Constitutive Model of Duplex Stainless Steel: Experimental Investigation and Genetic Algorithm-Based Parameter Calibration

Abstract

Duplex stainless steel (S22053) is increasingly favoured in construction and marine engineering due to its superior corrosion resistance, toughness, and high strength-to-weight ratio. This study presents a comprehensive investigation into the mechanical behaviour of duplex stainless steel under both monotonic and cyclic loading. First, monotonic behaviour is characterized, and the applicability of existing constitutive models is verified. Addressing the complexity of parameter identification for the cyclic constitutive model, a genetic algorithm (GA)-based calibration framework for the Chaboche model is proposed. This approach overcomes the subjectivity and inefficiency of traditional manual fitting. The proposed method is validated against experimental hysteresis curves, demonstrating high accuracy and providing a reliable basis for the seismic design of duplex stainless steel structures.

1. Introduction

Stainless steel is renowned for its exceptional corrosion resistance, durability, ductility, and fire resistance, in addition to its environmental sustainability and aesthetic appeal [1]. As a superior structural material, it has seen widespread adoption in the construction industry, particularly in structures exposed to harsh external environments [2]. Duplex stainless steel contains both austenite and ferrite phases in its microstructure. This dual-phase structure imparts the excellent toughness of austenite, as well as the high strength and crack resistance of ferrite. Compared to the commonly used austenitic stainless steels in building structures, duplex stainless steel S22053 exhibits higher yield and tensile strengths [3]. This increased strength enables designers to use thinner plates to achieve the same load-bearing capacity, providing advantages in structural lightweighting and cost savings, which makes it highly promising for future applications. Researchers have conducted both experimental and theoretical studies on the mechanical properties of stainless steel components [4,5,6,7,8,9,10,11,12,13], joint mechanics [14,15], and the seismic performance of frames [16,17].

Under seismic loading, steel structural components, particularly energy-dissipating elements, are typically subjected to large cyclic loads. Characterized by short durations, a limited number of hysteresis cycles, and substantial plastic deformation, this loading condition is often classified as ultra-low-cycle loading. Structural components resist seismic actions primarily through the elasto-plastic hysteretic behaviour, which differs markedly from its behaviour under monotonic loading. Consequently, many researchers have conducted elasto-plastic fatigue tests on stainless steel to investigate its cyclic response under various loading protocols [18,19,20]. To capture the true dynamic response of structures under seismic excitation, shaking-table experiments or elasto-plastic time-history analyses are commonly employed. However, because shaking-table tests are costly and allow only limited loading conditions, elasto-plastic time-history simulations have become a more practical and widely adopted approach in engineering design. In numerical simulations, accurately representing the cyclic constitutive model is essential for ensuring the reliability and precision of the results.

Stainless steel exhibits pronounced cyclic strengthening and a distinct Bauschinger effect under repeated loading. To accurately capture its cyclic elasto-plastic stress–strain behaviour, several factors must be considered, including the yield criterion, flow rule, and hardening model. An elasto-plastic cyclic constitutive model incorporating combined hardening rules can reasonably describe the stress–strain response of metals subjected to cyclic loading. The Chaboche model, introduced by Lemaitre and Chaboche, is widely used in structural engineering to characterize the nonlinear mechanical behaviour of steel [21,22]. This model has been implemented in the finite element software ABAQUS and is extensively employed in numerical simulations [23].

In recent years, many researchers have investigated the application of the Chaboche model to the stress–strain relationships of stainless steel under various loading protocols and plate thicknesses, calibrating the model parameters using experimental data [18,24,25,26,27,28]. The calibration of the Chaboche model is influenced by factors such as plate thickness, material batch, and loading protocol. Due to the high cost of extensive cyclic testing and the labour-intensive process of parameter calibration, the efficiency of engineering simulations and designs is significantly reduced. To address this challenge, the primary goal of this study is to reduce the computational cost associated with calibrating cyclic constitutive model parameters, enhance efficiency, and propose a novel calibration method based on intelligent computing techniques.

In recent years, various artificial intelligence–based optimization techniques have been introduced to improve the efficiency and objectivity of constitutive model parameter calibration. Particle swarm optimization (PSO) [29,30], genetic algorithms (GA) [31], global optimization approaches [32], and neural network (NN)-based methods [33] have been widely applied in this context. For example, Smith et al. [29] employed PSO to calibrate cyclic constitutive model parameters for ASTM A572 [34] Grade 50 structural steel, demonstrating improved agreement with experimental hysteresis responses. Pandey et al. [31] used genetic algorithms to optimize cyclic constitutive models for different engineering materials, showing that GA can reasonably predict both stress–strain responses and strain amplitudes. Among these methods, genetic algorithms are particularly well suited for calibrating cyclic constitutive models with strong nonlinearity and multiple coupled parameters, due to their global search capability and reduced dependence on initial parameter guesses. Therefore, a GA-based optimization framework is adopted in this study to calibrate the parameters of the Chaboche constitutive model for S22053 duplex stainless steel.

This study initially investigates the material behaviour of duplex stainless steel S22053 through monotonic tensile tests, followed by the calibration of the R-R-O and N-R-O models [35,36,37,38,39,40] to evaluate their applicability and accuracy. Furthermore, cyclic loading tests are conducted on S22053 to examine its stress–strain behaviour under various loading protocols. Additionally, a novel parameter calibration method for the Chaboche model, based on genetic algorithm optimization, is proposed. This method enhances calibration efficiency using cyclic test data, and its accuracy and computational performance are verified against experimental results.

2. Mechanical Behaviour and Constitutive Model of Duplex Stainless Steel Under Monotonic Loading

2.1. Tensile Tests and Results Analysis

This study begins with an experimental analysis of the monotonic mechanical properties of domestically produced duplex stainless steel EN 1.4462 (ASTM 2205, S22053) [41,42], focusing on the yield stress, ultimate tensile stress, and the tensile and fracture characteristics of the material. Dog-bone-shaped specimens with plate thicknesses of 6 mm, 8 mm, 10 mm, 12 mm, and 16 mm were selected, with two repetitions for each plate thickness to examine performance variations among materials of different thicknesses. The specimens were cut along the rolling direction. The measured thickness and width of the gauge length are listed in

Table 1. Material properties of monotonic coupon test.

Specimen	a	b	E0	σ0.2	ε0.2	σu	εu	A
	[mm]	[mm]	[MPa]	[MPa]	[%]	[MPa]	[%]	[%]
2205-16-1	8.12	8.05	197,892	677	0.542	860	12.9	24.0
2205-16-2	8.12	8.00	210,000	659	0.514	849	12.5	24.3
2205-12-1	8.10	8.08	182,434	547	0.469	754	21.5	34.3
2205-12-2	8.10	8.02	196,184	535	0.473	751	22.4	35.7
2205-10-1	8.15	8.15	197,042	533	0.465	751	21.9	33.7
2205-10-2	7.88	8.18	204,529	535	0.451	753	20.1	37.5
2205-8-1	7.86	7.98	182,031	628	0.549	789	18.1	31.0
2205-8-2	7.88	7.96	173,132	581	0.533	778	18.1	30.3
2205-6-1	5.75	6.00	173,649	555	0.527	751	22.2	33.7
2205-6-2	5.75	6.00	177,642	557	0.514	756	21.5	32.0
Mean	—	—	189,453	581	0.504	779	19.1	31.7
COV	—	—	0.066	0.088	0.067	0.051	0.184	0.134

. The tests adhered to the specifications outlined in “Tensile Test of Metallic Materials-Part 1: Room Temperature Testing Methods” (GB/T 228.1-2010) [43], and the monotonic tensile tests were performed using a Zwick/Roell Z100 electronic universal testing machine (ZwickRoell, Ulm, Germany).

Upon analysing the experimental results, it is evident that all monotonic tensile specimens exhibited necking and fracture in the gauge length. Figure 1 shows the stress–strain curves obtained from the experiments, which reveal that the stainless steel demonstrates significant nonlinear material behaviour without a yield plateau. Key mechanical properties were extracted from the curves, as shown in Table 1, including the elastic modulus E₀, ultimate tensile stress σ_u, stress σ_0.2 and strain ε_0.2 at 0.2% plastic strain, ultimate strain ε_u, and fracture strain A. The elastic modulus of the specimens ranged from 173 GPa to 210 GPa, while the ultimate tensile stress ranged from 751 MPa to 860 MPa, with the 16 mm thick specimen exhibiting the highest ultimate tensile stress. The ultimate strain ranged from 12.5% to 22.4%, and the fracture strain ranged from 24% to 35.7%, with the 16 mm thick specimen showing the lowest ultimate and fracture strains. The S22053 stainless steel plates used in this study meet the material property requirements of GB/T 4237-2015 “Hot-rolled Stainless Steel Plates and Strips” [44] in terms of material properties, and the obtained experimental data are reliable for fitting the constitutive model parameters.

2.2. Calibration of Monotonic Constitutive Model Parameters

Establishing a constitutive model that accurately describes and predicts the stress–strain behaviour is crucial for numerical simulations and structural design, as it forms the foundation for rational optimization in design. Currently, the most widely used and well-recognized constitutive model is the two-stage model proposed by Ramberg and Osgood, and subsequently refined by several researchers (hereafter referred to as the R-R-O model) [35,36,37,38,39], with the fundamental equation given in Equation (1).

$$\epsilon =\left\{\begin{array}{l}{\displaystyle \frac{\sigma }{E}}+0.002{\left({\displaystyle \frac{\sigma }{{\sigma }_{0.2}}}\right)}^n\mathrm{for}\sigma \le {\sigma }_{0.2}\\ {\displaystyle \frac{\sigma -{\sigma }_{0.2}}{E_{0.2}}}+\left({\epsilon }_u-{\epsilon }_{0.2}-{\displaystyle \frac{{\sigma }_u-{\sigma }_{0.2}}{E_{0.2}}}\right){\left({\displaystyle \frac{\sigma -{\sigma }_{0.2}}{{\sigma }_u-{\sigma }_{0.2}}}\right)}^m+{\epsilon }_{0.2}\mathrm{for}\sigma >{\sigma }_{0.2}\end{array}\right.$$

(1)

where n is the strain hardening exponent, m is the second strain hardening exponent, and E_0.2 is the tangent modulus at the 0.2% proof stress.

The model has been widely validated and demonstrates good accuracy across the entire strain range. However, studies have shown that it tends to overestimate the stress variation in the small strain range and fails to accurately predict the stress–strain behaviour under compression. Consequently, Chen et al. [40] proposed a new constitutive model (hereinafter referred to as the N-R-O model), which features simpler parameters, higher computational efficiency, and greater accuracy compared to the R-R-O model. The specific equation is given in Equation (2).

$$\left\{\begin{array}{l}\epsilon ={\displaystyle \frac{\sigma }{E}}+0.002{\left({\displaystyle \frac{\sigma }{{\sigma }_{0.2}}}\right)}^n\mathrm{for}\sigma \le {\sigma }_{0.2}\\ \epsilon =\ln \left(1-{\displaystyle \frac{V_q\left(\sigma -{\sigma }_{0.2}\right)}{H_q}}\right)/-V_q+0.002+{\displaystyle \frac{{\sigma }_{0.2}}{E}}\mathrm{for}{\sigma }_{0.2}<\sigma \le {\sigma }_{\mathrm{u}}\end{array}\right.$$

(2)

where H_q represents the initial hardening modulus in the hardening stage, and V_q represents the rate of degradation of the hardening modulus with increasing plastic strain.

The stress–strain curves obtained from the experiments were fitted using the two models mentioned above, and the fitting results are shown in Figure 2 and

Table 2. Parameter Fitting Results for the R-R-O and N-R-O Models.

Specimen	n	m	${\mathit{R}}_{\mathbf{R}\mathbf{R}\mathbf{O}}^2$	Hq	Vq	${\mathit{R}}_{\mathbf{N}\mathbf{R}\mathbf{O}}^2$
2205-16-1	6.69	7.18	0.9397	7407.91	40.21	0.9806
2205-16-2	4.81	7.41	0.9470	7822.17	40.00	0.9745
2205-12-1	7.95	5.29	0.9443	4301.82	20.43	0.9912
2205-12-2	5.29	6.00	0.9195	4540.28	20.71	0.9920
2205-10-1	5.23	5.74	0.9317	4558.27	20.61	0.9914
2205-10-2	2.11	5.36	0.9281	4837.35	22.84	0.9913
2205-8-1	6.21	5.45	0.9369	4025.87	24.66	0.9891
2205-8-2	3.95	6.68	0.9374	5317.86	26.64	0.9796
2205-6-1	5.72	5.71	0.9273	4044.76	20.36	0.9923
2205-6-2	4.04	5.51	0.9317	4181.09	20.69	0.9913
Mean	5.20	6.03	0.9434	5103.74	25.72	0.9873
COV	0.31	0.12	0.008	0.27	0.30	0.006

. The parameter n of the R-R-O model ranges from 2.11 to 7.95, with an average value of 5.20; the parameter m ranges from 5.29 to 7.41, with an average value of 6.03, and the coefficients of variation (COV) for both parameters are within a reasonable range. For the N-R-O model, the parameter H_q ranges from 4025.87 to 7822.17, with an average value of 5103.74; the parameter V_q ranges from 20.36 to 40.21, with an average value of 25.72. The calibrated N-R-O model parameters for S22053 duplex stainless steel obtained from the monotonic loading tests were further examined by comparison with the parameter ranges reported in the original study by Chen et al. [40]. It is observed that the values of the hardening-related parameters H_q and V_q identified in this study fall well within the ranges suggested in the original research. This consistency demonstrates that the N-R-O constitutive model remains applicable for S22053 duplex stainless steel. It is observed that the parameters for the 16 mm thick specimen are approximately 7000, significantly higher than those for the other plate thicknesses (ranging from 4000 to 5000). This is due to the more pronounced material inhomogeneity in thicker steel plates, which in turn affects the ductility. The strain hardening characteristics become more significant, leading to poorer plastic deformation. Consequently, the stress–strain curve for thicker steel plates is more rounded in the hardening phase compared to thinner plates, ultimately resulting in higher values of the initial elastic modulus E_q and the rate of elastic modulus degradation V_q for the thicker material in the N-R-O model. Additionally, the goodness of fit (R²) for both models was calculated, as shown in Table 2. The analysis results indicate that both models exhibit high fitting accuracy, but the N-R-O model provides better accuracy compared to the R-R-O model and offers a more conservative description across the entire strain range. Therefore, the N-R-O model is more advantageous for describing the monotonic stress–strain behaviour of duplex stainless steel.

3. Mechanical Behaviour and Constitutive Model Under Cyclic Loading

3.1. Cyclic Loading Tests and Results Analysis

Cyclic loading tests were conducted to investigate the mechanical response of duplex stainless steel S22053 under seismic conditions. These tests were performed using a universal testing machine capable of both static and dynamic loading, employing strain control throughout the entire process. The true response of structures under seismic loading is not constant, and the deformations experienced by the material are complex and difficult to measure. Therefore, a variety of loading protocols were designed to simulate seismic responses as comprehensively as possible. These loading protocols typically influence the cyclic hardening behavior of the material through both strain amplitude and loading sequence. In this study, eight distinct loading protocols were designed based on the relevant specifications, including both constant and variable amplitude loading, with strain amplitudes ranging from 2% to 6% and different loading sequences, as shown in Figure 3. These protocols were specifically designed to accurately capture the cyclic response of S22053 duplex stainless steel under cyclic loading. The loading protocols assigned to each specimen are listed in

Table 3. Specimens and loading protocol allocation.

Loading Protocols	Specimens
CL1	2205-6-1, 2205-8-1, 2205-10-1, 2205-12-1
CL2	2205-6-2, 2205-8-2, 2205-10-2, 2205-12-2
CL3	2205-8-3, 2205-10-3, 2205-12-3
CL4	2205-12-4
CL5	2205-10-4
CL6	2205-8-4
CL7	2205-6-3
CL8	2205-6-4

. For example, in specimen 2205-6-1, “2205” refers to the S22053 stainless steel material, “6” indicates that the specimen was cut from a 6 mm thick plate, and “1” represents the sequence number of the specimen from this plate thickness.

The stress–strain curves obtained from the cyclic loading tests are shown in Figure 4. As observed in Figure 4, the hysteresis loops of S22053 stainless steel under different loading protocols are well-defined, indicating excellent energy dissipation capacity. As the strain amplitude increases, the range of plastic strain also expands, and the hysteresis behaviour exhibits characteristics of both isotropic and kinematic hardening. Additionally, the loading history has a significant impact on the hysteresis behaviour of the material. At the same strain amplitude, the ultimate strength varies, meaning that the hysteresis loops do not overlap, demonstrating a certain degree of cyclic hardening.

Additionally, the skeleton curve was extracted from the cyclic loading data. This curve reflects the material’s response under cyclic loading and can be compared with the monotonic tensile curve. The Ramberg-Osgood model was employed to fit the cyclic loading skeleton curve, as shown in Equation (3).

$${\displaystyle \frac{\Delta \epsilon }{2}}={\displaystyle \frac{\Delta \sigma }{2E}}+{\left({\displaystyle \frac{\Delta \sigma }{2K^{\prime }}}\right)}^{{\displaystyle \frac{1}{n^{\prime }}}}$$

(3)

where Δε represents the strain amplitude, Δσ denotes the stabilized stress amplitude, n′ is the cyclic hardening index, and K′ is the cyclic hardening coefficient. The parameters of the skeleton curve, derived from the experimental data, are presented in

Table 4. Parameters of the cyclic skeleton curves.

Specimens	E/Gpa	K′	n′
2205-6-1	190	302	0.175
2205-8-1	177	348	0.112
2205-10-1	181	275	0.184
2205-12-1	173	289	0.197

. A comparison between the fitted cyclic skeleton curve and the monotonic tensile curve is shown in Figure 5. The results indicate that the Ramberg-Osgood model accurately characterizes the skeleton curve of duplex stainless steel S22053 under cyclic loading. Furthermore, a clear difference is observed between the monotonic tensile curve and the cyclic skeleton curve. As the strain amplitude increases, the stress at the same strain is significantly higher for the cyclic skeleton curve compared to the monotonic tensile curve, demonstrating a distinct cyclic hardening behaviour.

3.2. Calibration of Chaboche Cyclic Constitutive Model Parameters Based on the Genetic Algorithm Optimization Method

The Chaboche Cyclic Constitutive Model consists of two components: nonlinear kinematic hardening and isotropic hardening. The kinematic hardening component describes the movement of the yield surface in response to changes in the stress path during cyclic loading, represented by the shift in back stress. The isotropic hardening component accounts for the change in the material’s yield strength due to accumulated plastic deformation, with the size of the yield surface varying as a function of the equivalent plastic strain. The combination of these two hardening mechanisms enables the model to more accurately capture the evolution of nonlinear material behaviour in metals during repeated loading and unloading cycles.

The isotropic hardening component of the Chaboche model defines the variation in the yield surface size through a functional relationship between the yield surface and equivalent plastic strain, as shown in Equation (4).

$${\sigma }^0={\left.\sigma \right|}_0+Q_{\infty }\left(1-e^{-b_{\mathrm{iso}}{\overline{\epsilon }}^{\mathrm{pl}}}\right)$$

(4)

where ${\left.\sigma \right|}_0$ represents the initial yield surface size, Q_∞ is the maximum change in yield surface size, and b_iso indicates the rate of change in yield surface size with plastic strain development.

The ABAQUS 2021 user manual provides a commonly used method for calibrating the parameters of the Chaboche Cyclic Constitutive Model [45]. The calibration diagram for the isotropic hardening parameters is shown in Figure 6a.

${\sigma }_i^0$ denotes the size of the yield surface in the i-th cycle, which can be calculated using Equation (5).

$${\sigma }_i^0={\displaystyle \frac{{\sigma }_i^{\mathrm{t}}-{\sigma }_i^{\mathrm{c}}}{2}}$$

(5)

where ${\sigma }_i^t$ and ${\sigma }_i^c$ represent the upper and lower stresses at the ends of the elastic segment in the i-th cycle, respectively.

The equivalent plastic strain ${\overline{\epsilon }}_i^{\mathrm{pl}}$ corresponding to ${\sigma }_i^0$ can be calculated using Equation (6).

$$\stackrel{-\mathrm{pl}}{{\epsilon }_i}={\displaystyle \frac{1}{2}}\left(4i-3\right)\Delta {\epsilon }^{\mathrm{pl}}$$

(6)

The plastic strain amplitude $\Delta {\epsilon }^{\mathrm{pl}}$ can be calculated using the following equation.

$$\Delta {\epsilon }^{\mathrm{pl}}={\epsilon }_t^{\mathrm{pl}}-{\epsilon }_c^{\mathrm{pl}}\approx \Delta \epsilon -{\displaystyle \frac{2{\sigma }_1^{\mathrm{t}}}{E}}$$

(7)

Equations (5)–(7) can be used to calculate the values of the data points (${\overline{\epsilon }}_i^{\mathrm{pl}}$,${\sigma }_i^0$), which represent the dependent and independent variables in Equation (4). Using the obtained data points, the isotropic hardening parameters $Q_{\infty }$ and $b_{\mathrm{iso}}$ can be fitted.

The kinematic hardening component defines the evolution of the back stress. When the hysteresis loop reaches a stable shape, the back stress α and plastic strain ${\epsilon }^{pl}$ are related by the following function.

$${\alpha }_{\mathrm{k}}={\displaystyle \frac{C_{\mathrm{k}}}{{\gamma }_{\mathrm{k}}}}\left(1-e^{-{\gamma }_{\mathrm{k}}{\epsilon }^{pl}}\right)+{\alpha }_{\mathrm{k},1}{e}^{-{\gamma }_{\mathrm{k}}{\epsilon }^{pl}}$$

(8)

$$\alpha ={\displaystyle \sum _{k=1}^N{\alpha }_{\mathrm{k}}}$$

(9)

where ${\alpha }_{\mathrm{k}}$ is the k-th back stress on the hysteresis loop, ${\alpha }_{\mathrm{k},1}$ is the k-th back stress at the first data point, $C_{\mathrm{k}}$ is the initial creepage strengthening modulus, and ${\gamma }_{\mathrm{k}}$ is the rate of change in back stress with the increase in plastic strain. In this paper, two back stress was used to calibrate the model.

The ABAQUS user manual provides a method for calibrating the kinematic hardening parameters, as shown in Figure 6. First, stable hysteresis loops are determined based on experimental data. For variable amplitude loading, it is difficult to achieve a stable hysteresis loop, and the last loop can be taken as the stable hysteresis loop. Then, the data points (${\epsilon }_i^{\mathrm{pl}}$,${\alpha }_i$) used to fit the kinematic hardening parameters $C_{\mathrm{k}}$ and ${\gamma }_{\mathrm{k}}$ are determined using Equations (10) and (11).

$${\epsilon }_i^{\mathrm{pl}}={\epsilon }_i-{\displaystyle \frac{{\sigma }_i}{E}}-{\epsilon }_{\mathrm{p}}^0$$

(10)

$$a_i={\sigma }_i-{\displaystyle \frac{{\sigma }_1+{\sigma }_n}{2}}$$

(11)

where ${\epsilon }_i^{\mathrm{pl}}$ represents the plastic strain at the i-th data point on the stable hysteresis loop, and $a_i$ is the back stress component at the i-th point. After obtaining the data points, the kinematic hardening parameters are fitted in ABAQUS using the option

*PLASTIC, HARDENING = COMBINED, DATA TYPE = STABILIZED.

The calibration process for the Chaboche Cyclic Constitutive Model parameters using the method outlined above is cumbersome and requires substantial computational effort, particularly for parameter calibration under variable amplitude loading conditions. Additionally, the parameters calibrated through this method often require further adjustments for certain curves before they can be used in numerical simulations and calculations. To address these challenges, this study proposes a parameter calibration method for the Chaboche cyclic constitutive model based on genetic algorithm optimization. This approach not only streamlines the calibration process but also improves its accuracy.

Genetic algorithms are widely used artificial intelligence techniques that optimize solutions by simulating natural evolutionary processes. These algorithms are extensively applied to solve complex problems. The core concept is to mimic biological processes such as reproduction, mutation, and natural selection, gradually searching for the optimal solution in the search space. Key steps in the process include selection, crossover, mutation, and inheritance [46]. The detailed process of the genetic algorithm is illustrated in Figure 7.

The specific steps of the genetic algorithm-based calibration method for the Chaboche cyclic constitutive model parameters are as follows: First, determine the size of the yield surface based on experimental results; second, estimate the range of model parameters based on experimental data and existing literature; third, define the objective function for parameter optimization; and finally, perform the parameter optimization to obtain the optimal model material parameters. A schematic of the parameter optimization process is shown in Figure 8.

First, the framework for the genetic algorithm optimization is established, which involves determining the optimization parameters and the objective function. ABAQUS finite element software is then used to simulate cyclic loading, following the same loading protocol as the experimental setup, using the Chaboche cyclic constitutive model. In ABAQUS, the model is constructed based on the dimensions of the specimen’s gauge section. The linear reduced integration element C3D8R is used, with a mesh size of 0.5 mm. Boundary conditions are applied such that one end is fixed (U1 = U2 = U3 = UR1 = UR2 = UR3 = 0), while displacement loading is applied to the other end. The finite element results are compared with experimental data through data interaction with MATLAB R2025a software. Subsequently, the genetic algorithm is applied to perform global optimization within the defined parameter range. The optimized parameter values are then passed back to ABAQUS for further simulation through data interaction. This iterative process continues until the optimal parameters are determined.

Based on the research by Ning et al. [47], it is recommended to set the initial yield surface size to 0.75σ₀.₀₁. The objective function used for parameter optimization in this study is as follows.

$$F=\mathrm{Min}{\displaystyle \sum \left|{\sigma }_i^{\exp }-{\sigma }_i^{\mathrm{model}}\right|}$$

(12)

where ${\sigma }_i^{\exp }$ and ${\sigma }_i^{\mathrm{model}}$ represent the experimental stress value and the finite element simulation stress value at the i-th data point, respectively. The objective function F is defined as the minimum sum of the differences between the experimental and finite element simulation stress values for all data points.

The Chaboche cyclic constitutive model parameters, calibrated using the genetic algorithm optimization method, are presented in

Table 5. Parameters of Chaboche model.

Specimens	σ|0 /MPa	Q∞ /MPa	biso	Ckin,1 /MPa	γ1	Ckin,2 /MPa	γ2
2205-12-1	410	40	7	13,152	60	142,899	768
2205-12-2	349	110	3	34,013	204	208,171	1266
2205-12-3	296	68	1	43,408	228	393,968	2438
2205-12-4	347	43	2	23,111	123	266,975	1465
2205-10-1	380	1	1	9819	53	109,945	651
2205-10-2	328	214	1	30,018	175	251,492	1470
2205-10-3	343	41	8	36,203	179	372,327	1937
2205-10-4	300	87	7	18,596	126	188,229	1067
2205-8-1	400	30	1	13,474	62	145,530	788
2205-8-2	343	124	1	36,956	165	500,616	2674
2205-8-3	272	64	4	50,538	201	788,016	3415
2205-8-4	327	39	1	70,883	318	586,357	3480
2205-6-1	360	76	3	25,115	119	195,573	1278
2205-6-2	292	207	1	13,566	62	173,567	903
2205-6-3	321	84	6	50,666	273	297,232	2019
2205-6-4	349	56	9	23,204	130	142,174	987
COV	0.112	0.740	0.834	0.548	0.505	0.634	0.550

. Finite element simulations were conducted in ABAQUS using the calibrated parameters, and the comparison between the experimental and simulation curves is shown in Figure 9. As shown in Figure 9, the simulation results using the calibrated model parameters closely match the experimental data. The genetic algorithm-based calibration method for the Chaboche cyclic constitutive model effectively and consistently captures the hysteresis behaviour of duplex stainless steel S22053 under various loading conditions. Furthermore, as shown in Table 5, the calibrated hardening parameters exhibit significant dispersion, highlighting the substantial influence of plate thickness and loading protocol on the results.

4. Conclusions

This study systematically investigates the mechanical behaviour of duplex stainless steel under both monotonic tensile and cyclic loading conditions, utilizing both experimental and numerical simulation methods. The primary objective is to simplify the parameter calibration process for cyclic constitutive model, thereby improving computational efficiency and accuracy. Ultimately, this work provides an effective approach for the numerical simulation of the seismic performance of stainless steel structures. The main findings are summarized as follows:

(1)

Monotonic tensile tests reveal that duplex stainless steel exhibits significant nonlinear stress–strain behaviour under different plate thicknesses.

(2)

Through the calibration of experimental data using the R-R-O and N-R-O models, it is found that the N-R-O model offers superior accuracy in describing the monotonic stress-strain behaviour of this material. It provides more conservative and reliable predictions across the entire strain range, making it the preferred choice for monotonic constitutive modelling.

(3)

Cyclic loading tests demonstrate that duplex stainless steel possesses stable hysteresis loops and excellent energy dissipation capacity under various loading protocols. The material exhibits distinct isotropic and kinematic hardening characteristics, with the loading history significantly influencing its hysteretic behaviour.

(4)

To address the complexity and high computational cost of calibrating the Chaboche cyclic constitutive model, an optimized calibration method based on a genetic algorithm (GA) is proposed. Finite element simulations verify that this method efficiently and accurately identifies model parameters, showing excellent agreement with experimental data.