Elastoplastic Constitutive Model Research Articles

Quantifying damage zones width in strike-slip faults: Insights from a two-dimensional finite-element modeling approach

We use a two-dimensional finite-element modeling approach to investigate the structural evolution of strike-slip faults under five different confining pressures and determine how their damage zone widths vary depending on the kinematic. Three representative fault segments are modeled, accounting for movement obliquity forming in pure strike-slip, oblique convergence and oblique divergence scenarios. The elastoplastic constitutive model (Drucker-Prager) was employed to couple an associated flow rule into the initial stress state of a geostatic stage. We applied two empirical methods for determining the width of the damage zone from progressive model response. The first method involves using the plastic strain distribution curve's inflection points, to mathematically fixate the width. The second method uses the standard deviation obtained from a trend Gaussian/Normal probability distribution, with over 98% fit to the plastic strain curve data, simplifying the inference of the strain propagation along the model. The simulation results indicate inverse proportional relationships between confining pressure and both porosity and plastic strain intensity, while showing a direct proportional relationship with the damage zone width. For fault zone width quantification, results show convergence between the methods, revealing widths of 2.46–2.65 m for oblique divergence (displacement of 0.20 m), 2.65–3.55 m for pure strike-slip (displacement of 0.20 m), and 4.36–4.46 m for oblique convergence zones (displacement of 0.70 m). The pure strike-slip and the oblique convergence damage zone width results align well with outcrop observations of faults with similar kinematics from the literature, underscoring the significance of numerical modeling as a valuable tool for measure and study the mechanics of characterizing the nucleation of fault zones and quantifying the width of the damage zone.

Strength Characteristics and Double-Yield Elastoplastic Constitutive Model of Granite

Strength Characteristics and Double-Yield Elastoplastic Constitutive Model of Granite

A 3D Elastoplastic Constitutive Model Considering Progressive Damage Behavior for Thermoplastic Composites of T700/PEEK.

Due to their excellent mechanical properties, the carbon fiber-reinforced polymer composites (CFRPs) of thermoplastic resins are widely used, and an accurate constitutive model plays a pivotal role in structural design and service safety. A two-parameter three-dimensional (3D) plastic potential was obtained by considering both the deviatoric deformation and the dilatation deformation associated with hydrostatic stress. The Langmuir function was first adopted to model the plastic hardening behavior of composites. The two-parameter 3D plastic potential, connected to the Langmuir function of plastic hardening, was thus proposed to model the constitutive behavior of the CFRPs of thermoplastic resins. Also, T700/PEEK specimens with different off-axis angles were subjected to tensile loading to obtain the corresponding fracture surface angles of specimens and the load-displacement curves. The two unknown plastic parameters in the proposed 3D plastic potential were obtained by using the quasi-Newton algorithm programmed in MATLAB, and the unknown hardening parameters in the Langmuir function were determined by fitting the effective stress-plastic strain curve in different off-axis angles. Meanwhile, the user material subroutine VUMAT, following the proposed constitutive model, was developed in terms of the maximum stress criterion for fiber failure and the LaRC05 criterion for matrix failure to simulate the 3D elastoplastic damage behavior of T700/PEEK. Finally, comparisons between the experimental tests and the numerical analysis were made, and a fairly good agreement was found, which validated the correctness of the proposed constitutive model in this work.

Elastoplastic constitutive model for overconsolidated clays with an advanced dilatancy relation

AbstractThe dilatancy behavior of overconsolidated (OC) clays is a key factor in determining their strength and deformation characteristics. Recognizing the limitations of previous dilatancy relations for OC clays, a novel dilatancy relation is proposed that can effectively capture the changes in dilatancy point, volume dilatancy and contraction with the overconsolidation ratio (OCR). As OC clays revert to the normally consolidated (NC) state, the proposed dilatancy relation smoothly transitions to that of the modified Cam‐clay (MCC) model, ensuring a unified description of the dilatancy relation between OC and NC clays. The dilatancy relation can be easily incorporated into the constitutive model of different theoretical frameworks. Subsequently, this advanced dilatancy relation is integrated into a new elastoplastic constitutive model for OC clays within the framework of bounding surface and generalized plasticity theory. The validity of the proposed model is confirmed through drained triaxial compression and extension, undrained triaxial compression and extension, as well as complex stress path tests for clays with various OCRs, and the simulation results of the proposed model are compared with those of the SANICLAY model. The comparative analysis demonstrate that the model performs well in simulating the behavior of OC clays.

Experimental Investigation of Strain Rate Influence on Anisotropy of Uniaxial Tensile Mechanical Properties of CuFe2P Alloy Sheet.

Wire crimping, a process commonly used in the automotive industry, is a solderless method for establishing electrical and mechanical connections between wire strands and terminals. The complexity of predicting the final shape of a crimped terminal and the imperative to minimize production costs indicate the use of advanced numerical methods. Such an approach requires a reliable phenomenological elasto-plastic constitutive model in which material behavior during the forming process is described. Copper alloy sheets, known for their ductility and strength, are commonly selected as terminal materials. Generally, sheet metals exhibit significant anisotropy in mechanical properties, and this phenomenon has not been sufficiently investigated experimentally for copper alloy sheets. Furthermore, the wire crimping process is conducted at higher velocities; therefore, the influence of the strain rate on the terminal material behavior has to be known. In this paper, the influence of the strain rate on the anisotropic elasto-plastic behavior of the copper alloy sheet CuFe2P is experimentally investigated. Tensile tests with strain rates of 0.0002 s-1, 0.2 s-1, 1 s-1, and 5.65 s-1 were conducted on sheet specimens with orientations of 0°, 45°, and 90° to the rolling direction. The influence of the strain rate on the orientation dependences of the stress-strain curve, elastic modulus, tensile strength, elongation, and Lankford coefficient was determined. Furthermore, the breaking angle at fracture and the inelastic heat fraction were determined for each considered specimen orientation. The considered experimental data were obtained by capturing the loading process using infrared thermography and digital image correlation techniques.

Failure criterion and elasto-plastic constitutive model of seawater concrete incorporating coral aggregate subjected to triaxial loading

Recently, there has been a growing interest in utilizing coral reef debris as a replacement for river sands and natural coarse aggregates (NA). A novel type of seawater concrete, designated as CAC, was developed to effectively utilise raw coral debris and reduce material transportation costs. This study aimed to examine the mechanical properties of CAC under both uniaxial and triaxial loading conditions. Consequently, 18 prism uniaxial specimens and 90 triaxial cylinder specimens were prepared, considering concrete strength (C20, C40), replacement ratio of coral coarse aggregate (CA) (50 %, 75 % and 100 %), and lateral stress ratio (0, 0.1, 0.2, 0.3 and 0.5). The results indicated that the increase in peak stress and strain is associated with the triaxial stress ratio and the cylinder compressive strength of coarse aggregate. Furthermore, the compressive meridian of CAC is lower than that of conventional concrete. Based on the test results in this study, a modified William-Warnke failure criterion for CAC was established. Additionally, an elasto-plastic model considering a modified hardening and softening law was suggested for CAC under tri-axial loading. The proposed models were found to be well verified by the test results.

Identification of Elastoplastic Constitutive Model of GaN Thin Films Using Instrumented Nanoindentation and Machine Learning Technique

This study presents a novel inverse identification approach to determine the elastoplastic parameters of a 2 µm thick GaN semiconductor thin film deposited on a sapphire substrate. This approach combines instrumented nanoindentation with finite element (FE) simulations and an artificial neural network (ANN) model. Experimental load–depth curves were obtained using a Berkovich indenter. To generate a comprehensive database for the inverse analysis, FE models were constructed to simulate load–depth responses across a wide range of GaN thin film properties. The accuracy of both 2D and 3D simulations was compared to select the optimal model for database generation. The Box–Behnken design-based data sampling method was used to define the number of simulations and input variables for the FE models. The ANN technique was then employed to establish the complex mapping between the simulated load–depth curves (input) and the corresponding stress–strain curve (output). The generated database was used to train and test the ANN model. Then, the learned ANN model was used to achieve high accuracy in identifying the stress–strain curve of the GaN thin film from the experimental load–depth data. This work demonstrates the successful application of an inverse analysis framework, combining experimental nanoindentation tests, FE modeling, and an ANN model, for the characterization of the elastoplastic behavior of GaN thin films.

Development of an elastoplastic constitutive model in the framework of the multilaminate method for numerical analyses of geotechnical structures

Development of an elastoplastic constitutive model in the framework of the multilaminate method for numerical analyses of geotechnical structures

Experimental characterization and numerical prediction for mechanical aging of epoxy and its carbon fiber‐reinforced composite under hydrothermal conditions

AbstractThe Aqueous environment impairs the mechanical performance of carbon fiber‐reinforced polymers (CFRPs) and decreases the durability of engineering structures made of CFRPs primarily by degrading the resin matrix. Hence, the objective of this study is to investigate and accurately predict the influence of hydrothermal aging on the epoxy and its carbon fiber reinforced polymer (CFRP). Particularly, this work developed a modeling method that combined Fick's model, empirical aging model and elastoplastic constitutive model to predict the mechanical behavior of hydrothermally aged epoxy matrix. After the experimental characterization, this epoxy modeling method demonstrated its predictive capability on the mechanical response of the deteriorated epoxy under different hydro‐thermal‐salt conditions, with the mean absolute percent error (MAPE) of approximately 4.61%. Furthermore, the transverse compressive behavior of unidirectional (UD) CFRPs could be predicted by using the representative volume element (RVE) model with the degraded matrix behavior predicted via this epoxy modeling method. Integrated with this CFRP modeling, results from mechanical tests and fracture analysis further demonstrated that the hydrothermal aging effect on the transverse compressive performance of the UD CFRPs was dominated by the deterioration of their resin matrix. Therefore, this study demonstrates the feasibility of the finite element analysis (FEA) for mechanical aging of the epoxy matrix and its CFRP under hydrothermal conditions via employing the proposed integrated modeling method.Highlights Degradation of epoxy polymer under hydro‐thermal‐salt aging conditions. Integrated model to predict mechanical response of hydrothermally aged epoxy. RVE model to predict the mechanical behavior of hydrothermally aged CFRP. Hydrothermal aging on the transverse compressive behavior of UD CFRP.

An elastoplastic semi-analytical solution for enhanced geothermal wellbore stability considering temperature-sensitive failure criterion

Temperature alters the rocks’ mechanical behavior and influences the stability and operation of enhanced geothermal wells. The stability of the well is a concern during construction, just after the construction, at the time of production, and injection. Most available analytical and semi-analytical solutions for wellbore stability do not account for rock's temperature-dependent yield behavior. In the present study, we proposed an elastoplastic constitutive model based on the temperature-sensitive yield criterion and a semi-analytical solution for wellbore stability. The applicability of the constitutive model is demonstrated by comparing the experimental results of Comiso limestone with the model output. The model elastic perfectly plastic assumption reasonability captures the stress-strain behavior at elevated temperatures. Temperature-sensitive yield criterion effectively predicts the yield point of Comiso limestone, even the substantial decay in yield stress after the temperature of 400 οC. The semi-analytical solution of wellbore stability analysis is validated using FE (Finite element) analysis. An implementation of the semi-analytical solution is showcased for a vertical wellbore, considering changes in in-situ stresses and temperature. A parametric analysis establishes that external factors, like vertical stress increase, do not consistently decrease the size of the plastic zone. Instead, a specific threshold of vertical stress exists at which the plastic zone radius reaches its minimum value. In the presented case, the least radius of the plastic zone is observed for in-situ vertical stress of 80 MPa. Furthermore, the parametric study examines the impact of horizontal stress, support pressure, temperature, and dilation parameter, which followed the generally reported trends.

Influence of repeated surface surcharge loading on tunnel displacement considering the structural characteristics of soft clay

Shanghai soft clay is a typical marine clay with specific structural characteristics. However, the effects of surface surcharge loading on structured soft clay and existing tunnels remain unclear. In this study, the effect of repeated surface surcharge loading on tunnel displacement was numerically investigated, considering the structural characteristics of Shanghai Layer 4 soft clay. An elastoplastic constitutive model (Shanghai model) that describes the mechanical properties and structural characteristics of natural clay was used to simulate the soil response. The results indicate that the first cycle of repeated surface surcharge loading had the greatest effect on the displacement of the tunnel and overlying clay; subsequent loading cycles further increased the displacement. With repeated surface surcharge loading, the displacement of the overlying clay exhibited a significant decreasing trend with increasing depth. The maximum excess pore pressure of the clay exhibited a decreasing trend with increasing loading time. The displacements of the tunnel and overlying clay were greater when the effects of the soil structure were considered. However, the initial degree of the structure had no significant effect on the accumulation of excess pore pressure when the surface surcharge loading did not reach the ultimate bearing capacity of the clay.

A three-dimensional elastoplastic constitutive model incorporating Lode angle dependence

A comprehensive three-dimensional elastoplastic constitutive model is presented to characterize the stress-strain behavior of cement stone under the true triaxial stress state. This constitutive model incorporates a three-dimensional yield function and a three-dimensional potential function. The three-dimensional yield function is designed to accurately represent the true triaxial stress state during hardening. The three-dimensional potential function is devised to depict the plastic flow direction under true triaxial stress state. The yield and potential functions include parameters that control the shape of the deviatoric and meridian planes, and these parameters vary with the plastic internal variable. Consequently, the yield function can accurately describe the stress state, and the potential function can precisely capture the variations in plastic flow direction. Additionally, a detailed procedure for determining the parameters of the yield function and potential function is proposed based on the full deformation process. The constitutive model is presented in the form of analytical solution. The comparison of experimental data with the constitutive model confirms its accuracy and validity. A sensitivity analysis of the deviatoric and meridian parameters in the potential function is performed, shedding light on their impact on the model behavior. Furthermore, the significance of incorporating Lode angle dependence into the potential function is discussed, emphasizing its essential role in accurately capturing strain in the direction of the intermediate principal stress.

An elastoplastic constitutive model of lunar soil simulant considering shear dilatancy and softening characteristics

The study of the constitutive relationship of lunar soil is the key to a deep understanding of the mechanical properties of lunar soil and the subsequent construction of lunar bases. Previous models mostly focused on the strengthening behavior before the peak, while rarely reflected the post-peak softening and residual deformation stages during shear deformation. A new elastoplastic constitutive relation is derived with combining kinematic hardening model and initial shear stress, which effectively compensates for the shortcomings of existing constitutive models, and the validity of the model is verified by comparing with existed laboratory test results. The developed constitutive model not only effectively captures the shear dilatancy and softening characteristics of lunar soil simulant, but also requires fewer parameters to be easily determined by simple initial loading curves from direct shear tests, Furthermore, the influences of some key parameters on shear strength and softening behavior of lunar soil simulant can be easily obtained based on this constitutive model.

Numerical investigation on the effect of repeated surface surcharge loading on soil deformation and tunnel displacement in structured soft clay

Shanghai soft clay is a typical marine clay with specific structural characteristics. The tunnel and overlying soft clay may undergo repeated surface surcharge loading, such as the temporary soil stacking. Assessing the extent of structured soft clay deformation and tunnel displacement caused by repeated surface surcharge loading is of great significance for evaluating of the safety of ground structures and underground tunnels. In this study, the effects of repeated surface surcharge loading on the soil and tunnel displacement were numerically investigated. The finite element code DBLEAVES with an elasto-plastic constitutive model (Shanghai model) that describes the mechanical properties and structural characteristics of natural clay was used to simulate the soil response. The parameters of the constitutive model were obtained through geotechnical testing. The effects of the soil structural characteristics, seepage conditions, and loading conditions on the soil response and tunnel displacement were analyzed. The numerical results show that the maximum excess pore pressure of clay decreased as the number of loading cycles increased. The effects of the structural characteristics cause greater displacement, whereas the effects of the degradation parameters of the structure are more significant than the initial degree of the structure. The differences in the vertical displacement of the tunnel and overlying soils owing to the structural characteristics become apparent with an increase in surface surcharge loading. However, the effects of structural characteristics become less significant as the depth increases. The seepage conditions and loading method primarily affect the build-up of excess pore pressure and the development of effective stress paths. For soils inside the surcharge area, a flexible surcharge produces a greater vertical displacement than a rigid surcharge. As the burial depth increased, the effects of the seepage conditions and loading method showed a declining tendency.

Nonlinear seismic analysis of city gate architectural heritages using a sensitive-based model updating method

Due to the unknown accumulation of internal damage and severe degradation of structural mechanisms, updating numerical model related to current damage using Operational Modal Analysis and performing nonlinear seismic analysis pose significant challenges. In this paper, a nonlinear seismic analysis method is proposed involving a three-stage finite element model updating process. This method not only updates the global parameters and local parameters of substructure, but also updates the FEM to true current damage state based on elastic-plastic constitutive model considering current damage. First, on-site vibration and material performance tests were conducted to obtain modal data and material properties of the structure. Second, each component in the model was updated to detect damage, employing a sensitivity-based approach in Stage 1. Then, each element within the severely damaged components obtained from Stage 1 was updated for damage detection, again using a sensitivity-based approach in Stage 2. Finally, the current damage state was updated based on elastoplastic constitutive model considering the current damage and a seismic analysis was performed in Stage 3. The results indicate that, in Stage 1, updating the global parameters of the model aligns the calculated data with the measured data. In Stage 2, updating the local parameters to accurately identify the location and severity of damage within the heavily affected components is demonstrated by a simple example. These results can establish a scientific foundation for the nonlinear seismic analysis of city gate architectural heritages.

A Constitutive Model for Stud Connection in Composite Structures

The complexity of finite element analysis for composite structures can be significantly reduced by representing the connector and adjacent concrete as a macroscopic element. Nevertheless, the prevailing macroscopic models for shear connections predominantly employ nonlinear elastic theory. This approach introduces inaccuracies in estimating structural stiffness and load-bearing capabilities, primarily due to its inability to precisely capture the cumulative effects of plastic damage. In response, this study introduces a novel macroscopic elastoplastic model grounded in plasticity theory, aimed at accurately characterizing the nonlinear behavior of stud connections subjected to concurrent shear and tensile forces. This paper meticulously delineates the implementation of the elastoplastic constitutive model using the backward Euler method for numerical integration. It further articulates the derivation of the consistent tangent stiffness, which aligns with the convergence efficiency of the Newton–Raphson iterative approach. The computation of the element stiffness matrix for a two-node element is executed via the governing equation inherent to the finite element method. An exemplar macroelement test conducted in ABAQUS affirms the implicit backward Euler scheme’s stability and consistency across varying tolerances. Validation of the elastoplastic model against empirical test outcomes corroborates its efficacy, demonstrating the model’s precision in predicting the load–displacement behavior of stud connections under the influence of shear and tensile forces.

An elastoplastic model with egg-shaped yield surface for coastal soft clay

A novel elastoplastic constitutive model with an egg-shaped yield surface (ESE model) is proposed herein to elucidate the strength-deformation characteristics of marine soft clay. One of the key improvements offered by this model is its ability to address the singularity associated with plastic strain increments at yield surface corners—a limitation commonly encountered in traditional elastoplastic models. Additionally, the proposed model demonstrates flexibility, as it can transform into various forms under different conditions. Subsequently, to evaluate the efficacy of this egg-shaped elastoplastic model, numerical simulations are performed within the finite element software ABAQUS using an implicit integration algorithm through the user material subroutine interface (UMAT). The simulations encompass standard triaxial consolidation tests involving saturated soft clay sourced from the Itsukaichi marine clay as well as two types of saturated kaolin clays. The outcomes derived from these simulations by the ESE model are compared with both empirical data and numerical simulations originating from the widely employed Modified Cam-Clay (MCC) model. The simulations of the ESE model for three conventional triaxial tests on clay demonstrate superior concordance with experimental measurements in comparison to the MCC model. This underscores the efficacy of the proposed ESE model in predicting the strength and deformation characteristics manifested by coastal soft clays under undrained conditions. Finally, the predictions for deformation in an adjacent tunnel according to the ESE model closely align with experimental measurements and prior to the simulations conducted using the MCC model and advanced models such as the bounding surface model and the unified model, thereby affirming its practical utility in engineering applications.

Post-fire mechanical properties and constitutive model of Q690 high-strength structural steel

Fire hazard is one of the main threats to the integrity of steel structural buildings. Developing an accurate post-fire constitutive model for structural steel is crucial for enhancing the failure assessment of steel structures exposed to fire. In this study, the post-fire mechanical behavior of Q690 high-strength structural steel is investigated. Eighteen round bar specimens made of Q690 steel were heated with temperatures ranging from 20 °C to 900 °C. Tensile tests were conducted on these specimens to obtain the post-fire stress-strain curves and associated mechanical parameters of the material. To accurately characterize the post-fire behavior of Q690 steel, a temperature-dependent elastoplastic constitutive model combined with its numerical implementation algorithm is proposed. This model consists of four components: a temperature-dependent elasticity criterion, the von Mises yield criterion, an associated flow rule, and a temperature-dependent isotropic hardening law. The proposed constitutive model has a notable feature, i.e. the material parameters in the model can be defined as a function of temperature according to the test results. As a result, when utilizing this model for post-fire assessments of steel members, only three routine parameters, i.e. elastic modulus at room temperature, Poisson's ratio, and the temperature experienced by the material, are required in the numerical simulation to generate the material’s stress-strain relationships. To verify the proposed constitutive model, the new model was introduced into the numerical simulations of the tested round bar specimens after exposure to various temperature conditions. Both the load-displacement curves and local deformation of each round bar specimen obtained from the numerical simulations are compared with the test results to validate the accuracy of the new model. The constitutive model presented in this study provides a useful tool for assessing the post-fire behaviors of steel components.

Elastoplastic constitutive model of gravelly soil and its validation through numerical analysis of the Kobe Port Island liquefaction

The liquefaction of gravelly soil has been demonstrated in many earthquakes, but the constitutive model to predict its liquefaction behavior is limited. The dilatancy equation plays an important role in establishing elastoplastic models of geotechnical materials. Recognizing the unique dilatancy characteristics of gravelly soil, this study introduces an improved nonlinear dilatancy equation into the generalized plasticity model. Consequently, a unified elastoplastic constitutive model is proposed, aimed at accurately predicting both the monotonic and cyclic behaviors of saturated gravelly soil under diverse drainage conditions. A series of drained and undrained triaxial tests of gravelly soil under monotonic and cyclic loadings are carried out to validate the model performance. In addition, the model performance is also examined through monotonic and liquefaction tests of gravelly soil obtained from prior publications. Furthermore, the proposed model is implemented into the nonlinear finite element program GEODYNA and applied to the numerical simulation of the Kobe Port Island liquefaction to better validate the capabilities of the proposed model. From the comprehensive analysis of triaxial tests and numerical simulations, the proposed model performs well in predicting mechanical behavior of gravelly soil and can provide a powerful tool for seismic liquefaction analysis of gravelly soil sites.

A State-Dependent Elasto-Plastic Model for Hydrate-Bearing Cemented Sand Considering Damage and Cementation Effects.

In order to optimize the efficiency and safety of gas hydrate extraction, it is essential to develop a credible constitutive model for sands containing hydrates. A model incorporating both cementation and damage was constructed to describe the behavior of hydrate-bearing cemented sand. This model is based on the critical state theory and builds upon previous studies. The damage factor Ds is incorporated to consider soil degradation and the reduction in hydrate cementation, as described by plastic shear strain. A computer program was developed to simulate the mechanisms of cementation and damage evolution, as well as the stress-strain curves of hydrate-bearing cemented sand. The results indicate that the model replicates the mechanical behavior of soil cementation and soil deterioration caused by impairment well. By comparing the theoretical curves with the experimental data, the compliance of the model was calculated to be more than 90 percent. The new state-dependent elasto-plastic constitutive model based on cementation and damage of hydrate-bearing cemented sand could provide vital guidance for the construction of deep-buried tunnels, extraction of hydrocarbon compounds, and development of resources.