Traditional Constitutive Models Research Articles

Experimental Study on Mechanical Characteristics of Stabilized Soil with Rice Husk Carbon and Calcium Lignosulfonate.

In cold regions, the extensive distribution of silt exhibits limited applicability in engineering under freeze-thaw cycles. To address this issue, this study employed rice husk carbon and calcium lignosulfonate to stabilize silt from cold areas. The mechanical properties of the stabilized silt under freeze-thaw conditions were evaluated through unconfined compressive strength tests and triaxial shear tests. Additionally, scanning electron microscopy was utilized to analyze the mechanisms behind the stabilization. Ultimately, a damage model for rice husk carbon-calcium lignosulfonate stabilized silt was constructed based on the Weibull distribution function and Lemaitre's principle of equivalent strain. The findings indicate that as the content of rice husk carbon and calcium lignosulfonate increases, the rate of improvement in the compressive strength of the stabilized silt progressively accelerates. With an increase in the number of freeze-thaw cycles, the deviatoric stress of the stabilized soil gradually diminishes; the decline in peak deviatoric stress becomes more gradual, while the reduction in cohesion intensifies. The decrease in the angle of internal friction is relatively minor. Microscopic examinations reveal that as the number of freeze-thaw cycles increases, the soil pores tend to enlarge and multiply. The established damage model for stabilized silt under freeze-thaw cycles and applied loads demonstrates a similar pattern between the experimental and theoretical curves under four different confining pressures, reflecting an initial rapid increase followed by a steady trend. Thus, it is evident that the damage model for stabilized silt under freeze-thaw conditions outperforms traditional constitutive models, offering a more accurate depiction of the experimental variations observed.

Modeling nonlinear stress-strain model for sulfate dry-wet cycle erosion of concrete: considerations for the initial compaction stage

Sulfate dry-wet cycle erosion significantly affects the mechanical properties of concrete. Investigating the uniaxial compressive stress-strain relationship under these conditions is essential for developing accurate constitutive models. This study analyzes the uniaxial stress-strain curves of concrete subjected to dry-wet cycles in 5% and 15% sulfate solutions. The results show that the initial compaction phase in the stress-strain relationship is particularly pronounced under increasing sulfate concentrations and cycle counts. The concrete experiences an extended compaction phase, which accounts for up to 35.71% of the total strain process. This finding challenge traditional constitutive models, which struggle to accurately describe this phase. To address this issue, the study develops a nonlinear stress-strain model for concrete, incorporating the initial damage caused by sulfate dry-wet cycle erosion, based on Weibull statistical damage mechanics principles. The research indicates that the effects of sulfate concentration and cycle count are predominantly reflected in the pronounced nonlinearity of the skeleton strain function’s opening size (a) and shape characteristics (b), modeled using a fourth-degree polynomial. The model demonstrates an excellent fit to experimental data with an R2 value of 0.99989, showing that the proposed nonlinear stress-strain relationship effectively captures the uniaxial mechanical behavior of concrete under sulfate dry-wet cycle erosion and provides a robust framework for developing constitutive models in such environments.

Parameter identification of Johnson–Cook constitutive model based on genetic algorithm and simulation analysis for 304 stainless steel

Addressing the significant discrepancy between actual experimental cutting force and its predicted values derived from traditional constitutive model parameter identification methods, a reverse identification research of the Johnson–Cook (J-C) constitutive model for 304 stainless steel was conducted via genetic algorithm. Considering actual cutting zone and the influence of feed motion on the rake (flank) angle, an unequal division shear zone model was established to implement the theoretical calculation for shear zone stress. Through cutting experiments, the spindle speed was negatively correlated with the cutting force at first, and then became positively correlated; The empirical formula (EXP model) for turning force was corrected, revealing that the EXP model was unable to provide optimal predicted values for cutting force. The influence of the J-C constitutive parameter C on the cutting morphology was firstly investigated through simulation analysis, and determined an appropriate value for C, then obtained the precise values for the other four constitutive parameters by genetic algorithm. Moreover, the simulated values of cutting force in JC1 model (obtained from the Split Hopkinson Pressure Bar test) and JCM model (the improved model using genetic algorithm) were obtained by three-dimensional (3-D) simulation via FEM software. The results indicated that, the maximum error between actual experimental cutting force and its simulated values (by JCM model) was 14.8%, with an average error of 6.38%. These results outperformed the JC1 and EXP models, suggesting that the JCM model identified via genetic algorithm was more reliable.

Three-dimensional fractional plastic models for saturated sand using Caputo derivative and R-L derivative: A comparative study

The strength and dilatancy of sand are mainly influenced by the void ratio, confining pressure and stress path. In engineering, the stress-strain relationship of sand in three-dimensional stress state is complicated, where the state-dependent properties of sand are difficult to be described by traditional constitutive models. Thus, fractional plastic models based on different fractional derivatives were developed to capture such state-dependent behavior of sand. This paper attempts to make a comparative study of the fractional models based on two typical fractional derivatives, i.e., the R-L derivative and Caputo derivative. The results show that the different types of fractional derivatives are mainly reflected in the different order of differentiation and integration, which will have a significant impact on the calculation of plastic flow direction, stress-dilatancy ratio and fractional order parameter βin the constitutive model. By determining the constitutive parameters of the two models, the constitutive behaviors predicted by different models were compared with the corresponding test results of saturated sands under different initial mean pressures and different stress paths. The models can reasonably simulate the test results of saturated sands, where the dilatancy characteristic can be captured. Compared with R-L model, Caputo model can predict more volumetric strain in the dilatancy process, and has better prediction effect. Overall, the predicted effects of the two models are close, with a maximum difference of about 7 %.

Modified constitutive models and cutting finite element simulation of Ti-6Al-4V alloy at cryogenic

Mastering the high strain characteristics at cryogenics and constructing an accurate constitutive model are critical for establishing a cryogenic cutting simulation of Ti-6Al-4V alloy. The traditional constitutive model is inadequate for accounting for high and cryogenic conditions. In this paper, cryogenic split Hopkinson pressure bar (SHPB) experiments are conducted, specifically for Ti-6Al-4V alloy, to develop a modified Johnson–Cook (J–C) constitutive model that incorporates the cryogenic effect. A coupled two-dimensional orthogonal finite element simulation involving temperature displacement was conducted for the cryogenic cutting of Ti-6Al-4V alloy. This simulation was performed using ABAQUS, based on a modified J–C constitutive model subroutine. It was observed that the smallest discrepancy between the simulation results and the data from ice-fixed milling experiments was just 2.12%. The modified J–C constitutive model is more adept at simulating the chip morphology under cryogenic conditions. It was also found that cryogenic machining enhances the distribution of temperature and stress within the chip. For every 5°C reduction in processing temperature, the tool temperature diminishes by more than 2%.

Exploring shear nonlinearity of plain-woven composites at various temperatures based on machine learning

Plain-woven composites are extensively utilized across various fields; however, it exhibits significant shear nonlinearity, especially at high temperatures. This study aims to propose a machine learning (ML) based constitutive model using Gaussian Process Regression (GPR), which is able to effectively characterize the shear nonlinearity of plain-woven composites at different temperatures. The shear nonlinearity of T800 carbon fiber-reinforced epoxy-based plain-woven composites are investigated by carrying out in-plane shear experiments, and the data sets considering temperature effects are established accordingly. Compared with traditional constitutive models, the proposed ML-based model excels in predicting shear nonlinearity, even at temperatures not included in the training set. The integration of this ML-based constitutive model into the finite element (FE) simulation framework achieves high consistency between simulation and experimental results, thereby validating the significant application of ML in complex material behavior modeling and FE analysis.

Static properties evaluation for laser deposition repaired TA15 components based on a constitutive model considering annealing heat treatment

In remanufacturing field, the laser deposition repair technology combined with annealing heat treatment is widely used for repairing the damaged TA15 titanium alloy components owning to its low cost and high efficiency. But evaluating the properties of repaired components is still a challenging due to the damage test of the continued used components. To solve this, a new evaluation method for the static properties of the laser deposition repaired TA15 components is proposed in this study based on a new constitutive model (named as LRA constitutive model) with considering the annealing temperature and holding time in annealing heat treatment. The physical meanings of the model parameters are analyzed and illustrated from the static tensile experiments of several laser deposition repaired TA15 materials with different annealing heat treatment. In comparison with the experimental results and the predictions from the traditional constitutive model, the LRA constitutive model is validated and shows higher precision (>94 %) than the traditional constitutive model. After the application in the evaluation of static properties of a laser deposition repaired TA15 aircraft panel, the results exhibit that the proposed method has the advantage of low cost and high efficiency.

A hardness-based constitutive model for numerical simulation of blind rivet with gradient hardness distribution

A286 superalloy blind rivets find extensive applications in the structural connections of aerospace equipment owing to their exceptional strength and heat resistance. However, the gradient hardness distribution within the rivet sleeves complicates achieving precise numerical simulation results with traditional constitutive models. This study aims to establish a constitutive model suitable for materials exhibiting gradient hardness to support the development of A286 superalloy blind rivets. Initially, quasi-static compression experiments were conducted on A286 superalloy samples at different hardness levels (160–324 HV), strain rates (0.01–10 s⁻¹), and temperatures (25–600°C). Subsequently, the influence of material microstructural evolution on flow stress during compression was investigated using electron backscatter diffraction technique. Furthermore, a hardness-based Johnson-Cook (J-C) constitutive model was developed by introducing hardness and offset compensation onto the original J-C model and compared with its counterpart. Finally, the hardness-based model was employed to simulate the bulge compression forming of A286 blind rivets and validated through experimental trials. The findings reveal that dislocation strengthening predominantly contributes to the increased material flow stress with escalating strain rates and sample hardness. Compared to the original J-C model, the stress prediction error of the hardness-based model reduced from 26.8 % to 2.9 %, effectively depicting the variation in material flow stress under different hardness values. The simulated values of bulge morphology, dimensions, and load closely align with experimental data, affirming the efficacy of the hardness-based model in numerically simulating blind rivets with gradient hardness distribution.

Development of a modified hypoplastic model for calcareous sand considering particle crushing

In the field of ocean engineering, calcareous sand is frequently employed. However, particle breakage can significantly reduce its strength and dilatancy while increasing its compressibility, leading to potential safety and stability issues for foundations. Traditional constitutive models have limitations in accurately describing the mechanical behavior of calcareous sand. To address this issue, a modified hypoplastic model is proposed in this study, incorporating the quantified indicator of relative particle breakage rate, Br. The established stress-strain relationship is intricately linked to the Br index, effectively connecting it with the effective stress and deviatoric stress. The effect of particle crushing on the critical friction angle, CSL parameters and α parameter of the hypoplastic model were systematically analyzed. A VUMAT subroutine is developed to assess the precision and applicability of the proposed model by simulating triaxial drainage tests under three different densities. The simulation results exhibit good agreement with experimental data, demonstrating the superiority of the modified model over the conventional hypoplastic model. This modified model proves suitable for calcareous sands with varying densities, making it a valuable tool for enhancing stability and safety in ocean Engineering Geology.

A Structural Design and Motion Characteristics Analysis of an Inchworm-Inspired Soft Robot Based on Shape Memory Alloy Actuation

Inchworms are a widely adopted bio-inspired model for soft crawling robots. Taking advantage of the good controllability of Shape Memory Alloy (SMA), this paper designs and manufactures an inchworm-inspired soft robot driven by SMA. Firstly, in the structural design, the paper compares the heat dissipation performance and driving efficiency of SMA actuators with two assembly forms: embedded and external to the silicone body. The external structure assembly design with superior performance is chosen. Secondly, in the analysis of the motion characteristics of the soft robot, a kinematic model is developed. Addressing the issue of inaccurate representation in traditional constitutive models due to difficult-to-measure parameters, such as martensite volume fraction, this paper derives an exclusive new constitutive model starting from traditional models using methods like the Taylor series and thermodynamic laws. The kinematic model is simulated using the Simulink platform to obtain its open-loop step response and sinusoidal signal response. Finally, an experimental platform is set up to conduct crawling tests on the soft robot in different planes. The experimental results show that the inchworm-inspired soft robot can perform continuous crawling motion, with a crawling speed of 0.041 mm/s on sandpaper under a constant current of 4A.

Experimental research on heat transfer and mechanical properties of concrete subjected to elevated temperature during the water-cooling process

In this study, a series of experiments, including elevated temperature tests, cooling tests with different regimes, and compressive tests, were conducted on concrete to investigate the heat transfer and mechanical properties of the concrete during the cooling process after being subjected to elevated temperatures. According to the temperature curves during the water-cooling stage, there were two parts in the cooling process with a demarcation temperature of 100 °C, and an apparent temperature plateau was found at around 100 °C. The higher temperature caused more severe damage to the concrete, and the temperature difference caused by the thermal shock had a significant effect on the mechanical properties of the concrete during the cooling process, especially at temperatures of 400 °C and 600 °C, indicating that concrete structures subjected to fire may suffer severe and rapid deterioration of their mechanical properties during the fire-fighting process. Finally, the two constitutive models deduced in this paper show better agreement with the experimental test results than the traditional constitutive model.

Microstructural and constitutive relationship in process modeling of hot working: The case of a 60Mg-30Pb-9.2Al-0.8B magnesium alloy

Hot compression tests in the temperature range of 493-653 K and strain rates of 0.01-10.00 s−1 were used to evaluate the hot deformation behavior of 60Mg-30Pb-9.2Al-0.8B alloy. In order to optimize the hot working parameters, the Arrhenius constitutive equation and processing map with strain compensation were established on the dynamic material model (DMM). The results show that the stress-strain curves have three different stages of rising, peaking, and steady state during the hot compression with typical characteristics of work hardening (WH), dynamic recovery (DRV), and dynamic recrystallization (DRX). In addition, the improved Arrhenius strain compensation constitutive model has a higher precision than the traditional constitutive model. By dividing the processing map into three typical regions for analysis, the maximum power efficiency is obtained at ε = 0.4. The optimum hot working parameters are temperature range of 573K∼653K, and strain rate range of 0.01 s−1∼0.1 s−1. Instability usually occurs in the region with high strain rate and low temperature, and the main form of instability is cracking.

Machine learning based modeling of path-dependent materials for finite element analysis

Geological materials typically demonstrate a nonlinear and path-dependent behavior. Recently, data-driven techniques have emerged as a promising alternative to the traditional constitutive models or expensive micro-scale simulations, which can expedite simulations of complex geological systems. In particular, Recurrent Neural Networks (RNNs) are capable of capturing the history-dependent material behavior. However, one of the major limitations of RNNs is the dependence of the output stress on size of the strain increments. Since strain increments typically vary largely during simulations within nonlinear Finite Element (FE) solvers and are not known a priori, this limitation hinders the application of RNN constitutive models to FE modeling, leading to large errors and/or lack of convergence. In this work, we propose new model architectures and a random walk-based training data generation method to address this shortcoming. The proposed methodology is applied to J2 and Drucker–Prager plasticity models and tested in FE simulations of a range of boundary value problems with monotonic and cyclic linear and sinusoidal loading. Numerical results are presented to demonstrate the robustness of the proposed approach within the Newton’s method with varying strain increments and for unseen loading scenarios, as well as its consistency for decreasing/increasing rates of applied external loading.

Complex deformation histories and modeling mechanical behavior of glassy polymers

Historically the constitutive models for glassy polymers have targeted the stress-strain behavior observed in a single-step experiment – the constant strain rate (CSR) loading. However, a true test of a constitutive model is the ability to predict the complex multistep deformations. When the CSR loading is the last step of a multistep experiment, the magnitude of the stress overshoot depends on the previous steps, thereby providing a sensitive criterion for testing models. A comprehensive set of multistep experiments has been performed on PBMA/MMA copolymer lightly crosslinked with EGDMA for several temperatures below Tg, where the parameters of the intermediate steps have been systematically varied. None of the traditional constitutive models can even qualitatively predict the data. A recently proposed toy model captures the experimentally observed trends.

A deep CNN-based constitutive model for describing of statics characteristics of rock materials

The inhomogeneity, discontinuity, and elastoplasticity of the rock mass affect the deformation and failure of rock, and it is difficult to describe the stress–strain relationship of the rock mass by traditional constitutive models with a certain mathematical models. In order to address the complex problems caused by multiple variables, firstly, 77 rock specimens were collected from overburden of the working face 1012001 in Yuanzigou coal mine, China. Triaxial compression tests were carried out on these samples, and 673,632 data samples were output. Secondly, based on deep convolutional neural networks (CNN), a CNN-based rock constitutive model (CNNCM) was proposed. The structure and hyperparameters of deep CNN include M, ρ, Ed, υd, σz, and σy, as the input features, ɛz as the output features;Conv2D layers ×4; Max pooling2D layers×4; Dense layers ×4; learning rate_0.001; Epoch_ 200; Batch size_1024; Total params: 160801. Comparing the test results of eleven rock samples with the predicted results of CNNCM, the scope of MAPE and R2 from 0.52–1.94% and 0.999870–0.999988, which indicates the proposed CNNCM has good performance. The sensibility and correlation of physical parameters were analyzed, and the results show that the correlation of stress, Ed, υd, and ɛz is strong. Finally, considering the availability and simplicity of CNNCM, a new CNNCM is proposed though replacing the Ed and υd with E and υ, and different input features. The predictive performance of the trained CNNCMs(#6 and #2) is also performs well although the predicted results are worse than CNNCM #0. The different CNNCMs show that E has a great influence on the results and the rank of importance of other five features is E>σy>υ>M>ρ. This study proposes a machine learning method to describe the stress–strain relationship in the process of the rock failure.

Cyclic shear stress-strain prediction of saturated sand based on the unrolled seq2seq model and scheduled sampling

The simulation of stress-strain response of saturated sand under numerous cyclic loadings is of significant interest to the development of constitutive model, and the simulation results form basic data for soil dynamic characteristic estimation, such as pore water pressure build-up, liquefaction strength, dissipated energy, and damping ratio. Traditional constitutive models are usually constructed based on complicated theories and assumptions, and numerous model parameters complicate the calibration process, which limits their application in the rapid evaluation of soil dynamic properties. Although the data-driven model can effectively avoid these problems, it's difficult for a conventional data-driven model to simulate under numerous cyclic loadings due to the simpleness of the model and training strategy. In this study, a novel data-driven constitutive model is proposed to well simulate the stress-strain behaviour of saturated sand and rapidly estimate soil properties only based on a small amount of experimental data. The unrolled sequence-to-sequence recurrent neural network (RNN) is first introduced in soil data-driven constitutive model to modify conventional one-step ahead prediction to multistep one, and a novel RNN training strategy named scheduled sampling, is introduced to reduce the discrepancy of the model behaviour in the training phase and that in testing due to the unknown stress-strain information at next step. The performance of the proposed model is verified through a dataset collected from a triaxial test along with the comparison with feedback neural network, one-step RNN, and non-data-driven constitutive model. Based on the simulation of stress-strain, the dynamic properties of saturated sand are estimated. Both the simulation and estimation results show that the proposed method performs reasonably well.

Frame-independent vector-cloud neural network for nonlocal constitutive modeling on arbitrary grids

Constitutive models are widely used for modeling complex systems in science and engineering, where first-principle-based, well-resolved simulations are often prohibitively expensive. For example, in fluid dynamics, constitutive models are required to describe nonlocal, unresolved physics such as turbulence and laminar–turbulent transition. However, traditional constitutive models based on partial differential equations (PDEs) often lack robustness and are too rigid to accommodate diverse calibration datasets. We propose a frame-independent, nonlocal constitutive model based on a vector-cloud neural network that can be learned with data. The model predicts the closure variable at a point based on the flow information in its neighborhood. Such nonlocal information is represented by a group of points, each having a feature vector attached to it, and thus the input is referred to as vector cloud. The cloud is mapped to the closure variable through a frame-independent neural network, invariant both to coordinate translation and rotation and to the ordering of points in the cloud. As such, the network can deal with any number of arbitrarily arranged grid points and thus is suitable for unstructured meshes in fluid simulations. The merits of the proposed network are demonstrated for scalar transport PDEs on a family of parameterized periodic hill geometries. The vector-cloud neural network is a promising tool not only as nonlocal constitutive models and but also as general surrogate models for PDEs on irregular domains.

Research on the recurrent neural network-based fatigue damage model of asphalt binder and the finite element analysis development

The evaluation of the fatigue performances of asphalt binders is a difficult engineering problem due to the complexity of their polymer compositions. In the present work, a fatigue damage model of asphalt binders based on a recurrent neural network (RNN) is introduced. The proposed model was validated by the finite element method (FEM). It was found that the RNN could accurately predict the fatigue behaviors of asphalt under cyclic loading, and the loading frequency and the strain ranged from 0.1 to 10 Hz and from 0.005 to 1, respectively. Traditional constitutive models have difficulty operating under such large loading ranges. The average error of all the test specimens achieved by the proposed method was 0.078. As the RNN was purely linear in the FEM model, the FEM converged quickly.

Smart constitutive laws: Inelastic homogenization through machine learning

Homogenizing the constitutive response of materials with nonlinear and history-dependent behavior at the microscale is particularly challenging. In this case, the only option is generally to homogenize numerically via concurrent multiscale models (CMMs). Unfortunately, these methods are not practical as their computational cost becomes prohibitive for engineering-scale applications. In this work, we develop an alternative formulation to CMMs that leverage state-of-the-art micromechanical modeling and advanced machine learning techniques to develop what we call smart constitutive laws (SCLs). We propose a training scheme for our SCLs that makes them suitable for arbitrary loading histories, making them equivalent to traditional constitutive models. We also show how to implement a SCL into a traditional finite element solver and investigate the response of an engineering-scale component. We compare our results to those obtained via a high fidelity simulation. Our findings indicate that SCLs can dramatically boost the computational efficiency and scalability of computational homogenization for nonlinear and history-dependent materials with arbitrary microstructures, enabling in this way the automatic and systematic generation of microstructurally-informed constitutive laws that can be adopted for the solution of macro-scale complex structures.

Constitutive modeling and microstructure characterization of 2196 Al-Li alloy in various hot deformation conditions

• A constitutive model with comprehensive consideration of temperature, strain rate and strain compensation was proposed. • Processing maps under different strains were generated. • The peak power dissipation domain is located in high temperature and medium strain rate. • Dynamic recovery is the main softening mechanism with a small amount of continuous dynamic recrystallization. • The optimum deformation parameters of 2196 Al-Li alloy were determined. Isothermal compression tests of 2196 Al-Cu-Li alloy were carried out at different temperatures (633∼793 K) and strain rates (0.001∼10 s −1 ) on Gleeble-3500 thermal simulator until the compression reached 60 %. According to the obtained stress-strain data, the flow behavior of 2196 Al-Li alloy during thermal deformation was investigated. The Arrhenius constitutive equation of the alloy based on the hyperbolic sine function model was established. A modified constitutive model with comprehensive consideration of deformation temperature, strain rate and strain compensation was proposed. Compared with the traditional constitutive model of strain compensation, the modified model had higher prediction accuracy. The hot processing maps under different strains (0.2∼0.8) were established, it was found that the plastic instability domain mainly occurred at the low temperature and high strain rate, while the peak power dissipation domain was located in the high temperature and medium strain rate. The microstructure evolution of 2196 Al-Li alloy under different deformation conditions was characterized and analyzed by electron back scattering diffraction and transmission electron microscope. The results showed that the softening mechanism was mainly dynamic recovery with a small amount of continuous dynamic recrystallization. High temperature and low strain rate were conducive to the occurrence of dynamic recovery and recrystallization, and the microstructure was mainly characterized by low dislocation density, no dislocation entanglement and dislocation wall structure. The grain boundary was straight and smooth. Some discontinuous dynamic recrystallization occurred at low temperature and high strain rate. Based on the analysis of the hot processing maps and microstructure evolution, the optimum deformation parameters of 2196 Al-Li alloy were determined to be 733∼793 K and 0.01∼1 s −1 .