Compressive Constitutive Model Research Articles

Engineering compression constitutive model of closed-cell aluminum foams at high and low temperatures

Engineering compression constitutive model of closed-cell aluminum foams at high and low temperatures

Sulfate freeze–thaw resistance enhancement of cement mortar via a developed hydrophobic mica powder

This study developed hydrophobic mica powder (HMP) using mica powder and stearic acid through high-temperature stirring to enhance cement mortar’s resistance to freeze–thaw (F–T) cycles in sulfate environment. Initially, the impact of HMP content on water absorption and compressive strength was assessed. Further tests on cement mortar with varying HMP dosages evaluated sulfate resistance under F–T cycles, including mass loss rate, relative dynamic modulus of elasticity (RDME), and compressive strength. Results indicated that HMP modified mortar reduced water absorption by 62.75% and compressive strength by 5.43% compared to unmodified mortar. After 125 F–T cycles, HMP modified mortar showed minimal damage, with a 7.33% RDME reduction and a 9.12% compressive strength decline. Detailed stress–strain curve analysis led to an axial compression constitutive model incorporating the effects of F–T cycles and HMP contents. This paper elucidates the hydrophobic mechanism of HMP, demonstrating its potential to improve F–T resistance through experimental and microscopic analysis.

Dynamic compressive properties and constitutive model of waste crumb rubber (CR) modified ultra-high performance engineered cementitious composites (UHP-ECC)

Ultra-high-performance engineered cementitious composites (UHP-ECC) are well-known for their outstanding mechanical properties under static and dynamic loads. However, the effect of modifying UHP-ECC with crumb rubber (CR) on its performance, especially under high strain rates, remains poorly understood. This study systematically examined the dynamic compressive behavior and characteristic failure patterns of CR-modified UHP-ECC under high strain rates using a split Hopkinson pressure bar (SHPB) system. The study focused on evaluating the dynamic compressive strength, stress-strain response, and strain energy density (SED). A dynamic increase factor (DIF) formula was developed based on experimental data, and a nonlinear viscoelastic constitutive model was proposed to predict compressive behavior across various strain rates. Results indicate that while the addition of 10% CR slightly reduces the quasi-static compressive and flexural strength, it significantly enhances tensile ductility. Under high strain rates, CR-modified UHP-ECC shows no substantial effect on peak compressive stress but a marked increase in peak compressive strain. The SED also increased by 20.2%, outperforming other high-performance materials such as UHPC and normal ECC. These findings demonstrate that incorporating 10% CR into UHP-ECC offers considerable advantages, particularly in enhancing structural resilience under dynamic loading conditions. The proposed nonlinear viscoelastic model accurately predicts the compressive behavior of CR-modified UHP-ECC, presenting significant implications for practical engineering applications where high strain rate performance is crucial.

Research on the compressive mechanical behavior and constitutive model modification of novel refractory high-entropy alloy (Ti2Zr)1.5NbVAl0.25

Abstract In recent years, high-entropy alloys have been widely applied across various fields. To explore the mechanical properties of high-entropy alloys and their characteristics under extreme environments, ingots of a quinary high-entropy alloy (Ti2Zr)1.5NbVAl0.25 were prepared. The material’s compression mechanical properties were studied under quasi-static conditions at room temperature with strain rates ranging from 0.001s−1 to 0.1s−1, dynamic compression at strain rates ranging from 1300s−1 to 3100s−1, and compression at a strain rate of 1900s−1 and temperatures from -80°C to 400°C. Impact specimens subjected to strain rates of 1300s−1 and 3100s−1 at room temperature were recovered for metallographic analysis. The results indicate that (Ti2Zr)1.5NbVAl0.25 exhibits significant strain-hardening behavior and strain rate sensitivity. Under medium to high strain rates, the alloy undergoes a phase transformation from a single-phase BCC structure to a mixture of BCC and B2 phases upon impact, with 2500s−1 being the threshold strain rate for phase transformation. The original parameters of the Johnson-Cook constitutive model were fitted based on experimental data, and modifications were made to the strain rate hardening and temperature terms in the original model. The modified Johnson-Cook constitutive model demonstrates improved prediction of the mechanical properties of (Ti2Zr)1.5NbVAl0.25 high-entropy alloy at both room temperature and under extreme environments.

Numerical research on the constraint effect of double steel plate–concrete composite structures

Double steel plate–concrete composite structures comprise two outer steel plates, steel flange plates, connectors, and infill concrete. Owing to their superior mechanical properties, double steel plate–concrete composite structures have been extensively used in construction engineering. Outer steel plates and connectors create a significant constraint effect on the infill concrete. However, no confined concrete constitutive model applies to double steel plate–concrete composite structures. To address this gap, this study established approximately 2000 shell-solid finite element models and derived a confined concrete compression constitutive model suitable for double steel plate–concrete composite structures through regression analysis. The structural parameters potentially affecting the confined performance were initially identified through theoretical analysis. Subsequently, an Abaqus shell-solid finite element model was established, with its accuracy verified through experiments. Thereafter, regression analysis was conducted by varying different parameters in batch modelling. Ultimately, a uniaxial compression constitutive model for concrete suitable for double steel plate–concrete composite structures was established.

Experimental study on waterproof performance and freeze-thaw resistance of cement mortar using stearic acid modified mica powder

In this study, stearic acid modified mica powder (SAMMP) was formulated to enhance the water and corrosion resistance of cement mortar. The investigation focused on assessing the freeze-thaw (F-T) resistance of SAMMP modified mortar, including the water absorption, surface morphology, relative dynamic elastic modulus (RDEM), compressive strength, and uniaxial compression. The findings suggested that the water absorption of SAMMP modified mortar decreased by 53.9%–64.4%. In addition, the modified mortar exhibited excellent freezing resistance, with RDEM remaining above 90% after 90 F-T cycles, while the RDEM of the control specimens decreased to 60%. Concurrently, the compressive strength of unmodified specimens experienced a loss rate of 9.74%, which was 3.7 times, 4.29 times, and 1.92 times higher than the modified specimens, respectively. Furthermore, a uniaxial compression constitutive model was established to account for the effects of the F-T cycles and SAMMP contents on uniaxial compression behavior of cement mortar, demonstrating a strong and reliable correlation with the experimental data.

Effect of cementitious capillary crystalline waterproof material on the mechanical behavior of concrete

Cementitious capillary crystalline waterproof material (CCCW) is a material that can react with substances inside the concrete, generating crystals that fill the pores and cracks in the concrete. This chemical reaction is expected to improve the mechanical properties of the concrete. This study investigated the effects of CCCW content and water-cement ratio (W/C) on the compressive behavior of cementitious capillary crystalline waterproof concrete (CCCWC). The results indicated that as the CCCW content increased from 0 % to 1.5 % for W/C of 0.4, the compressive and tensile strength values of concrete slightly decreased. This is because excessive CCCW generates too many crystals within the concrete, leading to internal matrix expansion and crack formations. However, in the cases of W/C of 0.45 and 0.5, the compressive and tensile strength values of the CCCWC increased with increasing CCCW content from 0 % to 0.5 %, but declined with 1.5 % CCCWC addition. The reaction between CCCW and concrete generates numerous crystals, which densify the concrete matrix and enhance its strength. Moreover, with increasing W/C, the CCCWC's compressive strength and tensile strength decreased due to the increased porosity of the concrete matrix and the reduced availability of the concrete constituents that react with CCCW. Furthermore, the appropriate choice of CCCW content and W/C can significantly enhance the slope and peak stress of the stress-strain curve. Based on this, a compressive constitutive model of CCCWC was established. The findings showed that the optimal CCCW content varied with W/C. For instance, for a W/C of 0.4, the maximumcompressive strength of 54.82 MPa was achieved without any CCCW addition. In contrast, the addition of 0.5 % CCCW to concrete produced with W/C of 0.45 and 0.5 resulted in the highest compressive strengths of 50.98 MPa and 44.90 MPa, respectively.

Failure criterion and compressive constitutive model of seawater concrete incorporating coral aggregate subjected to biaxial loading

Failure criterion and compressive constitutive model of seawater concrete incorporating coral aggregate subjected to biaxial loading

Unified uniaxial compressive constitutive model for C20–C120 concrete based on stochastic damage theory

The concrete uniaxial compressive stress-strain model is essential for analyzing reinforced concrete members and structures. However, models applicable to C20–C120 concrete are still relatively rare. Moreover, the previous empirical model construction methods may not reflect the physical mechanisms and randomness of concrete failure well. To this end, the database was constructed by collecting and analyzing uniaxial compressive stress-strain curve test results from different scholars. The cubic compressive strength in the database ranges from 9.9 MPa to 137.3 MPa. The adaptability of the stochastic damage model was validated using the database of test curves. Subsequently, stochastic damage models for C20–C120 concrete were calibrated based on concrete compressive strength grouping curves, and practical analysis models were suggested. The results indicate that the calculated curves closely match the test curves when the plastic strain evolution parameters η1,c and η2,c in the stochastic models are taken as 0.001–0.30 and 0.19–0.25, respectively. The adaptability of the stochastic damage model is satisfactory, but the plastic strain evolution laws vary for different concrete compressive strengths, influenced by mix proportions and the probability of failure of each component on the meso-scale. When η1,c is calculated by the empirical formula proposed in this paper and η2,c is approximated as 0.22, the calculated curves for C20–C120 concrete are consistent with the mean values of the test curves. The proposed practical analysis models provide comparable accuracy to stochastic damage models, eliminating the need for iterative calculations, making them convenient for engineering applications.

Nonlinear mechanical behaviour and visco-hyperelastic constitutive description of isotropic-genesis, polydomain liquid crystal elastomers at high strain rates

The mechanical behaviour of isotropic-genesis, polydomain liquid crystal elastomers (I-PLCEs) at various strain rates is systematically investigated via experiments, theoretical analysis, and numerical modelling. Experiments encompassing SEM (scanning electron microscope), DSC (differential scanning calorimetry), TGA (thermogravimetric analyser), quasi-static and dynamic (SHPB – split Hopkinson pressure bar) mechanical tests, as well as drop-weight impact tests, are undertaken to identify the nonlinear, large-strain, rate-dependent relationship between compressive stress and deformation of the I-PLCEs studied. Subsequently, a three-dimensional compressible visco-hyperelastic constitutive model for the material is established based on the summation of Cauchy stress components. The as-used model yields good agreement with experimental data, particularly an excellent description of the mechanical responses at high strain rates of 103∼104 s−1. The fully-calibrated constitutive model is implemented in the commercial finite element code ABAQUS via a virtual user-defined material (VUMAT) subroutine. The inhomogeneous deformation processes of the I-PLCEs, corresponding to impact by a hemispherically-tipped drop weight, which induces complex stress states, are also well described. Finally, when evaluated by two dimensionless physical parameters, the I-PLCEs demonstrate a more pronounced strain rate sensitivity in terms of dynamic strength and impact toughness compared to other commonly used materials, highlighting their superior performance in dynamic loading scenarios. The present study is helpful for the design and development of impact-resistant LCE-based materials and structures.

Experimental Study on Mechanical Properties and Compressive Constitutive Model of Recycled Concrete under Sulfate Attack Considering the Effects of Multiple Factors

To investigate the mechanical properties and a compressive constitutive model of recycled concrete under sulfate attack considering the effects of multiple factors, two waste concrete strengths (i.e., C30 and C40), four replacement ratios of recycled coarse aggregates (i.e., 0, 30%, 50% and 100%), and two water–cement ratios (i.e., 0.50 and 0.60) were considered in this study, and a total of 32 recycled concrete specimens were designed and tested. The results indicated that the failure processes and patterns of recycled concrete were not significantly influenced by the replacement ratio of recycled coarse aggregates, the waste concrete strength, the water–cement ratio, or sulfate attack. The higher the replacement ratio of recycled coarse aggregates and the water–cement ratio and the lower the waste concrete strength, the more obvious the reduction in cubic compressive strength, with a maximum reduction of 38.48%. A prediction model for the cubic compressive strength of recycled concrete under sulfate attack was proposed. The higher the replacement ratio of recycled coarse aggregates and the water–cement ratio and the lower the waste concrete strength, the more significant the reduction in axial compressive strength, with a maximum reduction of 37.82%. A prediction model for the axial compressive strength of recycled concrete under sulfate attack was established. A compressive constitutive model of recycled concrete under sulfate attack considering the effects of the replacement ratio of recycled coarse aggregates, the waste concrete strength, and the water–cement ratio was established. The pore structure of recycled concrete was significantly destroyed by the expansion stress generated by Na2SO4 crystals: a large number of Na2SO4 crystals were attached to the surface of concrete matrix, and the concrete matrix became loose. The research results can provide a theoretical basis and data support for engineering applications of recycled concrete.

Compressive behavior and visco-hyperelastic constitutive of polyurethane elastomer over a wide range of strain rates

Polyurethane elastomers (PUEs) will experience different strain rates in different application scenarios. Therefore, it is of great significance to study the mechanical properties of PUE under a wide range of strain rates and establish a constitutive model that considers strain rates with high accuracy and few parameters. In this study, the quasi-static and dynamic compression tests of two types of PUEs (PUE55 and PUE85) were carried out, and investigated the strain rate effect of the materials. Based on the Mooney-Rivlin hyperelastic model and the Prony series, a compressible visco-hyperelastic constitutive model for PUE was established. Different from the conventional constant relaxation time in Prony series, two relaxation times that vary exponentially with principal stretch were proposed based on the relaxation test to describe the strain rate effect of the material at low and high strain rate respectively. In addition, using the visco-hyperelastic constitutive model to obtain the model inputs of the Simplified rubber/foam model in LS-DYNA, the impact process of the Metal/PUE composite projectile was reproduced under different impact conditions through the finite element simulation. Simulation results verified the visco-hyperelastic model in generating numerical model material parameters and the rationality of the Simplified rubber/foam model in describing PUEs.

Experimental design, mechanical performance and mechanism analysis of C30 phosphogypsum-based concrete

The present study aimed to increase the utilization of phosphogypsum and reduce cement consumption. Single-factor experiments were designed to the effects of water-cement ratio (0.45–0.30), silica fume (1 %∼7 %), cement dosage (0 %∼20 %), and the RPG/HPG (20/80–0/100) on mechanical properties of phosphogypsum-based concretes (PGBCs). A new phosphogypsum-based concrete was prepared to meet the compressive strength requirement of C30 grade. The maximum 28d compressive strength of this PGBC reached 45.1 MPa. Simultaneously, the effect mechanisms of above four factors on the mechanical properties of PGBCs were discussed by combining XRD and SEM results. Moreover, the volume stability, elastic parameters, and compressive constitutive model of this PGBC with compressive strength above 30 MPa were investigated. This PGBC used more than 80 % phosphogypsum and 10∼20 % cement, exhibiting well economy and environmental friendliness. Moreover, the constitutive model was established to well predict the compressive behavior of PGBC with different RPG/HPG relative ratios. This PGBC had better volume stability and weaker deformation resistance than cement-based concrete. The present results can provide more theoretical and technical supports for the large utilization of PG.

Mechanical properties, micro-mechanisms, and constitutive models of seawater sea-sand engineered cementitious composites

Three mixing proportions of engineered cementitious composites (ECCs) were prepared using seawater, sea-sand, and PVA fibers, corresponding to three strength grades of C30, C40, and C50, respectively. The mechanical properties of these three kinds of seawater sea-sand engineered cementitious composites (SS-ECCs), including compressive strength, tensile strength, flexural strength, elastic modulus, ultimate elongation, uniaxial compressive and tensile stress-strain relationship, and so on, were analyzed by compressive, tensile, and flexural tests. The tensile and flexural strength of SS-ECCs are influenced by their ductility. The SS-ECC with C40 strength grade exhibited the best ductility, with an average ultimate tensile strain reaching 3.42 %, and possessed the highest tensile and flexural strength. The C50 specimen had the worst ductility, but its tensile strength and flexural strength came in second place. As the strength grade increased, the elastic modulus gradually increased, while the Poisson's ratio decreased. Uniaxial compressive and tensile constitutive models for SS-ECCs were established. The uniaxial compressive constitutive model was divided into a nonlinear ascending stage and a bilinear descending stage. XRD and TGA results revealed that the improvement in the strength of SS-ECCs was mainly attributed to the increased content of Ca(OH)2 in the reaction products. Additionally, the gypsum content in the raw materials decreased with the increasing strength grade, resulting in a reduction in the generation of ettringite (AFt).

Axial Compressive Performance and Constitutive Model of CFST Columns with an Inner FRP Tube

Axial Compressive Performance and Constitutive Model of CFST Columns with an Inner FRP Tube

Time-varying compressive properties and constitutive model of EPDM rubber materials for tunnel gasketed joint

The stress relaxation of ethylene propylene diene monomer (EPDM) rubber material in a compressed state significantly increases the risk of water leakage at tunnel precast segmental joints. Additionally, EPDM rubber gaskets typically experience a complex precompression strain state, further complicating the prediction of long-term stress relaxation. Therefore, it is imperative to propose a novel constitutive model that realistically reflects the stress relaxation of rubber with arbitrary precompression strain, providing a reference for the long-term waterproof design of shield tunnels. In this study, the time-varying properties of EPDM rubber at material level were studied in detail. At first, a comprehensive set of accelerated aging tests were conducted on EPDM rubber samples with varying precompression strains. The hardening effect of rubber without precompression and the stress relaxation effect of rubber with precompression were explored. The time-varying law and mechanism governing rubber properties under these two effects were analyzed. Subsequently, a conversion relationship between the EPDM rubber test conditions and the actual service time was established. The predicted hardening coefficient for uncompressed EPDM after 100 years is 1.468, whereas the relaxation coefficient for compressed EPDM is 0.359. Comparative analysis revealed that the compression set index do not consider the beneficial effects of hardening, resulting in a 54.1% overestimation of the design water pressure. Finally, the analytical study on the constitutive model of EPDM rubber material was carried out. The error in compression curve for unaged sample obtained from empirical formulas exceeded three times that of the analytical model, underscoring the need to study time-varying constitutive models. An interpolation method was employed to extend the test curve, leading to the development of a new constitutive model that represents the stress relaxation characteristics of EPDM materials under arbitrary precompression strain states. By combining the proposed constitutive model with the timetemperature conversion relationship, the time-varying expressions of the constitutive parameters for relaxation and hardening effects during the service life were derived. In comparison with existing models, the proposed model demonstrates wider applicability, effectively captures the time-varying characteristics of EPDM materials under arbitrary precompression strains, offering an efficient approach for studying the long-term stress relaxation prediction of rubber gaskets in shield tunnels under complex precompression strain states.

Effects of Steel Fiber Content on Compressive Properties and Constitutive Relation of Ultra-High Performance Shotcrete (UHPSC)

Shotcrete is widely used in civil engineering as a supporting structure. In this paper, the compressive behavior of ultra-high-performance shotcrete (UHPSC) with different steel fiber content by volume (0, 0.5%, 0.75%, 1%, 1.25%, 1.5%) was investigated. The results showed that the failure pattern of UHPSC was changed from brittle failure to ductile failure with the increase in steel fiber content. The compressive strength, peak strain and compressive toughness of UHPSC increased with the increase in steel fiber content, but the elastic modulus and Poisson’s ratio did not change significantly. With content of 1.5% steel fibers, its axial compressive strength, peak strain and compressive strain energy were 122.7 MPa, 3749 με and 0.269 MPa, respectively, increased by 14%, 23.5% and 55.5% compared with those without steel fiber. The peak strain and compressive toughness were higher than that of ultra-high-performance concrete (UHPC), while the elastic modulus of UHPSC was lower than that of UHPC. Based on the experimental data, the relationship between compressive strength, peak strain, compressive toughness and the change in the characteristic value of steel fiber content (λf) were revealed. The uniaxial compressive constitutive model of UHPSC with different steel fiber content was established and reflected the change rule of the shape parameter of α (constitutive model ascending section) and β (constitutive model descending section) with λf. The experimental results were in good agreement with the model calculation results, which can provide theoretical support for the structural design of UHPSC.

Compressive mechanical properties of styrene-butadiene rubber under medium-low strain rates: Experiments and modeling

Styrene-butadiene rubber (SBR) is widely employed as a cushioning material in engineering applications to resist impact loadings due to its excellent mechanical properties and energy absorption capacity. This paper aims to investigate the compressive mechanical properties and constitutive model of SBR under medium–low strain rates both experimentally and theoretically. Firstly, quasi-static and dynamic compression tests of SBR were carried out under the strain rate up to 220 s−1 using an electronic universal testing machine and a drop-weight machine, respectively. Subsequently, the effect of loading rate on mechanical properties, strain rate sensitivity and energy absorption capacity was examined. The results indicate that SBR exhibits visco-hyperelastic characteristics with reversible compression deformation and strain rate dependency, ie., the yield stress, flow stress and dynamic increase factor (DIF) increase approximately exponentially with increasing logarithmic strain rate. In addition, the SBR exhibits excellent energy absorption capacity during compression, especially under higher strain rates and larger strain levels. Finally, a visco-hyperelastic constitutive model was proposed by replacing the nonlinear spring with a hyperelastic element in Zhu-Wang-Tang (ZWT) viscoelastic constitutive model to describe the nonlinear mechanical behaviors in SBR, and an acceptable agreement between experimental results and model predictions were observed. The findings of this research can provide a valuable guide for designing and optimizing the impact resistance of SBR structures.

Compression Mechanical Properties and Constitutive Model for Soft–Hard Interlayered Rock Mass

The properties of soft–hard interbedded rock masses are significantly impacted by the strength of rock layers and the characteristics of interface surfaces. This study investigates the mechanical properties of soft–hard interlayered rock masses by preparing rock-like specimens with different interface angles. Uniaxial and triaxial compression tests were conducted to examine the compression mechanical characteristics of the specimens. Experimental results demonstrated that in the uniaxial compression tests, the peak strength of the two-layer rock-like specimen exhibits an initial decrease followed by an increase as the interface angle increases. Similarly, the peak strength of the three-layer rock-like specimen also follows a “U-shaped” pattern. The failure of both specimens shifts from tensile failure to shear failure. In the triaxial tests, the strength of the two-layer rock-like specimen initially increases and subsequently decreases as the interface angle increases. In contrast, the intensity of the three-layer rock-like specimen exhibits a decreasing trend, transitioning from shear dilation or tensile failure to shear failure. By utilizing the damage constitutive model to compute the compressive strength of the composite specimen, it was observed that the deviation from the experimental value did not exceed 2.5%, and the overall shape of the curves was in good agreement. Consequently, it is affirmed that the damage constitutive model developed in this study can accurately capture the pre-peak phase of the stress–strain relationship in soft–hard interlayered rock-like specimens, thus providing a valid representation of their mechanical behavior.

Biaxial compressive failure criteria and constitutive model of high-strength geopolymer concrete after high temperature

This paper studies the effect of high temperatures (20℃, 200℃, 400℃, and 600℃) and stress ratios (σ2/σ3) (0.15, 0.3, 0.45, and 0.60) on biaxial compressive strength and strain development patterns of high-strength geopolymer concrete (HGPC). Experimental observations indicate that HGPC exhibits laminar damage similar to ordinary Portland concrete (OPC) before and after exposure to high temperatures, under biaxial compression. Unlike OPC, damage in HGPC initially passes through coarse aggregates at room temperature but shifts predominantly to the aggregate-mortar interface at 600℃. The biaxial compressive strength envelope of HGPC expands with rising temperatures. The increased multiple of biaxial compressive strength (σ3/fm) for HGPC at room temperature rises and then falls with increasing stress ratios, peaking at a stress ratio of 0.45 and surpassing the values for OPC and high-strength concrete (HSC). Before high temperature, the modulus of elasticity of HGPC is higher than that of OPC and decreases with increasing temperature, decreasing by about 45–60% for every 200°C increase, and the reduction is greater than that of OPC. The existing failure criterion is not suitable for HGPC after high temperature, this paper develops a new biaxial compression failure criterion for HGPC before and after high temperature based on Kupfer's criterion, taking into account the effect of temperature. The proposed failure criterion calculation results are well in agreement with the experimental data. A damage constitutive model for HGPC considering the effect of temperature and lateral pressure is also proposed, combining the Weibull distribution model for the ascending branch and a modified empirical model for the descending branch. This combined model effectively predicts the stress-strain relationship of HGPC under various temperature conditions.