Elastoplastic Model Research Articles

Experimental investigation and fractional elastoplastic damage constitutive modelling of gray sandstone under loading disturbance

Experimental investigation and fractional elastoplastic damage constitutive modelling of gray sandstone under loading disturbance

An Alternative Finite Element Formulation to Predict Ductile Fracture in Highly Deformable Materials

Abstract An alternative finite element formulation to predict ductile damage and fracture in highly deformable materials is presented. For this purpose, a finite-strain elastoplastic model based on the Gurson–Tvergaard–Needleman (GTN) formulation is employed, in which the level of damage is described by the void volume fraction (or porosity). The model accounts for large strains, associative plasticity, and isotropic hardening, as well as void nucleation, coalescence, and material failure. To avoid severe damage localization, a nonlocal enrichment is adopted, resulting in a mixed finite element whose degrees-of-freedom are the current positions and nonlocal porosity at the nodes. In this work, 2D triangular elements of linear-order and plane-stress conditions are used. Two systems of equations have to be solved: the global variables system, involving the degrees-of-freedom; and the internal variables system, including the damage and plastic variables. To this end, a new numerical strategy has been developed, in which the change in material stiffness due to the evolution of internal variables is embedded in the consistent tangent operator regarding the global system. The performance of the proposed formulation is assessed by three numerical examples involving large elastoplastic strains and ductile fracture. Results confirm that the present formulation is capable of reproducing fracture initiation and evolution, as well as necking instability. Convergence analysis is also performed to evaluate the effect of mesh refinement on the mechanical response. In addition, it is demonstrated that the nonlocal parameter alleviates damage localization, providing smoother porosity fields.

A Cam Clay constitutive relation for semi-analytical elasto-plastic modeling of wheel-soil interaction for fast applications

In this paper, a semi-analytical elasto-plastic (SAEP) model is proposed to simulate wheel motion on soft soil using a Modified Cam Clay (MCC) constitutive model. The focus is on enhancing computational efficiency by integrating the MCC model into the framework. The MCC-based model outperforms the Drucker-Prager with Cap hardening (DPC)-based model in terms of reduced computation time, stability, and convergence. Simulations with a 30% slip ratio show a significant reduction in solution time compared to the DPC-based model. For slip ratios of 50% and 90%, the computation time decreases even further. Overall, the MCC-based model demonstrates over 100 times reduction in the solution time compared to the DPC-based model, particularly with high slip ratios. Indeed, the DPC-based model was found to be highly sensitive to high values of slip ratios, whereas the MCC-based model is not. In comparison with existing methods in the literature, the proposed formulation is superior in terms of significantly reduced solution time and improved numerical stability, making it ideal for advanced applications where fast solutions are crucial.

Improving the roller screen efficiency to classify green iron pellets using DEM simulation, novel roll design and implementing banana configuration

Roller screens play a decisive character in the efficiency of pelletizing circuits and induration furnaces. Unlike vibrating screens, there have been no studies on roller screens to determine their capacity and dimensions. Most studies have utilized the discrete element method (DEM) simulation to assess roller screen performance by employing a spherical shape and the Hertz-Mindlin elastic model. However, this approach is unsuitable due to green pellets’ non-spherical shape and elastic–plastic properties. This study introduces the incorporation of the actual shape of green pellets and a hysteretic spring elastoplastic contact model. In this research work, a novel design of rolls with a grooved surface was recommended for the first time, resulting in a Total Screening Efficiency (TSE) of 96.4% compared to 87.1% for rolls with a smooth surface. Additionally, while exploring the impact of the decks number on the roller screen, a new design, known as the banana roller screen, was introduced. Under similar conditions, the TSE increased by 1.22% compared to the general roller screen type. It was also found that the roller screen’s capacity is directly related to the diameter, speed of rotation, and the number of rolls, while it has a reverse relationship with TSE and deck angle.

Investigation on the thermal deformation mechanisms and constitutive model of Ti-55511 titanium alloy

This study presents a comprehensive analysis of the hot deformation behavior of the Ti-55511 alloy over a temperature range of 700 °C to 950 °C and strain rates from 0.001 s⁻1 to 1 s⁻1, utilizing isothermal compression testing alongside electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). The investigation focuses on the influence of various hot deformation parameters on the microstructural evolution of distinct phase regions within the alloy. At higher strain rates (0.1 s⁻1 to 1 s⁻1), the primary softening mechanisms for β grains in the α+β two-phase region are identified as continuous dynamic recrystallization (CDRX) and dynamic recovery (DRV), while in the β single-phase region, discontinuous dynamic recrystallization (DDRX) and DRV predominate. Conversely, at lower strain rates (0.001 s⁻1 to 0.01 s⁻1), the softening of β grains in the two-phase region is primarily governed by DRV, whereas in the single-phase region, DDRX and CDRX are the dominant mechanisms. Additionally, based on stress-strain data corrected for friction and temperature effects, an elastoplastic constitutive model is developed, incorporating strain rate and temperature to predict peak stress in the two-phase regions of the Ti-55511 alloy. This examination of the thermal deformation behavior and microstructural evolution of the Ti-55511 alloy provides significant theoretical and practical insights for optimizing the manufacturing processes of aviation die forging, tailoring microstructures, and enhancing hot working techniques.

Evaluation of Wellbore Stability by Small Parameter Perturbation Nonlinear Elastoplastic Model

Abstract Wellbore instability is a frequent occurrence during drilling and a popular research topic among petroleum workers. Most of the previous studies simplified the hardening stage and ignored or classified it into the elastic stage. Engineering practice shows that the total stress–strain process of rock can more truly reflect the bearing and deformation characteristics of rock. This study establishes a total stress–strain constitutive model by combining the perturbation index equation with the linear elastic equation. Additionally, the physical model of rock around the well is presented using the total deformation theory for the plastic zone. The stress field of the rock surrounding the well is analyzed based on the physical model of the rock surrounding the well, taking into account the influence of rock strength and geostress state. The relationship between rock strength, geostress state, drilling fluid density, and plastic radius is given. The calculation method of drilling fluid density limit is also given. The practical application demonstrates that the stability of a borehole wall can be evaluated by analyzing the size and direction of the plastic radius, as well as the distribution of radial, tangential, and shear stress for various combinations of stress states and rock strengths. The maximum shear stress is always found in the softening zone, which is also the region where wellbore instability is most likely to happen. Therefore, the area within the softening radius is regarded as an unstable area, and the softening radius can be used to determine the range of wellbore instability.

A Closure Contact Model of Self-Affine Rough Surfaces Considering Small-, Meso-, and Large-Scale Stage Without Adhesive

Contact interface is essential for the dynamic response of the bolted structures. To accurately predict the dynamic characteristics of bolted joint structures, a fractal extension of the segmented scale model, i.e., the JK model, is proposed in this paper to comprehensively analyze the dynamic contact performance of engineering surfaces and revisit the multi-scale model based on the concept of asperities. The influence of asperity geometry, dimensionless material properties, and the elastic, elastoplastic, and full plastic mechanical models of a single asperity is established considering the asperity–substrate interaction. Then, a segmented scale contact model of rough surfaces is proposed based on the island distribution function in a strict sense. The mechanical contact process of determining rough surfaces is divided into small-scale, medium-scale, and large-scale stages. Moreover, cross-scale boundary conditions, i.e., al1′, al2′, and al3′, are provided through strict mathematical deduction. The results show that the real contact area and contact stiffness are positively correlated with fractal dimension and negatively correlated with fractal roughness. On a small scale, the contact damping decreases with an increase in load. In meso-scale and large-scale stages, the contact damping increases with the load. Finally, the reliability of the proposed model is verified by setting up three groups of modal vibration experiments.

Axial capacity of cold-formed steel channel sections with slits

Cold-formed steel (CFS) studs often include slits in their webs to improve thermal performance. However, the inclusion of such slits reduces their axial capacity. The literature contains limited experimental studies on the axial capacity of these studs with slits, and no non-linear elasto-plastic finite element studies have been reported. This research aims to address this gap. Non-linear elasto-plastic finite element models were developed and validated against experimental test results. A parametric study consisting of 960 finite element analysis (FEA) models was then conducted, covering the effects of different channel dimensions, slit sizes, section thicknesses, and stud lengths. Ultimate axial capacities obtained from these analyses were compared to the current codified direct strength method (DSM) predictions as per the Australian/New Zealand Standard AS/NZS 4600. Finally, design recommendations in the form of strength reduction factors are proposed. Based on these recommendations, modified DSM design equations with a reliability index above 2.5 are presented.

An elastoplastic beam bond model for DEM simulation of deformable materials and breakage behaviors

AbstractIn modern chemical engineering production, numerous elastoplastic materials, often formed into agglomerates, frequently undergo plastic deformation and rupture. Understanding how these materials behave under different conditions is crucial for improving manufacturing processes and material design. In this work, an elastoplastic beam bond model for discrete element method (DEM) simulation was developed, in which a yield criterion is introduced into Timoshenko beam bond method. The model can simulate not just the initial elastic (stretchy) behavior of the materials but also their plastic (permanent) deformation behaviors. The model was applied to central collision of two agglomerates, agglomerate uniaxial compression, and agglomerate‐wall impact cases. It is shown that the updated model could predict the behavior of materials that undergo permanent changes under stress, compared to previous models that only considered elastic behaviors. This could enable more accurate simulations of particulate materials and aid in better process design.

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

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

Determination of Dynamic Stresses and Displacements under the Action of an Impact Load on a Two-Layer Structure during the Indentation Process

Introduction. Numerous researchers of the reliability of building structures pay attention to hardness, an important characteristic of the structural material. It is determined by indentation — pressing the tip of the tool into the surface. The advantages of dynamic indentation methods and the distribution of stress intensity on the surface and inside the sample are investigated. However, the condition of layered materials on impact has been poorly studied. The objective of the presented work is to consider indentation for a two-layer sample and determine the sensitivity of the top layer to the strength of the substrate. This will allow us to identify significant characteristics of the strength properties of homogeneous and heterogeneous structures.Materials and Methods. An elastoplastic model of material behavior and a shock indentation scheme were used, which took into account the masses of the indenter and the striker coupled by linear springs. The surface of the indenter was conical, the opening angle was 120°. The impact was simulated in the MATLAB system. Finite element model in Ansys APDL was used to verify the data and analyze the results of the experiment. Traditional models of elasticity theory were used for calculations. The behavior of the material in the zone of plastic deformation was described using the options of multilinear isotropic hardening and the von Mises plasticity criterion.Results. The results of comparing three versions of varying the level of yield strength in the bottom layer are presented: when the yield strength in the bottom layer is half as high as the top one, equal to it, and twice as high. Displacements at different observation points for samples with a top layer of 2 mm and 1 mm were analyzed. In the first case, under horizontal shear, the displacement indices inside the sample did not change if the yield strength level was twice lower or higher than in the top one. If these indicators were equal, the difference became noticeable. In the second case (layer 1 mm), the difference in displacement was visible at all observation points. Thus, it can be reasonably concluded that a structure with a smaller top layer is more sensitive to impact. In the course of the research, it became known that vibrations associated with the transition to the plasticity zone occurred in the 2 mm zone, and elastic damping vibrations occurred below this zone. We solved the classification problem for the top layer of the material with changing characteristics of the base. The indicator for comparison was the Brinell hardness (HB) in the range of 200–600. The results were processed using a neural network and visualized in the form of graphs. The accuracy of its calculations was 98%.Discussion and Conclusion. To determine the strength properties of homogeneous structures, it is sufficient to characterize the speed of displacement inside the sample. For an inhomogeneous structure, additional parameters should be introduced — displacements on the surface and inside the sample at fixed observation points. An integrated approach to determining the strength properties of an inhomogeneous structure improves the accuracy of calculations, and the use of neural networks increases their speed.

Novel integration of PSO-enhanced damage mechanics and finite element method for predicting medium–low-cycle fatigue life in perforated structures

In this research, we introduce an innovative approach that combines the Continuum Damage Mechanics-Finite Element Method (CDM-FEM) with the Particle Swarm Optimization (PSO)-based technique, to predict the Medium-Low-Cycle Fatigue (MLCF) life of perforated structures. First, fatigue tests are carried out on three center-perforated structures, aiming to assess their fatigue life under various strengthening conditions. These tests reveal significant variations in fatigue life, accompanied by an examination of crack initiation through the analysis of fatigue fracture surfaces. Second, an innovative fatigue life prediction methodology is applied to perforated structures, which not only forecasts the initiation of fatigue cracks but also traces the progression of damage within these structures. It leverages an elastoplastic constitutive model integrated with damage and a damage evolution model under cyclic loads. The accuracy of this approach is validated by comparison with test results, falling within the three times error band. Finally, we explore the impact of various strengthening techniques, including cross-sectional reinforcement and cold expansion, on the fatigue life and damage evolution of these structures. This is achieved through an in-depth comparative analysis of both experimental data and computational predictions, which provides valuable insights into the behavior of perforated structures under fatigue conditions in practical applications.

Evaluating the impact of rail surface roughness post-grinding: An experimental and elastoplastic modelling approach

Grinding is regularly conducted on railway tracks to prevent crack propagation and surface deterioration. However, grinding can introduce roughness on rail surfaces, potentially leading to stress and strain concentration that increase the likelihood of crack initiation. This paper proposes the utilization of surface roughness obtained by replicating the ground rail surface to assess its impact on train wheel-rail interactions. A novel approach which integrates the replicated roughness into an elastoplastic contact model, allows for a detailed assessment of its effects on contact pressure, and residual strain and stress distributions. The findings highlight the importance of considering surface roughness in predictive maintenance planning for railway infrastructure, as it can significantly influence the structural integrity and long-term performance of the track system.

Enhanced Cyclically Stable Plasticity Model for Multiaxial Behaviour of Magnesium Alloy AZ31 under Low-Cycle Fatigue Conditions.

Magnesium alloys, particularly AZ31, are promising materials for the modern automotive industry, offering significant weight savings and environmental benefits. This research focuses on the challenges associated with accurate modelling of multiaxial cyclic plasticity at small strains of AZ31 under low-cycle fatigue conditions. Current modelling approaches, including crystal plasticity and phenomenological plasticity, have been extensively explored. However, the existing models reach their limits when it comes to capturing the complexity of cyclic plasticity in magnesium alloys, especially under multiaxial loading conditions. To address this gap, a cyclically stable elastoplastic model is proposed that integrates elements from existing models with an enhanced algorithm for updating stresses and hardening parameters, using the hyperbolic tangent function to describe hardening and ensure a stabilised response with closed hysteresis loops for both uniaxial and multiaxial loading. The model is based on a von Mises yield surface and includes a kinematic hardening rule that promises a stable simulation of the response of AZ31 sheets under cyclic loading. Using experimental data from previous studies on AZ31 sheets, the proposed model is optimised and validated. The model shows promising capabilities in simulating the response of AZ31 sheet metal under different loading conditions. It has significant potential to improve the accuracy of fatigue simulations, especially in the context of automotive applications.

Numerical investigation on effects of blast loading on anti-fragment performance of hollow cylindrical UHMWPE cross-ply laminate

Ultra-high-molecular-weight polyethylene (UHMWPE) fiber composites are widely applied for bullet and explosion proofing. This study numerically investigated the dynamic response of a hollow cylindrical UHMWPE cross-ply laminate subjected to combined blast and fragment loading produced by an improvised explosive device (IED). A strain-rate-dependent, anisotropic, elastoplastic constitutive model with progressive failure was adopted for the laminates via a user subroutine and comprehensively verified against the experimental results from the literature. Three sets of simulations of fragment-only loading, blast-only loading and the combined loading were performed on different configurations of IEDs and laminates. It was found that the effects of the blast loading were much weaker than those of the fragment loading and caused very small deformation of the laminate’s middle, including somewhat pre-tension along the circumferential direction but almost no fiber fracture. Both with and without blast loading, the dense penetrations of the multiple fragments dominated the response of laminates, including perforated holes that were interconnected with each other and global ply splitting. As a result, the blast effects barely affected the anti-fragment performance of the laminates.

Research on the Gap Effect of Circular Concrete-Filled Steel Tubes Using the Improved Cohesive Zone Model

Understanding the influence of gap distribution characteristics on the mechanical properties of circular concrete-filled steel tubes (CCFSTs) under bending load is important for stability and support design in engineering projects. In this study, the improved cohesive zone model considering friction was used to describe the mechanical behavior of mortar interfaces. Meanwhile, the concrete damage plastic model and isotropic elastoplastic model were applied for core concrete and steel tubes. The improved cohesive zone model has a unified potential function that governs the Mode I and Mode II failure processes of mortar interfaces to realize the mechanical interaction between concrete and steel. A smooth frictional function was utilized in the elastic stage to calculate the accurate frictional effect. Furthermore, the capability of the model in addressing unloading and reloading was verified, and the fracture energy varied accordingly during the cyclic loading. Then, the mechanical response of CCFSTs was investigated under bending loads by setting different gap sizes and angles between the gap and loading direction. The results show that under three-point bending, the equivalent plastic strains at the middle part of CCFSTs are much larger and the peak bearing forces are much lower than the other degrees when the angles between the coronal gap axis and loading direction equal 0° and 180°. In addition, the order of the peak bearing forces, from highest to lowest, is when the height of the coronal-cap gap increases from 0.0 mm to 2.5 mm, 5.0 mm, and 7.5 mm. The significant effect makes it inappropriate to ignore the weakening of the structural performance caused by coronal gaps in structural design.

Phase-field finite element modelling of creep crack growth in martensitic steels

Creep fracture presents a major concern for structural materials and critical components operating at elevated temperatures, thus requiring effective computational models. This study presents a phase-field framework for modelling creep crack growth and fracture behaviour of modern high-temperature materials such as Creep Strength Enhanced Ferritic (CSEF) martensitic steels. The model was formulated using the thermodynamic principles of the variational phase field theory of fracture and considering some physical aspects of creep fracture. Within the modelling framework, a dissipation potential dependent on creep damage is introduced to capture the effect of creep cavitation on the fracture energy and the creep crack growth resistance of the solid in a phenomenological manner. An elastoplastic power-law creep model is coupled to the phase-field formulations to account for the non-linear deformation processes ahead of the crack tip due to inelastic deformations, as well as their contribution to fracture at high temperatures. The capability of the proposed model is assessed against experimental data from compact tension (CT) creep tests conducted on P91 and P92 steels. Good agreement was obtained between the FE-predicted creep crack growth behaviour and the experimental measurements, showcasing the model’s feasibility. Further, numerical experiments were conducted using the proposed model to elucidate some key aspects influencing the fracture behaviour of martensitic steels. The proposed computational framework not only demonstrated good capability but was also able to offer improved mechanistic insights into the influence of material tendency to develop creep cavities on crack growth behaviour. This work contributes valuable insights into understanding the fracture process of CSEF steels at elevated temperatures and further demystifies the role of creep ductility.

A modified cyclic elastoplastic constitutive model considering the variational dynamic recovery term of back stress for FGH95 under asymmetrical cyclic loading

The asymmetric cyclic loading process occurs in aero-engine turbine discs. A constitutive model that accurately describes the cyclic elastoplastic behaviour of the material is important for structural design and low cycle fatigue life prediction of turbine discs. In this paper, the low cycle fatigue test of FGH95 was carried out at 620℃ under 0.5%, 0.6%, 0.7%, 0.8%, 0.9%, 1.0% and 1.1% strain amplitude with strain ratio equal to 0. The material exhibited cyclic hardening followed by cyclic softening at high strain amplitudes and cyclic softening at low strain amplitudes. The mean stress relaxation rate was similar for each strain amplitude. In addition, the evolution of effective stress and back stress was obtained through the method of internal stress division. Then, the relationship between the change in stress amplitude and the change in internal stress was discussed. The results showed that with cyclic loading, cyclic hardening/softening of FGH95 was affected by the competition mechanism of back and effective stresses. Considering that slip deformation and crystal lattice rotation coexist in plastic deformation, the dynamic recovery term of the Abdel-Karim and Ohno model was used. In order to characterize the different magnitudes of back stress change in materials at different plastic strain intervals, a dynamic recovery term coefficient was introduced to the dynamic recovery term and the critical surface of the back stress. The modified model was used to compare with experimental results. Then, it gives a good description of the material’s mean stress relaxation and strain amplitude variation and gives good agreement on the hysteresis loop.

A “poor-man’s” deformation plasticity based approach to topology optimization of elastoplastic structures

This paper presents a topology optimization framework utilizing a deformation plasticity model to approximate the isotropic hardening von-Mises incremental elastoplasticity model under monotone proportional loading. One advantage of the model is that it is based on a yield surface allowing for precise matching to uniaxial elastoplastic isotropic hardening response. The deformation plasticity model and the incremental plasticity model coincides for proportional loading and since the deformation plasticity model is path-independent, the computational cost and implementation complexity reduce significantly compared to the conventional incremental elastoplasticity. To investigate the deformation plasticity model combined with topology optimization, we compare three common elastoplastic optimization objectives: stiffness, strain energy and plastic work. The possibility to limit the peak local plastic work while maximizing the strain energy is also investigated. The consistent analytical sensitivity analysis which only requires the terminal state is derived using adjoint method. Numerical examples demonstrate that the proportionality assumption is reasonable and the deformation plasticity model combined with topology optimization is a competitive alternative to cumbersome incremental elastoplasticity.

Development and experimental verification of an advanced 3D elastoplastic progressive damage model for composite materials

This study develops a sophisticated three-dimensional elastoplastic progressive damage finite element analysis (FEA) model for stiffened composite materials under axial compression. The model integrates the Hashin and Ye criteria to capture the inception of damage within the composite and introduces a cohesive zone model (CZM) to simulate debonding between stiffeners and panels. Furthermore, damage evolution based on energy release rate and plastic flow rules grounded in Hill’s criteria are employed to thoroughly explore the progressive failure behavior of stiffened composite materials. Implemented within Abaqus/Explicit through user-defined ‘VUMAT’ subroutines, the model ensures computational accuracy and reliability. Comparative evaluations against standard linear elastic progressive damage models demonstrate a statistically significant improvement of at least 5% in predicting ultimate load capacities. Additionally, this model accurately captures different failure modes, providing a nuanced understanding of stiffened composite material failure under compressive loads.