Elastic-plastic Material Model Research Articles

Description of the constitutive behaviour of stainless steel reinforcement

This paper presents a comprehensive analysis of the constitutive relationship of stainless steel reinforcement and proposes new material models for both austenitic and duplex stainless steel bars. These are an advancement on existing models which have largely been developed for structural stainless steel plate, rather than for reinforcement bars. Current design guidance for material modelling of reinforcing bars does not include representative stress-strain relationships which capture the unique mechanical properties of stainless steel reinforcement. Codes include idealised elastic-plastic material models which are inappropriate and inefficient for the highly nonlinear and ductile material response of stainless steel. The present study aims to address this issue by first conducting a series of tensile tests to ascertain the stress-strain material responses and then employing this data to examine the validity of existing approaches and propose new material models where required. It is shown that new material models are required and those that are developed are able to accurately capture the stress-strain response of stainless steel reinforcement, and provide a better, more accurate, representation than existing methods.

Numerical parameter sensitivity analysis of residual stresses induced by deep rolling for a 34CrNiMo6 steel railway axle

To optimise the benefits of the deep-rolling process in the service life context of treated components, the process application must be investigated. In addition to the reduction in surface roughness and near-surface material strengthening, compressive residual stresses are introduced, which are primarily responsible for the increase in service life for components, especially in the case of high-strength steel materials. A numerical parameter sensitivity analysis is performed in order to investigate the introduced residual stresses in detail. For this purpose, a validated deep-rolling simulation model is used, which replicates the deep rolling of a railway axle made of the high-strength steel material 34CrNiMo6. The model is based on an elastic-plastic Chaboche material model parameterised on uniaxial tensile and LCF test results and validated with residual stress measurements. Using this model as a basis, the effect of the main process parameters deep-rolling force, feed rate, friction coefficient, number of overruns, tool geometry, and shaft geometry on the resulting residual stress state are investigated. The results reveal that the deep-rolling force has the most significant influence on the introduced residual stress state and should therefore be highlighted. In the case of applying a deep-rolling force of more than 10 kN, maximum compressive residual stresses of around − 1000 MPa are introduced, and a strong saturating behaviour is shown. Maximum compensating tensile residual stresses of + 100 MPa occur below the surface. The main influence of the deep-rolling force is the effective depth achieved, which is determined by the depth of the zero crossing. This varies from 1 mm with an applied force of 2 kN to more than 3.5 mm with 20 kN. Furthermore, the results are analysed to conclude suggestions for the process’s applicability, and a proposal for an optimised deep-rolling treatment is presented. There multiple deep rolling with decreased deep-rolling forces is used to achieve a comparably optimised residual stress state. In summary, with the presented results, a contribution to a deeper understanding of the deep-rolling process can be achieved; the influence of the most important process parameters on the residual stress in-depth profiles is established; an optimisation proposal is presented; and correlations are found. Thus, the base work for further fatigue strength assessments and the optimisation of the deep-rolling process regarding the increase of service is laid.

NUMERICAL INVESTIGATION OF THE INFLUENCE OF THE LINK POSITIONING IN THE CORONARY STENT INSIDE THE NORMAL ARTERY: A COMPARATIVE STUDY OF TWO COMMERCIAL STENT DESIGNS

This paper investigates the performance of two commercial stent designs inside the normal artery for induced Von Mises Stress and radial displacement pattern. Investigation focuses on identifying the key design feature of the stent structure responsible for varied stress and displacement pattern. Two commercial stent designs, Supraflex (Stent S) and Yukon Choice (Stent T),are modeled using micro CT images and MIMICS® while idealized models are used for investigation. ANSYS Workbench is used to numerically expand the stent inside an idealized normal artery with inflation pressure. The stent and the artery are modeled using elastic-plastic and hyperelastic material models, respectively. The results suggest crucial influence of the link positioning in inducing an area of higher Von Mises Stress and stress gradient. The locations of a higher stress gradient are those in line with unbound stent crowns. Also, higher and uniform arterial displacement can be observed in the locations in line with the bound crown. Results also suggested a considerable difference in arterial distortion induced by two designs, causes for which can also be attributed to the differences in the link placement. The study suggests that the link connections play a crucial role in setting up stress field/radial displacement. Suitable modification of the link positioning can reduce the higher stress gradient and arterial distortion, which probably can reduce arterial injury.

SIMULATION OF ELASTOPLASTIC FRACTURE OF A CENTER CRACKED PLATE

The strength of a square plate with a central crack at normal separation was studied within the framework of the Neuber–Novozhilov approach using a modified Leonov–Panasyuk–Dugdale model using an additional parameter, the diameter of the plasticity zone (width of the pre-fracture zone). As a model of a deformable solid body, a model of an ideal elastic-plastic material with a limiting relative elongation was chosen. This class of materials includes, for example, low-alloy steels used in structures operating at temperatures below the cold brittleness threshold. In the presence of a singular feature in the stress field in the vicinity of the crack tip, it is proposed to use a two-parameter discrete integral strength criterion. The deformation fracture criterion is formulated at the tip of a real crack, and the force criterion for normal stresses, taking into account averaging, is formulated at the tip of a model crack. The lengths of real and model cracks differ by the length of the pre-fracture zone. The constitutive equations of the analytical model are analyzed in detail depending on the characteristic linear dimension of the material structure. Simple formulas suitable for verification calculations for the critical breaking load and the length of the pre-fracture zone are obtained. Numerical modeling of the propagation of plasticity zones in square plates under quasi-static loading has been performed. In the numerical model, the updated Lagrangian formulation of the equations of mechanics of a deformable solid body is used, which is most preferable for modeling the deformation of bodies made of an elastic-plastic material at large deformation. The plastic zone in the vicinity of the crack tip is obtained by the finite element method. The results of analytical and numerical prediction of plate fracture under plane deformation are compared. It is shown that the results of numerical experiments are in good agreement with the results of calculations using the analytical model of fracture of materials with a structure under normal separation. Diagrams of quasi-brittle and quasi-ductile fracture of a structured plate are constructed.

The elasto-plastic numerical study of crack initiation in notched PMMA specimens under uniaxial loading conditions – Tension and torsion

This paper presents the results of FEM numerical calculations aimed at describing the plastic strain and stress fields under critical loading conditions: tensile force or torsional moment. The calculations were carried out with reference to the results of experimental tensile and torsional tests of flat PMMA specimens weakened with V-notches of different root radii: 0.5, 2 and 10 mm. The procedure for conducting nonlinear numerical analyses is described, including the determination of the actual hardening curve by the hybrid method. A high level of consistency between the results of the experimental and numerical calculations was obtained through description of PMMA with the elastic–plastic material model. The points of occurrence of stress maxima and plastic strain were indicated, which were taken as potential crack initiation sites. On the basis of the stress and plastic strain values measured at the critical points, a stress–strain fracture criterion was formulated, which was then positively verified.

Finite element analysis of ball burnishing: evolution of residual stresses and surface profile in Ti-6Al-7Nb alloy

In the present study, the effect of feed on the residual stress distribution and surface profile generated during the ball burnishing of titanium alloy (Ti-6Al-7Nb) was investigated using finite element simulation. The elastic-plastic material model with isotropic hardening was used for performing the simulations. The created finite element model containing a rigid ball and deformable specimen was optimized and validated using experimental data. It was observed that the effect of burnishing feed is significant on the surface profile compared to residual stresses. The maximum residual stress obtained during the simulation of the process was achieved for the burnishing feed of 0.2 mm. This confirmed the variation of residual stress when the burnishing feed is varied. Whereas the surface roughness was the least for the 0.05 mm burnishing feed which was due to uniform deformation of the surface during the process.

Comparative performance evaluation of microarchitected lattices processed via SLS, MJ, and DLP 3D printing methods: Experimental investigation and modelling

Additively manufactured mechanical metamaterials are gaining prominence in lightweight energy-absorption applications due to their exceptional mass-specific properties. Herein, we examine the energy absorption characteristics of micro-architected truss-, shell- and plate-lattice structures, namely, Octet, Kelvin, Gyroid, SC, BCC and FCC over a range of relative densities under quasi-static compression via both experiments and finite element analysis (FEA). Employing different 3D printing methods, namely, Digital Light Processing, Selective Laser Sintering and Material Jetting, the lattices were fabricated using PlasGray™ (photo-resin based plastic), PA12 (Nylon) and VeroWhite (photo-resin based rigid plastic) respectively. Our results indicate that the SC lattice structure outperforms in terms of stiffness and strength, while the Gyroid lattice outperforms in terms of energy absorption efficiency (η). At lower relative densities (<0.3), η reaches up to 61% for the Gyroid lattices made of PlasGray, while only at high relative densities the Octet truss lattices compete with the Gyroid lattices. For Gyroid lattices made of PA12 with a relative density of 0.23, an energy absorption efficiency of 68% was observed. Design maps are presented for all lattice structures processed and tested herein, to demonstrate their relative merits. Moreover, a two-step FEA was executed on a chosen array of lattices to thoroughly investigate the extensive design possibilities, utilising the elastic-plastic, Drucker-Prager, and concrete damage plasticity material models for PlasGray, PA12, and VeroWhite, respectively, with calibration based on experimental results. The results highlight that the tailored design of Gyroid lattices enabled by AM positions them as promising candidates for lightweight energy-absorbing applications.

Identification of temperature-dependent parameters for an elastic–plastic-damage material model of 3D-printed PETG

The presented paper focuses on identifying temperature-dependent parameters for a newly designed material model of 3D-printed PETG (polyethylene terephthalate glycol). An uniaxial elastic–plastic material model with damage and different properties in tension and compression was developed to describe this material’s non-linear behaviour. The monotonic and cyclic tests were carried out in tension and compression at several temperatures. The specimens were printed using FDM (fused deposition modelling) technology on the printer from Prusa Research. The principal material parameters such as Young’s modulus, yield stress and ultimate tensile stress were derived directly from the force–displacement diagrams obtained experimentally. Other necessary material characteristics were identified using numerical simulations combining the finite element method and parametric optimization. The model was implemented for the software Abaqus using subroutine UMAT and the optimization was performed using software Isight.

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.

Structural behaviour of point-by-point wire arc additively manufactured steel bars under compressive loading

Wire arc additive manufacturing combined with optimization tools for computational design shows a big potential with respect to the current efforts in the architecture, engineering, and construction industry of reducing the consumption of materials by using them more efficiently. These technologies allow to design and fabricate steel components, connections, and structures with material deposited only were structurally necessary. The findings presented in this paper focus on wire arc additively manufactured bars, robotically printed by point-by-point deposition and subjected to compressive loading. Such elements can be used for realizing stand-alone components or connections between existing parts, either alone or in combination with continuous deposition, and are generally susceptible to flexural buckling due to their slenderness. The influence on the flexural buckling behaviour of aspects like printing directions, slenderness, and support conditions was investigated by experiments and finite element simulations. In addition, the irregular geometry of the wire arc additively manufactured bars was evaluated based on three-dimensional scans, the identified characteristics were correlated with the flexural buckling results, and the relevance of the irregular surface geometry in predictive buckling simulations was assessed. The experiments showed consistent results indicating that such bars could be produced in a reliable and repeatable manner. The conducted simulations with the scanned geometry and an elastic-plastic material model allowed for an overall satisfactory prediction of the flexural buckling resistance. With regard to future design approaches, it was shown that the existing buckling curve for solid sections is suitable for point-by-point wire arc additively manufactured nearly straight bars and simulations with a constant equivalent diameter can be used for predicting the flexural buckling resistance if a rather low equivalent geometric imperfection is assumed.

Developing Elastic–Plastic Material Models for Pressure Measurement Films in a Steel–Steel Contact for Smooth and Rough Surfaces

AbstractThe contact zone between two steel components can be identified by utilizing a pressure measurement film in the contact between them. To reduce the number of necessary experiments, it is possible to simulate the contact situation using “finite element analysis.” This analysis requires material models for the contact partners and for the pressure measurement films. It is known that the pressure measurement film deforms not only elastically but also plastically. Taking this plastic deformation into account requires an appropriate material model such as the Drucker–Prager model. Based on published data of experiments with pressure measurement films that had been inserted between smooth and rough Hertzian bodies, we developed material models for three pressure measurement films. The roughness of a Hertzian body was studied by determining multiple pressure–clearance curves for three different surface roughnesses and for three different pressure measurement films. These curves were developed with micromodels, which represented a small section of the rough contact surface. An average curve for each material was then implemented in the macromodel for each roughness representing the contact situation. Subsequently, the resulting contact areas were compared with the published experimental data. This comparison showed that the material model for the smooth contact was able to emulate the experimentally determined contact areas. Including the pressure–clearance curves in the material model allowed the simulation of the rough contact situation. However, the deviation between the simulated and the experimental data was slightly larger for the rough surface than for the smooth surface.

Computational and experimental study of longitudinal stability of the thin-walled flat bar structure

The paper studies longitudinal stability of the centrally compressed flexible flat bars using computational and experimental methods. Calculations were carried out according to the dynamic analysis methodology in the LS-DYNA software package. This methodology is based on three determining factors, i. e. volume, technological deviations and real-time mode. When constructing a hinged bar model, 3D finite elements, elastic-plastic material model, asymmetrical cuts of small volumes simulating geometric technological deviations were used. Critical forces determined by the methodology were compared with the Euler forces and with the experimental data. The experiment was carried out on bars with pointed ends, which were abutted against the angular technological equipment and provided with free rotation of the bar ends. As a result of the computational and experimental study of the flexible bars stability, it was established that in real bar designs there appeared initial shape imperfections noticeably affecting the critical forces magnitude, and the more flexible the bar was, the stronger this effect was. Quantitative relationship was also found between the experimentally measured critical forces and those calculated by the methodology and by the Euler formula. The issues of the origin of initial form imperfections in real bars were touched upon. Three possible directions for searching for a solution to the problem of bar stability using the methodology of dynamic analysis are shown depending on the method of introducing technological deviations into the structure calculation scheme. Diagrams of the hinged flat bars deformation during compression tests are provided.

Cross-section behaviour of cold-formed high strength steel irregular hexagonal hollow section stub columns under combined compression and bending

Cross-section behaviour for cold-formed high strength steel (HSS) irregular hexagonal hollow section (IHexHS) stub columns under combined compression and bending is studied and presented in this paper. Finite element models were developed and validated using the existing experimental data collated from the previous research. Upon the validated finite element models, extensive parametric studies were subsequently carried out to generate more numerical data covering a wider range of cross-section dimensions, steel grades and load combinations from pure compression to pure bending. The obtained numerical results were utilised to assess the accuracy and the applicability of the current design codes, such as Eurocode of EN 1993-1-12 (EC3) and the North American code of ANSI/AISC 360-16 (AISC) for cold-formed HSS IHexHS stub columns under combined loading. It was demonstrated that the existing design codes can be safely applied and can be extended for cold-formed HSS IHexHS stub columns design under combined loading. In cross-sectional resistance predictions, conservative results were provided from the existing design codes. The over-predictions were primarily due to the neglect of the strain hardening and plate element interaction. The end points used in the interaction curves of EC3 and AISC adopt an idealised elastic-plastic material model to derive the corresponding resistance in cross-sectional level. The employment of Continuous Strength Method (CSM) leads to improved accuracy in cross-sectional resistance prediction with updated end points in the interaction curve. More consistent and reliable predictions were revealed by carrying out reliability analysis in accordance with EN 1990.

Global stiffness and residual stresses in spinal fixator systems: A validated finite element study on the interconnection mechanism

Posterior spinal fixation systems are the gold standard to treat different column disorders using rods and screws. The proper connection between them is guaranteed by the Interconnection Mechanism (IM), consisting of different metallic subcomponents held together through the application of tightening torque. The response of the fixation system is defined by its overall stiffness, which in turn is governed by the local residual stress field arising during tightening. Although literature computational models for studying spinal fixation are becoming increasingly anatomically complex, most studies disregard completely the realistic modeling of the IM, namely choosing elastic-plastic material models and proper contact interactions. In this frame, the present study aims at increasing awareness in the field of spinal fixation modeling by investigating the mechanical response of the IM in terms of overall stiffness and local residual stresses. Once validated through dedicated experiments, the results of the proposed model have been compared with the current literature, highlighting the key role of the IM in the reliable modeling of spinal fixation.

Evaluation of a nonlinear viscoelastic-plastic constitutive model in numerical simulation of thermoplastic polymers for stent application

Abstract To simulate the specific material properties of thermoplastic polymers a suitable constitutive model is essential. The parallel rheological framework (PRF) model was calibrated and evaluated in this study as potential constitutive model for polymer stent application. Tensile as well as recovery tests with different loading rates were performed using PLLA specimens. In order to calibrate the constitutive model, the conducted material tests were simulated accordingly. The parameters of the model were iteratively varied to obtain good accordance of the simulation with the material tests. In contrast to elastic plastic material models, viscoelastic material behavior can be represented with the nonlinear viscoelastic-plastic PRF model. The generated and possibly further refined model can be used for the simulation of polymer stents.

Modeling of soil–rock mixture landslides with the generalized interpolation material point method

The new numerical model for studying the dynamic evolution of soil–rock mixture landslides is presented in this article. The numerical model based on the generalized interpolation material point method analyzes a simplified slope. The gravity is linearly loaded, and the linear elastic model is used to update the stress to obtain the initial state of the slope. A small soil cohesion is set to trigger the slope sliding until the equilibrium state is reached again. During this period, the elastic–plastic material model based on the Drucker–Prager criterion is adopted for soil and stones. The differences in dynamic evolution between the homogeneous soil slope and soil–rock mixture slope are studied. Under the same stone content, the influence of the size and shape of stone on the dynamic evolution of slope is studied.

NUMERICAL ANALYSIS OF BFRP REINFORCED CONCRETE SLAB EXPOSED TO IMPACT LOADS

This paper describes advanced numerical analysis of a simply supported reinforced concrete slab exposed to close range explosion of a TNT charge. Finite element method (FEM) has been utilized in order to conduct the analysis. Non-linear material model for concrete slab is adopted. Reinforcing bars made of basalt fibre reinforced plastic (BFRP) are considered by elastic-plastic material model. 3D numerical model has been created, and a software with explicit solver (LS-Dyna) has been used in order to conduct analyses. A simplified modelling method of the blast loading has been utilized, which is based on the consideration of the load effects as a time dependent pressure. Several cases with different mesh size or different finite element formulation are investigated. The results are compared with experimental data based on study of fellow researchers. Match between the numerical analyses and measurements is discussed and considered as satisfying.

Finite element analysis of ball burnishing for large flat surface: Comparisons between experimental and numerical results

A three-dimensional (3D) finite-element (FE) based-model is developed for ball-burnishing in which an elastic–plastic material model is anticipated in the FE analysis framework. The model is used for better analysis of the experimental results when processing large flat surfaces and provides insights into the optimization of burnishing parameters. In this study, normal preload of 300 N, applied to the ball, is kept constant during the simulation. This case obtained in a previous work, was the optimal value which yielding a best surface quality of AISI 1010 steel plates. The numerical simulation results (residual stresses, plastic strain) will be extracted when the tool penetration will be stable, and a homogeneous treated area will be formed. Under the same ball burnishing conditions, the distributions of residual stresses (in feed direction and in cross-feed direction) from 3D simulations will be shown and compared with X-ray findings. In addition, the effect of number of passes on the finite element results has been studied. It is shown that a second pass of the ball on the burnished surface increases considerably these stresses and the strain in the surface layer. Preliminary results obtained from the confrontation of the distribution of residual stresses induced by mechanical treatment of AISI 1010 steel plates indicate good agreement between the experimental and FE results.

Mesoscale analysis of Fiber-Reinforced concrete beams

Unlike traditionalconcrete,steel fiber reinforcementimproves durability and crack control. The current work developed an extensive numerical study, using a three-dimensional mesoscale model, to investigate the effect of steel fibers on the mechanical properties of steel fiber-reinforced concrete (SFRC) beams. The proposed model was developed using the numerical computing environment MATLAB. Concrete was simulated using solid elements with a damaged plasticity model. The steel fibers were randomly located and modeled by truss elements with an elastic–plastic material model, while the interface was represented by springs connecting the nodes of the concrete and steel fiber elements. Traction separation model behavior was assumed for the springs at the direction tangent to the fibers’ major axis and elastic with high stiffness in the normal directions. The proposed model was validated using experimental results with different fiber ratios. Moreover, a parametric study was conducted to investigate the effect of steel fiber ratios and orientations as well as the effect of the beam size. Good agreement with differences of 3%−5% at the peak loads and 3%−18% at the post-peak loads were obtained. The orientation of the steel fibers had a big effect on the behavior of the SFRC beams. A 73% increase in the peak load of the SFRC beams with aligned fibers in the flexural direction was obtained relative to the random alignments. Whereas the beams with steel fibers aligned in different directions showed unchanged behavior and strength. The beams with smaller sizes experienced higher variation between realizations and higher peak stresses than those with larger sizes for all fiber ratios. A clear size effect of type II in peak stresses was obtained for beams with different fiber ratios.

Additively manufactured AlSi10Mg lattices – Potential and limits of modelling as-designed structures

Additive manufacturing overcomes the restrictions of classical manufacturing methods and enables the production of near-net-shaped, complex geometries. In that context, lattice structures are of high interest due to their superior weight reduction potential. AlSi10Mg is a well-known alloy for additive manufacturing and well suited for such applications due to its high strength to material density ratio. It has been selected in this study for producing bulk material and complex geometries of a strut-based lattice type (rhombic dodecahedron). A detailed characterisation of as-built and heat-treated specimens has been conducted including microstructural analyses, identification of imperfections and rigorous mechanical testing under different load conditions. An isotropic elastic–plastic material model is deduced on the basis of tension test results of bulk material test specimens. Performed experiments under compression, shear, torsion and tension load are compared to their virtual equivalents. With the help of numerical modelling, the overall structural behaviour was simulated using the detailed lattice geometry and was successfully predicted by the presented numerical models. The discussion of the limits of this approach aims to evaluate the potential of the numerical assessment in the modelling of the properties for novel lightweight structures.