Constitutive Model Research Articles

Dynamic Constitutive Model of Tungsten‐Whisker‐Reinforced Aluminum/Polytetrafluoroethylene Composite Material and Quantitative Determination of Impact Reaction Release Energy in Vacuum Environment

Dynamic Constitutive Model of Tungsten‐Whisker‐Reinforced Aluminum/Polytetrafluoroethylene Composite Material and Quantitative Determination of Impact Reaction Release Energy in Vacuum Environment

A passive-tuned damper based on magnetorheological porous fabric composite

Abstract This paper proposes a novel passive-tuned magnetorheological (PTMR) damper based on developed magnetorheological (MR) porous fabric composite, in which the damping force is tuned by a permanent magnet (PM). Firstly, the influences of the porous fiber structure of composite on the suspended phase are considered, and a continuous constitutive model based on the dipole model is proposed for the first time, which can accurately predict its rheological properties. Subsequently, a stable passive damper for special conditions is designed, and the unique design concept is to achieve completely different damping characteristics for different application scenarios by adjusting the position of the PM relative to the magnetic circuit. The experimental results show that the damping force is relatively stable under specific condition, and can be adjusted within the range of 16.8–77.4 N, with a dynamic range of about 4.6. Moreover, the PTMR damper can exhibit unidirectional negative stiffness characteristic by adjusting the PM to a specific position. The PTMR damper has stable vibration reduction performance, wide dynamic range, and compact structure, which can be comparable to some conventional MR dampers.

Use of Advanced Constitutive Models for the Mechanical Behavior of Soft Soils With Diatoms From Bogotá (Colombia)

ABSTRACTMost constitutive models did not initially consider special behaviors in some soils with singular characteristics (e.g., soft soils with diatom content). For example, at first, these models did not consider the effect of soil structure and viscosity. However, in the last decades, these variables have been incorporated into several constitutive models to describe the mechanical behavior of the soil in its natural state. Structure and viscosity laws that adequately reproduce the soil behavior had to be developed to include these variables. This paper compares the mechanical behavior of soft soils in Bogotá with different constitutive models. Bogotá’s soft soils are lacustrine deposits with a high content of diatoms in their structure. Natural soil samples with intact structures show a high‐water content, which can be higher than 300%, liquid limits of up to 400%, void ratios higher than five, and friction angles of almost 40°. In addition, the model validations were made through the simulations of triaxial tests in compression and shear paths. Modified Cam Clay (MCC), hypoplastic (HP), and subloading Cam Clay (SCC) were the constitutive models used. Two models are based on an elastoplastic framework, and the third uses a HP framework. Several lessons were learned from the simulations regarding the strengths and weaknesses of the models compared to the tests carried out. Finally, the extensive discussion revolves around determining the most suitable model for simulating the mechanical behavior of soft soils containing diatoms in Bogotá.

Study on Hot‐Compressive Deformation Behavior and Microstructure Evolution of 12Cr10Co3MoWVNbNB Martensitic Steel

Herein, to improve the microstructure homogeneity of 12Cr10Co3MoWVNbNB steel for turbine blades after forging, the hot deformation behavior and microstructure evolution of the steel are systematically investigated using a hot‐compression experimental setup under the conditions of 950–1150 °C and strain rate of 0.001–10 s−1. A strain‐compensated constitutive equation is established based on the flow curves and the accuracy of its prediction is verified. By combining hot processing map with microstructure observation, the optimal hot processing window is determined to be 1075–1150 °C and 1–10 s−1, within which the grain size can be refined to 14.24 μm. Electron backscatter diffraction is employed to investigate the microstructural evolution and dynamic recrystallization (DRX) nucleation mechanism of the deformed samples, revealing that discontinuous DRX characterized by strain‐induced grain‐boundary migration is the dominant nucleation mechanism. Additionally, the deformation conditions significantly affect the distribution of dislocation density and local misorientation, as well as the transition from low‐angle grain boundaries to high‐angle grain boundaries, which ultimately lead to the differences in DRX fraction and microstructure.

Experimental Study on Damage Constitutive Model of Rock under Thermo-Confining Pressure Coupling

Underground engineering frequently encounters the challenges of high temperatures and high confining pressures. The combined effects of temperature and confining pressure can significantly alter the mechanical properties of rock. Evaluating the impact of these factors on rock is a crucial aspect of engineering. This study investigates the mechanical properties of rocks under various temperature and stress conditions, focusing on the deformation and failure characteristics of four typical rock types: granite, red sandstone, gray sandstone, and shale under temperature-confining pressure coupling. The results indicate that high temperatures cause internal structural damage and crack propagation in rocks, leading to a reduction in compressive strength and elastic modulus. Conversely, high confining pressures can inhibit crack propagation and enhance rock deformation capacity. Additionally, significant differences were observed in the mechanical responses of different rocks; red sandstone and shale predominantly exhibited shear failure under the coupled effects of temperature and confining pressure, whereas granite and gray sandstone exhibited bulging failure. Based on the experimental results, an elastic modulus fitting model considering the temperature-confining pressure coupling effect was proposed, and the parameters of the Drucker–Prager criterion were modified. A constitutive model was constructed to accurately reflect the stress–strain state of rocks under the coupled effects of temperature and confining pressure. The constitutive model results show good agreement with the experimental findings.

Optimization method of parameters inverse identification for hot deformation constitutive model of 2Cr13 martensitic stainless steel using genetic algorithm

Constitutive models are considered a key prerequisite to investigate the thermal deformation behavior of materials. Accurate identification of their parameters is crucial for enhancing the predictive precision of the models. A novel optimization method for accurate inverse identification of parameters using the genetic algorithm (GA) in the Modified Zerilli-Armstrong (MZA) model was proposed in this work. Under conditions of temperatures ranging from 1223 K to 1473 K at intervals of 50 K and strain rates of 0.01, 0.1, 1, and 5 s−1, uniaxial isothermal hot compression tests were performed on 2Cr13 martensitic stainless steel (MSS) employing a Gleeble-1500D thermal simulation test machine. Based on the experimental data, the conventional linear regression method was utilized to solve the MZA model of 2Cr13 MSS. Initial values for the material constants I1, S1, C5, and C6 to be optimized were assigned drawing from the calculated results. The GA-based iteratively optimized MZA (G-ZA) model was established by minimizing the mean squared error as an objective function between the experimental and predicted flow stress values. Compared to the MZA model, a significant enhancement in predictive performance was achieved with the G-ZA model, while good generalization was also demonstrated. Both models were successfully integrated into the Forge® finite element analysis software through the secondary development of user subroutines. Numerical simulation results indicated that the G-ZA model demonstrated a better agreement with the experimental data in predicting the load-displacement curve. This validated that a more accurate constitutive model for the hot deformation of 2Cr13 MSS can be effectively constructed using the GA-based parameter inverse identification strategy.

Mesoscopic coupled plasticity-damage model of rough surface considering size-dependent plasticity

Metallic materials exhibit significant size effect at mesoscopic scale have been revealed by many experiments. Thus, it is essential to consider size effect when conducting mesoscopic scale studies in tribology. However, there is no constitutive model considering both ductile fracture and size effects of rough surface in the literature. At the same time, the simulation of friction and wear at the mesoscopic scale suffer from computational inefficiency using the conventional theory of mechanism-based strain gradient (CMSG) plasticity theory. To address the aforementioned challenges, we propose a mesoscopic coupled plasticity-damage model by combining the coupled plasticity-damage model and the simplified CMSG plasticity theory. This model can take into account not only the effect of stress state, temperature, strain rate on plasticity and fracture, but also the effect of the effective plastic strain gradient. Meanwhile, the model is able to solve the effective plastic strain gradient by a simplified method, thereby enhancing the computational efficiency. Then, model parameters for bearing bushing material of an engine are calibrated. Finally, scratch simulation and scratch tests of bearing bushing material at the mesoscopic scale are conducted to validate the effectiveness of the mesoscopic constitutive model. The residual scratch depth and width, coefficient of friction at different normal loads are investigated by experiment and simulation, respectively. Results proved the effectiveness of mesoscopic coupled plasticity-damage model, which is applicable for investigating issues related to wear, friction, and contact.

Hot deformation behavior and microstructural evolutions of a Mg-Gd-Y-Zn-Zr alloy prepared by hot extrusion

The hot deformation behavior of extruded Mg-9.5Gd-4Y-2Zn-0.5Zr alloy was studied through hot compression tests conducted at deformation temperatures of 350–500 °C and strain rates of 0.001–1 s−1. Under most deformation conditions, the flow stress first reached a maximum before decreasing to a stable value, demonstrating characteristics of dynamic recrystallization (DRX). The constitutive equation of the alloy was established as ε.=1.03*1011sinh0.01287*σp2.422exp(−171150/RT) through calculations and derivation. The influences of the deformation temperature and strain rate on the microstructure and DRX of the alloy during the hot compression process were investigated using electron backscatter diffraction. It was found that at temperatures between 350 °C and 450 °C, the alloy texture exhibited multiple {0001} peak rings distributed around the normal axis of the compression direction. When the strain rate was 0.001 s−1, the average equivalent grain diameter significantly increased from 3.3 μm to 22.4 μm with the rise in deformation temperature, whereas when the deformation temperature was 450 °C, the volume fraction of DRX grains noticeably decreased from 87.6 % to 13.2 % with the increasing strain rate. Further research revealed that due to the restriction of strain rate on grain boundary migration, discontinuous dynamic recrystallization and continuous dynamic recrystallization were the predominant DRX mechanisms at low and high strain rates, respectively.

An Elastoplastic Constitutive Model Considering Bonding Effects for Methane Hydrate-Bearing Sand

An Elastoplastic Constitutive Model Considering Bonding Effects for Methane Hydrate-Bearing Sand

Investigating the interfacial vertical shear behavior of BFPMPC mortar and cement concrete with pothole repair

Magnesium phosphate cement (MPC) has both traditional cement properties and ceramic properties with fast setting and hardening characteristics. To rapidly reopen traffic and extend its service life, MPC has been widely used in the rapid repair of highway and airport cement concrete pavement. This study utilizes basalt fiber-reinforced polymer-modified magnesium phosphate cement (BFPMPC) developed in previous research to rapid repair the typical potholes on cement concrete pavement, aims to reveal the interface properties between BFPMPC mortar and cement concrete and further investigate the underlying mechanisms for such properties. Firstly, the optimal mixture ratio was determined by orthogonal test design. Then, the shear strength of the repair interface was measured by composite BFPMPC mortar and cement concrete specimens. The mechanical characteristics of the repair interface and the microscopic mechanism were characterized by nano-indentation technology and SEM/EDS. Finally, the interface constitutive model was established by DIGIMAT and finite element model was developed to simulate the interface failure. Results showed that the no new hydration products were produced by the addition of polymer in BFPMPC. BFPMPC matrix became denser with the increase of age, resulting in the better bonding between fiber and paste. The interface vertical shear strength at 6 h and 3 d were 3.1 MPa and 3.9 MPa, respectively. SEM/EDS results showed that polymer has a certain self-healing ability to decrease the crack width with increase of curing age, and a variety of inclusions in the repair interface were observed. The elastic modulus of each inclusion phase can be effectively analyzed by nanoindentation. The simulation results showed that the pressure on upper surface of BFPMPC mortar transfers to the bottom through the repair interface. As the tensile stress on the bottom over the maximum interface tensile stress, the cracks were extend from the bottom to upper, then the structure was failed. Interface vertical shear strength of numerical simulation was, respectively, 3.149 MPa and 3.957 MPa. It is close to the plain shear strength experimental value, validating the proposed interface constitutive relationship.

Experimental and Modeling Analysis of the Tensile Properties of Heavy-Duty Coatings for Steel Structures

Coatings are essential for protecting steel structures from corrosion and mechanical stresses, especially under challenging environmental conditions. To this end, this study systematically examines the effects of temperature (20 °C to 50 °C), strain rate (6.67 × 10−4 s−1 to 1.67 × 10−2 s−1), and intermediate coat thickness (140 μm to 700 μm, the layer between the primer and topcoat) on the uniaxial tensile properties of heavy-duty coatings for steel structures. Experimental and theoretical analyses were conducted to quantitatively assess the influence of these factors on the mechanical properties of the coatings. A multifactor constitutive model was developed based on the Sherwood–Frost model by integrating material characteristics and fitting experimental data, incorporating response functions for temperature, strain rate, and intermediate coat thickness. The results reveal that increased temperature causes temperature-induced softening, while higher strain rates lead to strain rate-dependent strengthening of the coatings. In contrast, the effect of layer thickness on mechanical properties follows a non-monotonic trend, influenced by the structural and material characteristics of the coatings, with the most significant mechanical response occurring at 560 μm thickness. These findings suggest that optimal coating design must consider multiple factors to enhance mechanical performance. Additionally, the correlation coefficients (r) between the model predictions and experimental results are 0.97 or higher, indicating the model’s effectiveness in predicting and optimizing the mechanical performance of heavy-duty coatings under complex conditions.

Application of G-Ori metamaterials as sports equipment baseball bat in an electro-magneto-elastic sandwich composite beam

In this work, a higher order thickness stretched model is employed for electro-magneto-elastic results of a shear deformable baseball bat as a sandwich beam. The formulation is performed using the two dimensional constitutive relations as well as electric potential and magnetic induction relations for a shear deformable baseball bat. The proposed model can be used as a baseball bat in sport equipment. The principle of virtual work is employed to derive governing equations in the presence of thermal, electrical and magnetic loads. The physical model is a sandwich baseball bat beam composed of graphene origami reinforced copper matric core integrated with two piezoelectric/piezomagnetic face-sheets in thermal environment excited by electric and magnetic potentials.

Two-state free-volume model for anomalous dynamics in supercooled water macromolecules undergoing liquid–liquid phase transition

Modelling anomalous dynamics of complex liquid water is a huge challenge due to its various condensed molecular structures and the associated liquid–liquid phase transitions (LLPTs). In this study, we considered, for the first time, the influences of free volume and entropy on LLPTs for both low-density liquid (LDL) and high-density liquid (HDL) waters. Firstly, we proposed a two-state free-volume model and combined with the Adam-Gibbs models to investigate the dynamic equilibria with free diffusion coefficient, viscosity, glass transition temperature and the anomalous dynamics in the two-state water. Free-energy equation was then developed to explore the constitutive relationships of free volume, entropy and anomalously dynamic behaviors. Finally, analytical results of the proposed two-state free-volume model were compared with the experimental data of two-state water reported in literature, and good agreements between them were demonstrated. This study offers a new physical insight into free volume for the anomalous dynamics and LLPTs in the two-state water.

Prediction of flow stress of Ta–W alloys using machine learning

Abstract The primary aim of this article was to predict the flow stress of Ta–W alloys using the eXtreme Gradient Boosting (XGBoost) machine learning model and to explain the outcome using SHapley Additive exPlanations (SHAP). The article details the effect of temperature, strain rate, and alloying content on the deformation behavior. Though grain size, dislocation density, texture and impurities are also important factors affecting the deformation behavior, these have not been considered in this work. Data and constitutive models from the literature were used to find and compare the predictiveness of the flow stress in Ta–W alloys. XGBoost predicted flow stress with a root mean square error of 12 MPa during training and 40 MPa during testing, while constitutive models such as Johnson–Cook (JC), Zerilli–Armstrong (ZA) and mechanical threshold stress (MTS) models showed a root mean square error of 208, 131 and 149 MPa respectively. The linear correlation between the predicted and experimental flow stress at 10% strain was calculated using the Pearson correlation coefficient and found to be 0.64, 0.93, and 0.70 for JC, ZA and MTS models respectively, while XGBoost showed 0.99 during training and 0.98 during testing. The optimized XGBoost model was validated using five-fold and leave-one-group-out cross-validations. The flow stress at 10% strain was predicted using XGBoost at various temperatures, strain rates, and alloying content. The flow stress was low at temperatures above 1000 K and strain rates below 10−2 s−1. From SHAP analysis, it was found that the base flow stress value (at which the SHAP value is zero) was 477 MPa. For temperatures less than 275 K, strain rates greater than 1 s−1, and alloying content greater than 2.5 wt.% W, the flow stress showed an increase from its base value.

Long‐Term Creep Prediction of NEPE Propellant Based on SSM Method

AbstractThroughout the entire operational lifespan of a solid rocket motor, the propellant grain experiences creep due to gravitational forces, potentially influencing the motor′s reliability. To enhance the efficiency of creep tests for solid propellants, short‐term (3000 seconds) creep tests were conducted on nitrate ester plasticized polyether (NEPE) propellant at stress levels of 0.15 MPa, 0.20 MPa, 0.25 MPa, and 0.30 MPa using both the step stress method (SSM) and the conventional constant creep test (CCT). Furthermore, mid‐term (10000 seconds) and long‐term (7 days) creep tests were conducted. Based on the traditional generalized Kelvin model, the Saint‐Venant body was incorporated to derive a visco‐elastic‐plastic model with overstress considered, and constitutive model parameters were determined through data fitting. The findings demonstrate the efficacy of the constitutive model in well characterizing propellant creep behavior. According to the model, the yield stress of NEPE propellant was determined to be 0.2302 MPa, representing a significant 64.03% reduction compared to its design strength. This insight holds relevance for structural integrity analysis and the evaluation of solid motor storage life.

Shear-induced migration of rigid spheres in a Couette flow

Concentration inhomogeneities occur in many flows of non-Brownian suspensions. Their modeling necessitates the description of the relative motion of the particle phase and of the fluid phase, as well as the accounting for their interaction, which is the object of the suspension balance model (SBM). We systematically investigate the dynamics and the steady state of shear-induced migration in a wide-gap Couette flow for a wide range of particle volume fraction, and we test the ability of the SBM to account for the observations. We use a model suspension for which macroscopic particle stresses are known. Surprisingly, the observed magnitude of migration is much lower than that predicted by the SBM when the particle stress in the SBM is equated to the macroscopic particle stress. Another noteworthy observation is the quasi-absence of migration for semidilute suspensions. From the steady-state volume fraction profiles, we derive the local particle normal stress responsible for shear-induced migration according to the SBM. However, the observed dynamics of migration is much faster than that predicted by the SBM when using this stress in the model. More generally, we show that it is not possible to build a local friction law consistent with both the magnitude and the dynamics of migration within the standard SBM framework. This suggests that there is a missing term in the usual macroscopic constitutive law for the particle normal stress driving migration. The SBM is indeed capable of accurately predicting both the magnitude and the dynamics of migration when a tentative phenomenological term involving a concentration gradient is added to the particle normal stresses determined in macroscopic experiments.

Performance study of explosively formed projectile using CoCrFeNi high-entropy alloy as a liner

Based on mechanical tensile experiments on the CoCrFeNi high-entropy alloy (HEA), this study explores the forming patterns of the eccentrically shaped sub-hemispherical lined explosively formed projectile (EFP) made of the HEA material. The CoCrFeNi HEA material is initially prepared, and mechanical tensile tests are conducted at various temperatures and strain rates. The Johnson–Cook (J–C) constitutive equation for this material is derived by fitting the experimental data. Scanning electron microscopy and the energy dispersive spectrometer characterize the fracture surface of the tensile specimens, providing insights into the mechanical ductility and fracture mechanism of CoCrFeNi HEA. The EFP forming process under various charge configurations is simulated using AUTODYN software, leading to the identification of the optimal charge configuration. In addition, the damage performance is evaluated. This study provides a theoretical basis for applying HEA materials in the field of shaped charges and offers new ideas and methods for designing more efficient shaped charge warheads.

Three-Dimensional Site Response Analysis of Clay Soil Considering the Effects of Soil Behavior and Type

To understand changes in bedrock motion at the ground surface, frequency effects, and spatial distribution within the soil, it is important to look at how a site responds to earthquakes. This is important for soil–structure interaction in structural and geotechnical earthquake engineering. This study deals with the effect of classifying clays according to shear wave velocity (stiff/medium/soft) and nonlinearity in behavior (linear/nonlinear) on the analysis of the site response. A 3D soil model with a combination of free fields and quiet boundaries and advanced constitutive models for soil to obtain accurate results was used to conduct this study. A strong TABAS earthquake was used to excite the compliant base of the model after converting the velocity record of TABAS to an equivalent surface traction force using a horizontal force–time history proportional to the velocity–time history. This study reveals that the site response analysis is affected by the type of clay soil and the soil material behavior, with soft clay soil causing higher PGV and PGV values in the linear case and lower values in the nonlinear case due to soil yielding, which causes soil response attenuation. This results in extremely conservative and expensive building designs when linear soil behavior is adopted. On the other hand, the applied earthquake exhibits greater attenuation at longer frequencies and greater amplification at mid and short frequencies. However, at frequencies near the applied earthquake frequency, neither attenuation nor amplification occurs. Furthermore, nonlinear soil behavior is crucial for soil evaluation and foundation design due to higher octahedral shear strain and settlement values, especially in softer soils, resulting from extensive plastic deformation.

Numerical study on the lateral behavior of pile groups in Toyoura sand using the hypoplastic constitutive model

A pile group under lateral loading is a complex pile‒soil-pile interaction problem. In this study, numerical analysis was used to investigate the lateral behavior of pile groups arranged in a 3 × 3 configuration with varying piles spacings. The hypoplastic constitutive model embedded into ABAQUS software through the UMAT subroutine was used to characterize the stress‒strain relationship of Toyoura sand. The effects of the pile spacing on the load‒displacement relationship of the pile group, the bending moment-depth relationship of each pile in the pile group, the deflection-depth relationship, and the soil resistance distribution were investigated. The results indicate that the lateral bearing capacity of the pile group decreases by more than 50% when the pile spacing is reduced from 7D to 3D. When the pile spacing is greater than 5D, the “edge effect” of the laterally loaded pile group gradually decreases, and when the pile spacing is greater than 7D, the “shadowing effect” can be negligible, and the wedge-shaped failure zone of the pile group occurs within a depth of 5D below the mud surface.

Two-species model for nonlinear flow of wormlike micelle solutions. Part I: Model

We develop a rheological model to approximate the nonlinear rheology of wormlike micelles using two constitutive models to represent a structural transition at high shear rates. The model is intended to describe the behavior of semidilute wormlike micellar solutions over a wide range of shear rates whose parameters can be determined mainly from small-amplitude equilibrium measurements. Length evolution equations are incorporated into reactive Rolie-Poly entangled-polymer rheology and dilute reactive-rod rheology, with a kinetic exchange between the two models. Although the micelle length is remarkably reduced during flow, surprisingly, we propose that they are not shortened by stress-enhanced breakage, which remains thermally driven. Instead, we hypothesize that stretching energy introduces a linear potential that decreases the rate of recombination and reduces the mean micelle length. This stress-hindered recombination approach accurately describes transient stress-growth upon start-up shear flow, and it predicts a transition of shear viscosity and alignment response observed at high shear rates. The proposed mechanism applies only when self-recombination occurs frequently. The effect of varying the relative rate of self-recombination on the rheology of wormlike micelles at high shear rates is yet to be explored.