Elastic-plastic Constitutive Model Research Articles

Impact of surface roughness on the formation of necking instabilities in additive manufactured porous metal plates subjected to dynamic plane strain stretching

This paper investigates the influence of surface roughness on multiple necking formation in additive manufactured porous ductile plates subjected to dynamic plane strain stretching. For this purpose, we have developed a computational model in ABAQUS/Explicit which includes surface texture and discrete voids measured from 3D-printed metallic specimens using optical profilometry and X-ray tomography analysis, respectively. The mechanical behavior of the material is described using an elastic–plastic constitutive model, with yielding defined by the isotropic von Mises criterion, an associated flow rule, and a power-law function for the yield stress evolution which depends on plastic strain, plastic strain rate, and temperature. The finite element calculations have been conducted across a broad range of strain rates, from 5000s−1 to 50000s−1, to explore the interactions among inertia, surface roughness, and porosity in determining the necking pattern that emerges in the plates at large strains. The finite element results show that surface roughness induces perturbations in the deformation field of the specimen, which lead to early necking localization, while the location and number of necks formed are primarily controlled by the porous microstructure and the loading rate. The results for the neck spacing have shown quantitative agreement with the analytical stability analysis predictions and the unit-cell finite element calculations reported by Rodríguez-Martínez et al. [1]. Moreover, integrating discrete voids into simulations that already account for surface roughness results in a minor reduction in necking strain: surface roughness and porosity demonstrate similar quantitative impacts on necking ductility, which is primarily influenced by inertia effects at the highest strain rates studied. To the best of the authors’ knowledge, this paper presents the first calculations that explore dynamic plastic localization in additive manufactured metals, incorporating actual surface roughness and explicit void representation derived from experimental measurements. This work marks progress in the analysis of 3D-printed structures under impact loading, aiming to understand and predict the mechanics influencing their energy absorption capacity at high strain rates.

Numerical study on the effects of alloying variations on the crushing behaviour of an aluminium profile

The effects of variations in the chemical composition of an aluminium alloy AA6005 on the axial crushing and bending behaviour of a double chamber extruded profile are investigated by shell-based finite element analyses. A novel sequential modelling method, including nanostructure modelling, virtual tensile testing and localisation analyses, is used to determine the yield strength, work-hardening, and ductility of several variants of the AA6005 alloy. The data obtained from the models are used to calibrate the parameters of an isotropic elastic–plastic constitutive model and an uncoupled damage criterion. Explicit finite element analyses of axial crushing and three-point bending of the double chamber extruded profile are conducted for all variants of the AA6005 alloy in temper T6. By comparing the results of the finite element analyses with existing experimental data, the results reveal how variations in the chemical composition significantly influence the structural integrity of the extruded aluminium profile in axial crushing and bending.

A computational study on buckling strength of pressurised submarine pressure hull structures under combined static load and asymmetric impact load

Through the reconstructed kernel particle method (RKPM), the dynamic buckling characteristics of submarine pressure hull under hydrostatic pressure and impact load is investigated in this study. First, a large deformation buckling calculation model for stiffened shell structures was established using RKPM and elastic–plastic constitutive models. To study the influence of load asymmetry on the buckling strength of the structure and provide fundamental technical support for submarine structural design, the dynamic buckling phenomenon of the structure was studied under three conditions: hydrostatic pressure acting alone, hydrostatic pressure and impact load acting simultaneously, and hydrostatic pressure and uniformly distributed impact load acting simultaneously. The starting time of buckling was used as the criterion for determining the critical load of dynamic buckling. The results indicate that under the combined action of static and dynamic loads, asymmetric dynamic loads can seriously affect the buckling strength of the structure.

An Elastic-Plastic Constitutive Model for Unsaturated Structural Loess

An Elastic-Plastic Constitutive Model for Unsaturated Structural Loess

A nonlinear elastic-plastic model describing the bending and fracture behavior of Caragana korshinskii Kom. branch wood

ABSTRACT Caragana korshinskii Kom. branch (CKB), a vital biomass source in northwest China, has not been thoroughly studied in terms of its bending fracture mechanics. This research aims to establish a nonlinear constitutive model that clarifies the fracture behavior of CKB when subjected to bending loads. The nonlinear bending fracture process of CKB was characterized through a three-point bending test, revealing stages of elastic deformation, elastic-plastic transition, and plastic fracture. A power-enhanced elastic-plastic model combined with continuous damage mechanics theory was used to develop an intrinsic bending fracture model, from which the equations governing bending damage evolution were derived. The model's accuracy was validated with simulations in Abaqus/Explicit, showing that CKB from various growth sites demonstrated distinct nonlinear bending behaviors. At the critical damage strain, cumulative damage led to a reduction in the effective elastic modulus, with the bending fracture curve exhibiting a power function trend. The parameters of the nonlinear elastic-plastic constitutive model were derived through curve fitting, yielding coefficients of determination (R²) exceeding 0.99. The consistency between the trends observed in actual tests and simulations, along with a peak bending force error of 7.7%, validated the finite element model's reliability and confirmed the intrinsic model's accuracy.

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.

Structural Design and Life Prediction of Sheet Metal Parts for Gas Turbine Vane

In the cooling design of gas turbine vane, sheet metal parts were used to arrange the impact cooling holes in the platform and inner cavity, and divided the chamber space for impact cooling. During the service period, due to the impact of temperature load and air flow, the sheet metal parts were prone to bulge, crack, fall off, which worsen the cooling effect. In order to ensure the safe and reliable operation of blade and sheet metal parts, it was necessary to design reasonable sheet metal structure and accurately predict the service life. In this paper, material mechanical property test of GH3536 was carried out to obtain its constitutive equation and fatigue performance parameters. The structure of sheet metal parts were designed, then the temperature field of the blade and the sheet metal was simulated by using the fluid-thermal-solid coupling method, and the stress-strain analysis was carried out by using the elastic-plastic constitutive model. Finally, the fatigue life of the sheet metal was obtained, and the service life meet the design requirements. This work was helpful to prolong the life of sheet metal structure and ensure the cooling effect of blade.

Influence of the Elastic-Plastic Dynamic Artificial Boundary on the Progressive Collapse Performance of Truss Structures

The traditional fixed boundary could not transmit the elastic-plastic stress waves in the progressive collapse analysis of the truss structures, leading to discrepancies in understanding the true response of structures. To solve the critical problem, a new dynamic artificial boundary is proposed and integrated into the truss structure to transmit elastic-plastic stress waves. The new dynamic artificial boundary is established through the integration of the elastic-plastic constitutive model into the governing equation of the stress wave. This boundary is subsequently implemented within the ABAQUS finite element software for the purpose of conducting progressive collapse analysis of the truss structures. The progressive collapse simulation of the truss structures involves a comparative analysis between the new dynamic artificial boundary and the traditional fixed boundary. Numerical analysis demonstrates that the dynamic artificial boundary led to varied initial failure and collapse compared to the fixed boundary. The failure typically occurs at the mid-span under the dynamic boundary. In contrast, additional failures occur near the support columns under the fixed boundary due to stress wave reflections. The dynamic artificial boundary more closely reflects the physical reality and provides a new method for the progressive collapse analysis of the truss structures in practical applications.

Effect of shell spacing on mechanical behavior of multi-span soil-steel composite structure

This study analyses the effect of lateral shells on central shell at a different spacing in a multi-span soil-steel composite structure subjected to quasi-static moving loads. The displacements and internal forces of the central shell during consecutive truck passages over the structure are investigated by finite element (FE) analysis. Field measurements from a site in Niemcza, Poland, are used to calibrate input parameters. Next, the simulations for different spacing between the shells are investigated. The backfill soil is modeled as elastic-perfectly plastic, while the shells and sheet piles are linear elastic. The non-linear contact zone between the shell and the soil backfill is assumed to reflect an elastic-plastic constitutive model. The analysis reveals that both vertical and horizontal displacements increase significantly when the ratio of shell spacing to span length is less than 0.5. Maximum stress occurs when the shells are placed adjacent to each other, i.e., without spacing. The stress is almost doubled in this position compared to the reference case—a single-span structure. The shifting of extreme deflections and stress is observed in the direction of truck movement. Nevertheless, the influence of lateral shells on the central shell's performance under moving loads is nearly negligible when the spacing-to-span ratio exceeds 0.5.

An incremental elastic-plastic cohesive constitutive model with considering damage

An incremental elastic-plastic cohesive constitutive model with considering damage

Mechanical Analysis and Constitutive Modeling of Nonlinear Behavior of Silver-based Conductive Ink

Stretchable electronic devices are progressively deployed in many applications of mechanical, electrical, and bio-medical engineering. These circuits are made of stretchable and flexible substrate, as well as conductive ink, and various electronic components. The choice of components and layouts for the substrate and conductive ink can regulate the stretchability of stretchable circuits. On top of that, the substance utilized to create the conductive ink must have high electrical conductivity and strong adherence to the substrate in order to produce a high-quality stretchable printed circuit. Thus, this study focused on the development of stretchable conductive ink using silver powder as a conductive filler and PDMS-OH as a binder. The mechanical properties of the synthesized ink were investigated via simple uniaxial tensile testing method and nanoindentation technique, respectively. Accordingly, the modulus of elasticity, tensile stress and yield stress of the ink were obtained as 5.72 MPa, 1.195 MPa, and 0.86 MPa, congruently at 137% strain before undergoing failure. The experimental stress-strain data was then employed on the elastic-plastic constitutive model to investigate the elastomeric properties of the ink as it is an alternative method of lengthy and expensive procedures of validating different polymers. Moreover, the hardness and reduced modulus of the ink were evaluated by nanoindentation method using 5 mN maximum load with 0.5 mN/s loading/unloading rate and 2 secs holding time. Consequently, the hardness and reduced modulus values were obtained as 1.45 MPa and 34.53 MPa, respectively. These values were further validated by Oliver-Pharr method, and were in a good agreement.

Modeling, testing, and optimization of novel lattice structures for enhanced mechanical performance

Cellular materials have drawn increasing interest in numerous applications due to their promising specific stiffness, strength and energy absorption capacity. In this work, a variety of rather novel lattice topologies pertinent to additive manufacturing are derived and examined. A number of these are derived by free-domain and constrained domain topology optimization procedures, while others are inspired by the triply periodic minimum surface (TPMS) sheet-based topologies. The topology optimization module utilized a single objective function of minimizing strain energy under linear elastic conditions. A total of fifteen different lattice topologies are investigated numerically, including both novel and conventional topologies (e.g. strut-based lattices) and their effective elastic properties are determined with respect to relative density through finite element analysis (FEA). Based on the preliminary FEA results, a number of these topologies are selected of which tessellated lattice structures are fabricated through laser powder bed fusion (LPBF) additive manufacturing technique out of Nylon thermoplastic material. The tessellated lattice structures are experimentally tested in compression and their mechanical performance, including uniaxial modulus, yield strength, and energy absorption capacity (EAC), is assessed. FEA simulations have been conducted using an elastic-plastic constitutive model for the Nylon base material. Both the experimental and numerical results reveal that the mechanical performance of the novel tube-based TPMS lattice P-100 and the combined loading (CL) topology derived through free-domain topology optimization surpasses all other topologies. P-100 uses a primitive TPMS with equal-length tubular connections in each direction, where the tubular length percentage compared to the primitive lattice size is 100%, while CL lattice topology is a free domain topology optimized under compressive loads on the centers of faces, edges, and vertices toward the center. The innovative lattice topologies proposed in the current study, particularly the P-100 and CL topologies, can become crucial in applications where it is necessary to improve the energy absorption capacity, such as sandwich panel cores, supports, and infills for 3D printed components.

Selection and Optimization Design of PDC Bits Based on FEM Analysis for Drilling Long Horizontal Sections of Shale Formations

Well structures with ultra-long sections have become one of the most applied technologies in the field of shale gas development. While there have been many technical challenges, enhancing the breaking efficiency and stability of polycrystalline diamond compact (PDC) bits has become an essential issue of focus. Since 2013, the well structure in the Duvernay area has been optimized multiple times, and the rate of penetration (ROP) of the entire wellbore has nearly doubled. However, there are significant differences in terms of the performances of different PDC bits, and there is still room for improvement to optimize these drill bits. For this reason, a confined compressive strength test was conducted to obtain the rock mechanical parameters from shale cores extracted from the long horizontal section. Using these data, a finite element model (FEM) was developed with a corresponding scale. A calibration of the elastic-plastic damage constitutive models was then performed using the FEM. The breaking mechanism of three different PDC bits was examined using a “PDC bit-bottom hole” interaction FEM model, facilitating guidance for bit selection and design optimization: (1) The type B PDC bit, which has four blades and 20 cutters, exhibited the highest mechanical specific energy (MSE) and the lowest vibration across three directional mechanical characteristics. This design is recommended for engineering applications. (2) Lower axial vibrations were produced when the CDE was used as the rear element when compared to those when using the BHE. However, an increase within an acceptable range was observed in the TOB and circumferential vibrations. Thus, for redesigning work on the type B bit, the assembly of the CDE is suggested. (3) A decrease in the MSE and vibration in three directional mechanical characteristics was observed when the depth of cut (DOC) was varied between 1.5 and 2.0 mm. A broadening in the range of lateral forces was noted when a DOC of 2.0 mm was used. Therefore, for the redesign of the type B bit, the assembly of CDEs as rear elements at a DOC of 1.5 mm is recommended. In conclusion, a new practical method for the selection and optimization of PDC bit design, based on rock mechanics and the FEM theory, is proposed.

Numerical analysis for tunnelling-induced stress and plastic evolution causing instability of multilayered surrounding rock by varying three-dimensional in situ stresses

PurposeThe induction of geological disasters is predominantly influenced by the dynamic evolution of the stress and plastic zones of the multilayer rock formations surrounding deep-rock roadways, and the behaviours and mechanisms of high in situ stress are key scientific issues related to deep-resource exploitation. The stress environment of deep resources is more complex owing to the influence of several geological factors, such as tectonic movements and landforms. Therefore, in practical engineering, the in situ stress field is in a complex anisotropic three-dimensional state, which may change the deformation and failure law of the surrounding rock. The purpose of this study is to investigate the tunnelling-induced stress and plastic evolution causing instability of multilayered surrounding rock by varying three-dimensional in situ stresses.Design/methodology/approachBased on data from the Yangquan Coal Mine, China, a finite difference model was established, and the elastic-plastic constitutive model and element deletion technology designed in the study were analysed. Gradual tunnelling along the roof and floor of the coal seam was used in the model, which predicted the impact tendency, and compared the results with the impact tendency report to verify the validity of the model. The evolutions of the stress field and plastic zone of the coal roadway in different stress fields were studied by modifying the maximum horizontal in situ stress, minimum horizontal in situ stress and lateral pressure coefficient.FindingsThe results shown that the in situ stress influenced the stress distribution and plastic zone of the surrounding rock. With an increase in the minimum horizontal in situ stress, the vertical in situ stress release area of the roof surrounding rock slowly decreased; the area of vertical in situ stress concentration area of the deep surrounding rock on roadway sides decreased, increased and decreased by turn; the area of roof now-shear failure area first increased and then decreased. With an increase in the lateral pressure coefficient, the area of the horizontal in situ stress release area of the surrounding rock increased; the area of vertical in situ stress release area of the roof and floor surrounding rock first decreased and then increased; the area of deep stress concentration area of roadway sides decreased; and the plastic area of the surrounding rock and the area of now-shear failure first decreased and then increased.Originality/valueThe results obtained in this study are based on actual cases and reveal the evolution law of the disturbing stress and plastic zone of multilayer surrounding rock caused by three-dimensional in situ stress during the excavation of deep rock roadways, which can provide a practical reference for the extraction of deep resources.

Constitutive model of interfacial bond-slip between steel fibers and concrete matrix after exposing to high temperature

In the current study, the bonding properties between two kinds of steel fiber with different shapes and concrete matrix after exposing to high temperatures are investigated experimentally and theoretically. A total of 55 samples were prepared and divided into five groups, subjected to different temperatures ranging from 25 °C to 800 °C, then the residual fiber pull-out strength was measured after naturally cooling down to room temperature. The results of the fibers pulling-out experiment and microstructure analysis show that the bond-slip property of hooked-end steel fiber is better than that of straight steel fiber at any temperature. The influence of temperature on the fiber-pulling performance is mainly due to the change of microstructure in the cement matrix. With the increase of temperature, the cracks of the matrix gradually increase, and the fiber will degrade after 800 °C. According to experimental analysis, a new elastic-plastic constitutive model of bond-slip is developed within the thermodynamic framework. A unified yield function is proposed to describe the pull-out process of fibers of different shapes, which only needs to determine the hardening characteristics. Combined with the principle of free energy dissipation, a damage evolution model of the interface after exposing to high temperature is proposed. The model requires several parameters with definite physical meanings to be obtained from the experiment. Compared with the experimental results, the model proposed in this paper is reliable and provides a basis for further research on the mechanical properties of fiber-reinforced concrete after high temperatures.

Multiscale experimental characterisation of mode-I interfacial fracture behaviour of vitrimer composites

Vitrimer composites with bond- exchange reactions offer significant advantages in terms of repair and recyclability. The mechanical properties of such composites can be designed by modifying the epoxy/anhydride ratio, thus allowing their interface properties to be customised. In this study, the mode-I interfacial fracture properties of vitrimer carbon fibre composites with different epoxy/anhydride ratios are investigated experimentally and numerically. The results show that composites with an epoxy/anhydride group ratio of 1:0.5 exhibit the highest fracture toughness, with a maximum value of 1.6 mJ/mm2. Meanwhile, the analysis of the composites’ microscopic fracture morphology indicates their good bonding performance with carbon fibres. Subsequently, a multiscale numerical approach is developed to simulate the mode-I fracture response of composite laminates and establish a trilinear cohesive model to simulate the macroscopic interfacial fracture behaviour. In this approach, a matrix elastic–plastic constitutive model and the J-integral method are applied to obtain the stress distribution in the fibre-bridging phase via a double cantilever beam fracture test. The macroscopic fracture behaviour obtained via simulation is consistent with the experimental results. Therefore, the proposed multiscale numerical simulation method, which correlates the matrix properties with macroscopic fracture parameters, allows the interlaminar properties of composites with novel matrices to be evaluated effectively.

Research on Rolling Contact Fatigue Failure of the Bearing Used in High-Speed Electric Multiple Units’ Axle Box Based on a Damage-Coupled Elastic–Plastic Constitutive Model

The axle box bearing is a crucial component of high-speed electric multiple units (EMU) and is exposed to harsh working conditions, making it susceptible to subsurface-induced rolling contact fatigue (RCF) under long-term alternating stress. The objective of this paper is to develop a damage-coupled elastic–plastic constitutive model that can accurately predict the RCF life of EMU axle box bearings made from AISI 52100 bearing steel. The total damage is divided into elastic damage related to the shear stress range and plastic damage associated with plastic deformation. Material parameters are determined based on experimental data from the literature, and validation is conducted to ensure the validity of the model. Finally, the RCF behavior of the EMU axle box bearing, including crack initiation, crack propagation, and spalling, is simulated, and reasonable results are obtained. This study provides valuable insights into the RCF behavior of EMU axle box bearings and contributes to the accurate prediction of the fatigue life.

A coupled mechanical-electrochemical phase-field formulation for understanding the evolution of lithiated-silicon sponge

The unexpected formation of lithiated-silicon sponge during cyclic charge of lithium-ion batteries with silicon anodes has been observed in recent reports. The severe hollowing of silicon electrodes leads to an irreversible deformation and the generation of new surfaces, which greatly affects the structural integrity and cycling stability of the cells. However, the understanding of lithiated-silicon sponge still remains as a great challenge. In this work, a coupled mechanical-electrochemical model based on the phase-field method is proposed, which can describe the void evolution and the surface instability in Si electrodes. The model combines a description of the lithium diffusion, vacancy nucleation and annihilation, and an elastic-plastic constitutive model with concentration-dependent material properties. The simulation results reveal that the void within/on the silicon electrode tends to grow toward/along the electrode surface and toward other voids, leading to the electrode surface disruption and void merging, as well as the intra-electrode tunnel formation and electrolyte intrusion. Importantly, it is found that mechanical pressure can not only suppress the growth of a single void but also prevent the linkage and merging between multiple voids. The proposed theoretical framework and the findings of this work provide an in-depth understanding of the complicated mechanical-electrochemical coupling behavior of Si electrodes.

Multifactorial analysis of a gateroad stability at goaf interface during longwall coal mining – A case study

Purpose. Creating a generalized algorithm to account for factors (coal seam thickness, enclosed rock mechanical properties, the dimension and bearing capacity of artificial support patterns) causing a gateroad state under the effect of longwall face and goaf. Methods. The assessment of the gateroad stability is based on numerical simulation of the rock stress-strain state (SSS). The finite element method is used to find out the changes in the SSS of surrounding rocks at various stages of longwall mining. The elastic-plastic constitutive model and Hoek-Brown failure criterion implemented in codes RS2 and RS3 (Rocscience) are applied to determine rock displacements dependently on the coal seam thickness, enclosed rock strength, width and strength of artificial support (a packwall comprised of hardening mixture “BI-lining”). To specify the mechanical properties of the packwall material a series of experimental tests were conducted. A computational experiment dealing with 81 combinations of affecting factors was carried out to estimate the roof slag and floor heaving in the gateroad behind the longwall face. A group method of data handling (GMDH ) is employed to generalize the relationships between rock displacements and affecting factors. Findings. The roof-to-floor closure in the gateroad has been determined at the intersection with the longwall face and goaf dependently on the coal seam thickness, enclosed rock strength, width of the packwall, and strength of hardening material. It is revealed that the support material gains the strength value of 30 MPa on the 3rd day from its beginning to use which is fully corresponding to the requirements of protective element bearing capacity. The possibility of using untreated mine water to liquefy the mixture is proved, that allows simplifying and optimizing the solute mixing and pumping technology. Originality. This study contributes to improving the understanding of the factors that influence the stability of underground mining operations and highlights the importance of utilizing numerical simulations in optimizing mining designs. The impact of each factor on the resulting variable (decrease in cross-section of gate road by height) based on the combinatorial algorithm of structural identification of the model is estimated as follows: the packwall width is 48%, the thickness of coal seam is 25%, the strength of enclosing rocks is 23%, and the strength of the packwall material is 4%. Practical implications. The findings provide stakeholders with a technique to determine reasonable parameters for support and protective systems, and the predictive model developed can be used to mitigate potential instability issues in longwall mining excavations. The results have implications under similar geological settings and can be valuable for mine design and optimization in other regions.

Application of continuum damage mechanics in fatigue assessment of A516 steel specimens considering residual stresses

The present study evaluates the effects of tensile residual stresses on fatigue behaviour of ASTM A516 pressure vessel steel specimens. In this regard, fatigue specimens containing a smooth notch region are studied. A damage coupled elastic-plastic constitutive material model is developed to investigate effects of residual stresses on fatigue life. Isotropic and kinematic hardening parameters of the material are experimentally determined. Additionally, the damage model parameters are specified from fatigue experiments conducted on standard specimens in different stress ratios. Tensile residual stresses are introduced into the smooth notched specimens through employing four-point-bending method. The hole drilling technique is utilized to measure the residual stress magnitudes. The results indicate that about two third of fatigue life of the specimens is decreased due to the existed tensile residual stresses. Furthermore, fatigue crack initiation and propagation behaviour in the specimens containing residual stress are studied based on the developed continuum damage model.