–unloading large-scale plane strain tests were conducted on two types of coarse-grained soils. The effects of coarse-grained soil properties on shear behavior and various modulus relationships were analyzed. The research results showed that coarse-grained soils with better particle roundness exhibit significant shear dilation deformation; it was also found that low parent rock strength can lead to strain softening, and an increase in confining pressure suppresses shear dilation deformation. During the cyclic loading–unloading process, the initial unloading modulus (Eiu) > unloading–reloading modulus (Eur) > initial reloading modulus (Eir) > initial tangent modulus (Ei), with the unloading modulus considerably greater than the others. In finite element simulations and model calculations, it is essential to select appropriate modulus parameters based on the stress conditions of the soil to ensure calculation accuracy. In this work, an elastoplastic and nonlinear elastic theory was used to establish a cyclic loading–unloading constitutive model. By comparing the values obtained using this model with experimental measurements, it was found that the model can reasonably predict stress–strain variations during cyclic loading–unloading of coarse-grained soils under plane strain conditions.

An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results. The improved model assumes that total strain is a combination of plastic, elastic, and crack strains. The constitutive relationship between the crack strain and the stress was further derived. The evolutions of mechanical parameters, i.e. strength parameters, dilation angle, unloading elastic modulus, and deformation parameters of crack, with the plastic strain and confining pressure were studied. With the increase in plastic strain, the cohesion, friction angle, dilation angle, and crack Poisson's ratio initially increase and subsequently decrease, and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease. The increasing confining pressure enhances the strength and unloading elastic modulus, and decreases the dilation angle and Poisson's ratio of the crack. The theoretical triaxial compressive stress-strain curves were compared with the experimental results, and they present a good agreement with each other. The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

A strain rate and temperature dependent model for describing nonlinear unloading stress-strain response after warm and hot compression deformation

For an accurate numerical simulation of springback behavior and control of shape and dimensional accuracies of the manufacture component under warm and hot precision plastic forming, the use of an appropriate material model dependent with strain, strain rate and temperature describing the nonlinear unloading process is vital, which is remained to be developed. The thermo-mechanical coupling effect in difficult-to-form material deformed at elevated temperature makes the unloading process more complicated and thus more difficult to model. In this paper, by using face-centered cubic (FCC) aluminum alloys as case study materials, loading-unloading experiments with different strains and strain rates at warm and elevated temperatures of 300 – 500 °C were conducted, the effects and contributions of strain, strain rate and temperature on unloading chord modulus (elastic modulus) and nonlinear unloading stress-strain response were quantified. A unique strain-, strain rate- and temperature-dependent nonlinear unloading coupled model was established. By validating and applying the nonlinear unloading coupled model in the both monotonous loading-unloading and cyclic loading-unloading warm and hot compression deformation, the calculation results agree well with experimental results, indicating that the model can describe perfectly the nonlinear unloading stress-strain responds and springback behavior. From the discussion on calculated results and capabilities of model, it was found that the proposed unified equation incorporating strain rate and temperature is also able to be coupled with the existing strain-dependent chord modulus model such as modified Yoshida-Uemori (Y-U) model. The capability of predicting nonlinear unloading curves and springback strains of aluminum alloys deformed at various strains, strain rates, and temperatures demonstrates the potential applicability of the model to a wide range of warm and hot forming process conditions.

Monitoring early age elastic and viscoelastic properties of alkali-activated slag mortar by means of repeated minute-long loadings

This study investigates the development of elastic and creep properties of sodium hydroxide-activated blast furnace slag mortar, utilizing three different molarities of the activator solution and two solution-to-binder ratio and a reference OPC-based mixture, since the earliest age. The experimental phase involves a series of hourly-repeated 5-min long creep tests on the aging material. This approach enables continuous monitoring, facilitating the characterization of early-age elastic stiffness and creep properties. Linear regression is employed to calculate the tangent unloading (elastic) modulus and Poisson's ratio. To model short-term creep behaviour, a power-law creep function is utilized. The integration of these findings with calorimetry-derived evolutions of cumulative heat release establishes linear correlation between (compressive) strength and heat release, along with a power function relationship between unloading (elastic) modulus and heat release. An optimal alkali dosage (Na2O content) appears to be vital for long-term strength development. Additionally, the creep parameters, namely amplitude (A) and kinetic (K), demonstrate a gradual decrease, although they maintain values higher than those of the corresponding OPC mixture, as the heat release progresses.

Experimental study on cyclic deformation properties of saturated Fujian sand at different loading frequencies

In this study, a series of undrained cyclic torsional shear tests were conducted to investigate the effect of cyclic loading frequency f on the pre-liquefaction (shearing contractive (SC) period and initial shearing dilative (ISD) period) and post-liquefaction (late shearing dilative (LSD) period) deformation properties of saturated Fujian sand. The secant shear modulus G and damping ratio λ in the entire cyclic loading process, and the unloading tangent shear modulus GL1 and flow deformation tangent shear modulus GL2 in the ISD and LSD periods were adopted to quantitatively characterize the evolution of hysteresis loop with an increase in shear strain amplitude γa. The test results show that the effect of f on G of saturated Fujian sand in the SC period is not apparent. However, all the G-γa, GL1-γa, and GL2-γa curves in the ISD and LSD periods showed a downward trend with an increase in f. This study also proposes a modified method for calculating λ to compensate for the analytical error caused by the non-closure of hysteresis loop. Compared with the classical curves that mainly applied in geotechnical engineering, the λ first increases and then decreases with the increase of γa. Furthermore, the λ evaluated by the modified method is approximately 10%–15% more than the λ evaluated by the traditional method when the λ reaches its peak value.

The Influence of Cyclic Load Amplitude on Mechanical Response and Acoustic Emission Characteristics of Granite

Cyclic loading and unloading tests with varying stress amplitudes were carried out to study the evolution trends of the elastic modulus, plastic strain, dissipated energy density, and acoustic emission events for granite under cyclic loading with accidental extreme stress. The results were as follows: (1) The loading deformation modulus before and after extreme stress is different. In addition, at extreme stress levels, the loading deformation modulus of granite specimens decreases by approximately 5~13%, but the unloading deformation modulus does not change significantly. (2) When extreme stress causes rock damage, most of the plastic deformation potential of the rock at this stress level is released in advance. The stress constantly varies in the subsequent low-amplitude cycle, and the plastic strain caused by the extreme stress is partly recovered. (3) As the extreme stress increases, the cumulative dissipated energy density of granite increases significantly. Compared with the control group without a stress extremum, the cumulative dissipated energy density of samples in two groups with stress extrema of 20 kN and 40 kN increased by 48% and 153%, respectively. (4) A significant acoustic emission event occurs only when the rock is subjected to a load exceeding the maximum historical stress for the first time, and the acoustic emission intensity is positively correlated with the difference between this stress and the historical maximum value. (5) Extreme stress values below the crack damage threshold reduce the crack growth potential of the rock in advance, and extreme stress above the crack damage threshold aggravates rock damage.

Drainage effects on shear behaviour and stiffness of subgrade soils and pavement drainage implications

Adequate drainage will generally benefit pavement structures and thus extend pavement life. In this study, drainage effects on subgrade and pavement response were quantitatively studied based on laboratory tests and simulation analysis. Single-stage and multistage loading triaxial tests were conducted, including consolidated undrained and drained triaxial tests. Stress–strain behaviour and unloading modulus were obtained for the silty sand. Particularly, pavement analysis was performed using unloading modulus to represent subgrade modulus. The results show that with drainage between loading stages, the specimen showed significant increases in peak and critical state shear strength. Due to drainage, the unloading modulus also showed a significant increase. Power-function relationships were observed between unloading modulus and effective confining pressure changes. The pavement analysis results indicate that drainage effectiveness could be impaired without considering actual engineering conditions, e.g. subgrade drainage improvement for a fatigue-critical pavement may be uneconomic. This study may facilitate the understanding of drainage effects on soil behaviour and pavement response.

Influence of volume compression on the unloading deformation behavior of red sandstone under damage-controlled cyclic triaxial loading

A reasonable evaluation of unloading deformation characteristics is of great significance for the effective analysis of deformation and stability of surrounding rocks after underground excavation. In this study, the damage-controlled cyclic triaxial loading tests were conducted to investigate the pore compaction mechanism and its influences on the unloading deformation behavior of red sandstone, including Young's modulus, Poisson's ratio, volumetric strain, and irreversible strain. The experimental results show that the increases of volumetric and irreversible strains of rocks can be attributed to the compaction mechanism, which almost dominates the entire pre-peak deformation process. The unloading deformation consists of the reversible linear and nonlinear strains, and the irreversible strain under the influence of the porous grain structure. The pre-peak Young's modulus tends to increase and then decrease due to the influence of the unloading irreversible strain. However, it hardly changes with the increasing volumetric strain compaction under the influence of reversible nonlinear strain. Instead, the initial unloading tangent modulus is highly related to the volumetric strain, and clearly reflects the compaction state of red sandstone. Furthermore, both the reversible nonlinear and irreversible unloading deformations are independent of confining pressure. This study is beneficial for the theoretical modeling and prediction of cyclic unloading deformation behavior of red sandstone.

Influence of specimen size and density variation in the foam rise direction on the compressive behavior of PVC foams

Mechanical properties governing the localized deformation mechanisms, apparent elastic modulus and their correlation to specimen geometry in polymeric foams are important phenomena that are not well understood. Despite the well-studied density variation in Functionally Graded Foams (FGF), density variation in the foam rise direction of conventional foams has not received adequate attention in the current literature. The influence of specimen size and density variation on the deformation mechanisms and mechanical properties observed in the rise direction of H-series rigid PVC foams were experimentally investigated in this study by considering four distinct specimen sizes and five nominal densities. PVC foams with different nominal densities exhibited various density variation patterns, in a range of 2.6–26.3 % variation, in the foam rise direction which were found to govern the polymeric foams’ localized deformation mechanisms and the post-yield stress drop-off behavior. The plateau stress was observed as most sensitive to the foam density; specimens with higher densities exhibited up to 19 % higher plateau stress within the foam panel with a 200 kg/m3 nominal density. While specimen thickness significantly influenced the loading elastic modulus. Intermittent unloading-reloading cycle testing was conducted on thick and thin specimens to characterize the influence of specimen thickness on the apparent elastic modulus. The influence of thickness on the unloading elastic modulus was negligible, for example, reducing the specimen thickness from 25.40 mm to 6.35 mm decreased the loading and unloading elastic moduli by 39 % and 7 %, respectively, for PVC foams with a nominal density of 200 kg/m3. Therefore, the unloading elastic modulus should be utilized in future studies for more accurate cross-comparison between the mechanical properties of specimens with significantly different thicknesses.

A plastic-damage material model for foam concrete under blast loads

Foam concrete is a prospective material in defense engineering to protect structures subjected to intense dynamic loadings such as impact and blast through wave impedance mismatch as well as energy absorption. In the near-field of intense dynamic loadings, the foam concrete is always suffered from a high-pressure stress state associating with complex failures such as pore collapse, shear fracture and tensile fracture. A well-established material model is needed to capture above-mentioned behaviors. In this paper, a plastic-damage material model for foam concrete is proposed focused on its mechanical behavior under high pressures. Firstly, a closed form yield function, a partially-associative flow rule and a new piecewise hardening law are introduced. The yield function is composed of a fracture function describing the mechanical behavior due to microcracks and a continuous cap function describing the mechanical behavior due to pores. The partially-associative flow rule is used to avoid the overestimation of plastic strain induced by the classical associative flow rule. In particular, a new piecewise hardening law is proposed instead of frequently-used exponential ‘‘crush curve’’, which is flexible for fitting test data and can capture the experimentally-observed increase of unloading bulk modulus with increase of pressure. The rate dependency of yield surface is considered to capture the strain-rate effect of foam concrete. And then three independent damage indexes with clear physical background are proposed to describe irreversible degradation caused by microcrack growth and pore collapse. The shear damage caused by shear cracks, tensile damage caused by tensile cracks, and hydrostatic compression damage caused by pore collapse, are separately identified and proposed in the framework of continuum damage mechanics. The proposed model is embedded into the LS-DYNA through the subroutine of user-defined material model. Its performances for predicting complex failures under various stress states at a Gaussian point level are numerically evaluated using a single element, and further used to predict blast response of foam concrete. All the numerical predictions agree with test data well.

Numerical Method for the Deformation Calculation of the Shallow Buried Tunnel Caused by the Excavation of Overlying Soil Based on Soil Rebounding Characteristics

In view of strict deformation control standards, it is important to calculate the shallow tunnel deformation caused by the unloading of overburdened soil for analyzing tunnel structure safety. Due to the obvious nonlinear characteristics and the significantly smaller rebound deformation of soil under unloading conditions, previous numerical calculation methods need to be improved and adapted to the soil deformation characteristics under unloading. Based on the above background, cyclic loading and unloading tests were carried out to study the deformation characteristics of soil under different loading levels, stress history, and unloading levels. Secondly, a unified modulus calculation model was established, especially for the unloading modulus, which considers the unloading stress history and current unloading stress level, and can provide the value of soil modulus in different states. The relationship between the unloading rebound modulus Esc and the rebound modulus Ec0 used in the numerical simulation was studied. Finally, a set of numerical calculation and analysis methods for shallow tunnel deformation caused by overlying soil excavation based on its rebounding characteristics is proposed. The rationality of the method is verified by two examples, and is applied to a practical project.

Mechanical Behavior and Energy Dissipation of Woven and Warp-Knitted Pvc Membrane Materials under Multistage Cyclic Loading.

In order to study the mechanical behavior and energy dissipation of architectural membrane materials under multistage cyclic loading, the deformation behavior, energy dissipation, and damage characteristics of four kinds of warp-knitted and woven polyvinyl chloride (PVC) membrane materials were analyzed using multistage cyclic loading experiments. The results show that, compared with the uniaxial tensile strength, the peak values of the cyclic loading and unloading of the four material samples are lower in the warp direction but higher in the fill (weft) direction. Under multistage cyclic loading, the loading and unloading moduli of the warp knitting membrane increase with the increase in fabric density. At the same fabric density, the loading modulus and the unloading modulus are smaller than those of the warp knitting material. The total absorbed strain energy, elastic strain energy, and dissipation energy of the fill samples are higher than those of the warp samples at a low load level but lower than those at a high load level. PVC membrane materials’ use strength should be controlled below a 15% stress level under long-term external force loading. In the cyclic loading process, the four PVC membrane materials are viscoelastic–plastic, so it is reasonable to define the damage variable based on the accumulation of plastic deformation.

Analysis of ground surface settlement in anisotropic clays using extreme gradient boosting and random forest regression models

Excessive ground surface settlement induced by pit excavation (i.e. braced excavation) can potentially result in damage to the nearby buildings and facilities. In this paper, extensive finite element analyses have been carried out to evaluate the effects of various structural, soil and geometric properties on the maximum ground surface settlement induced by braced excavation in anisotropic clays. The anisotropic soil properties considered include the plane strain shear strength ratio (i.e. the ratio of the passive undrained shear strength to the active one) and the unloading shear modulus ratio. Other parameters considered include the support system stiffness, the excavation width to excavation depth ratio, and the wall penetration depth to excavation depth ratio. Subsequently, the maximum ground surface settlement of a total of 1479 hypothetical cases were analyzed by various machine learning algorithms including the ensemble learning methods (extreme gradient boosting (XGBoost) and random forest regression (RFR) algorithms). The prediction models developed by the XGBoost and RFR are compared with that of two conventional regression methods, and the predictive accuracy of these models are assessed. This study aims to highlight the technical feasibility and applicability of advanced ensemble learning methods in geotechnical engineering practice.

Wellbore instability mechanism of hard brittle rock under unloading condition in the ultra-deep wells

Limestone, igneous rock and dolomite are widely distributed in ultra-deep wells in Tarim Basin. Hard brittle rocks show different mechanical properties under high stress conditions in ultra-deep wells. Traditional wellbore stability theory states that the greater the rock strength the more stable the wellbore. The actual drilling in Tarim oilfield (more than 7000 m true vertical depth) shows that in the same section of hard dolomite and mudstone formation, there are more dolomite enlargement and block falling during drilling, while the caliper of mudstone formation is regular. The unloading mechanical experiment of hard brittle rock shows that the deformation and failure characteristics of rock during unloading are different from those during loading. In the process of unloading confining pressure, the axial stress and confining pressure decrease linearly with the increase of strain, and the unloading modulus increases with the increase of the decreasing rate of confining pressure. The smaller the unloading rate of confining pressure, the more obvious the axial plastic flow becomes. The failure of unloading rock occurs mainly due to its brittleness. By comparing the failure degree under different stress paths, the unloading confining pressure before peak is greater than that after peak, and the unloading confining pressure after peak is greater than that of the loading test. Most of the unloading cracks are tensile cracks, but there are shear cracks in the sample, and tensile flakes on the surface of the sample after unloading confining pressure. Within the experimental range (unloading rate), there may be an unloading rate that causes the most severe damage to the rock sample, that is, with the increase of the rate of penetration (ROP), the degree of rock damage caused by stress unloading does not increase monotonously, and there may be a certain ROP that causes the greatest damage to the wellbore. Large unloading will aggravate the damage evolution and failure of tight brittle rock. For the safe drilling of such rock formation, the drilling rate and drilling fluid density should be optimized based on complete understanding of the geo-mechanical environment to minimize the damage and instability of surrounding rock caused by drilling unloading.

Effects of high temperatures and unloading confining pressures on granite

The mechanical and permeability properties of rocks under unloading stress path and high temperature are critically important for hot dry rock. A series of unloading confining pressure and gas permeability tests were conducted on granite samples after heating and rapid cooling treatment. Five levels of temperature and three levels of confining pressures were used. The stress–strain curves of unloading confining pressure were obtained. The strength parameters and deformation parameters were further discussed and analysed. When the heat treatment temperature is higher than 600°C, the granite samples experience a significant degree of thermal damage. With the increase in heat treatment temperature and the decrease in confining pressure, the gas permeability increases. Beyond 600°C, the gas permeability of the samples increases significantly. With the increase in temperature, the internal friction angle decreases slightly from 25 to 400°C, while it increases beyond 400°C. The cohesion exhibits an inverse evolution. The initial unloading elastic modulus and deformation modulus decrease gradually during relief of confining pressure. The decrease rate of the deformation modulus increases with the increase in heating temperature. The experimental results could improve knowledge about the effect of thermal shock and stress on the physico-mechanical properties of granite.

Energy and Fatigue Damage Evolution of Sandstone under Different Cyclic Loading Frequencies

To study the energy dissipation characteristics and damage evolution law of sandstone under cyclic loading, uniaxial cyclic loading tests are conducted on sandstone specimens under different frequencies with an MTS-815 rock testing machine. Furthermore, the characteristics of elastic modulus and energy evolution law during cyclic loading and unloading are explored. The results show that the loading and unloading moduli increase with the loading frequency. Under higher frequencies, the deformation resistance of the specimen is stronger, the elastic energy stored in a single cycle of loading is larger, the released energy is less, and it is less likely for the specimen to be damaged. At the beginning of loading, the energy dissipation ratio K decreases slowly with increasing loading cycles, and it then remains stable. When the specimen is close to failure, an inflection point of K appears, and K increases rapidly. Furthermore, the evolution equation of the damage variable is derived according to the strength characteristics and energy evolution law in the process of cyclic loading, and the reasons for the failure of sandstone specimens are explained from the perspectives of energy and fatigue damage.

Prediction of bending springback of the medium-Mn steel considering elastic modulus attenuation

The improvement of lightweight and safety is the development requirement of automobile parts. Therefore, the demand of thin-walled parts with ultra-high strength is more urgent. However, with the increase of strength, the springback phenomenon of parts is particularly serious, which greatly affects the forming quality of parts. Generally, the springback of automobile parts should be controlled within 5%. Thus, the accurate simulation and prediction of springback can provide important support for the manufacture of ultra-high strength automobile thin-walled parts. In this paper, the bending springback of the medium-Mn steel, as one of the third-generation automobile steels, was studied based on experiment and simulation under different conditions. Tensile tests were carried out to evaluate comprehensive mechanical properties with high strength and high plasticity. Cyclic loading-unloading tests were conducted to analyze the changing rules of unloading elastic modulus and inelastic recovery with strain. The correlation model between unloading elastic modulus and true plastic strain was further established and the model parameters were obtained. Furthermore, V-shaped bending tests were carried out under different conditions to analyze the effects of rolling direction, bending angle, and punch fillet radius on springback. The effect of rolling direction on springback angle is negligible. The bending angle has a positive effect on springback angle, while the punch fillet radius has a negative effect. Finally, the material model with constant and variable elastic moduli were developed by using user-defined material subroutines for the medium-Mn steel. V-shaped bending tests under constant and variable elastic moduli were simulated and compared with the experimental result. The simulated result with variable elastic modulus was closer to the experimental one, which proves the importance of considering the change of unloading elastic modulus in the numerical simulation of medium-Mn steel. The research result of this paper is helpful to enhance the simulation accuracy of springback of medium-Mn steel part and promote its industrial application.