Elasto-plastic Material Properties Research Articles

An algorithm based on B-differentiable equations method for solving problems involving frictional contact coupled with concrete plastic damage

In this paper, an algorithm is proposed to solve the frictional contact problems while considering elasto-plastic material properties. The static and dynamic solution procedures are derived in incremental form, respectively. The proposed method employs a two-layer iteration strategy. In the outer iteration layer, the equilibrium equations are solved, with the stress and stiffness matrix updated at each iteration. Within the inner iteration layer, the contact force is calculated, where the contact equations, expressed as B-differentiable equations, incorporate only contact conditions in normal and tangential directions, and the contact flexibility matrix, obtained by applying unit force pair to all contact node pairs in turn, is introduced. Consequently, the solution for nonlinear equilibrium equations and contact equations is decoupled, requiring only one decomposition of the stiffness matrix for each calculation of the contact flexibility matrix, as it remains constant within the contact iteration layer. In addition, the constitutive model of concrete developed by Lee and Fenves is utilized. This model adopts two independent variables to describe tensile and compressive damage, together considering the strength recovery of the concrete. Numerical examples demonstrate the accuracy of the proposed method by comparing the results from Abaqus. Furthermore, the present algorithm is applied to static and dynamic analyses of a concrete arch dam with several transverse joints, where the effects of gravity, water level, the number of contact surfaces, and seismic load are considered, and some conclusions are obtained.

Plastic collapse behavior of plate to CHS connection under biaxially symmetric load

This study investigates the plastic collapse behavior of a non-diaphragm type connection with flange plates connected to a circular hollow section (CHS) column, where four flanges were joined from two orthogonal directions. The analysis was conducted using the finite element method (FEM). The focus was on determining the collapse load of the flange joint under a biaxially symmetric load from the four flanges. In an initial numerical analysis, the fundamental collapse behavior of the cylindrical wall was explored. Finite element models of CHS tubes with perfectly elasto-plastic material properties were employed. The analysis revealed that the plastic collapse mechanism of the cylindrical wall was influenced by the axial force in the transverse flanges. Prediction equations for the collapse load of the joint were formulated, assuming four representative collapse mechanisms and employing the principle of virtual work based on the numerical analysis results. Additionally, the ultimate strength of the joint, determined by the plastic collapse of the cylindrical wall, was computed using finite element models of CHS tubes with realistic hardening properties. A comparison between predictions from the equations based on perfectly elasto-plastic CHS tubes and numerical solutions through finite element analysis (FEA) of CHS tubes with realistic hardening properties validates the accuracy of the proposed prediction equations, even when applied to realistic steel tubes.

M-Voronoi and other random open and closed-cell elasto-plastic cellular materials: Geometry generation and numerical study at small and large strains

The present study deals with a numerical design strategy of a novel class of three-dimensional random Voronoi-type geometries, called M-Voronoi. These materials comprise random, non-quadratic convex void shapes and non-uniform intervoid ligament thicknesses, and can span high-to-low relative densities. The starting point for their generation is a random adsorption algorithm (RSA) construction with spherical voids embedded in an incompressible, nonlinear elastic matrix phase. The initial RSA geometry is subjected to large elastic volume changes by prescribing Dirichlet boundary conditions. Due to the incompressibility of the matrix phase, the externally imposed volume changes lead to significant void growth. The numerical growth process may be stopped at any desired porosity. The proposed M-Voronoi process is general and allows the formation of isotropic (or anisotropic) designs. As a byproduct of the developed approach, we also present a novel remeshing technique allowing to read arbitrary geometries of one or multiple phases. The elasto-plastic properties of the M-Voronoi porous materials are numerically investigated at small strains as well as large compressive and shear loads. Their response is assessed by comparison with other well-known random and periodic porous geometries such as polydisperse porous materials with spherical voids (RSA), classical TPMS Gyroid geometries and random Spinodoid topologies. The results show that M-Voronoi and RSA (with spherical voids) geometries exhibit the stiffest elastic and highest flow stress response compared to the other two geometries. This study shows unambiguously that randomness may or may not lead to enhanced mechanical response such as higher stiffness or flow stress.

Numerical and experimental study of the conical connection of the blade of a rotary machine

The paper presents an experimental and numerical study of the tapered socket of the aluminum blade root of the mine main ventilation fan, which is based on the tests of a simplified full-scale model with a discarded airfoil and its subsequent finite element analysis. The calculation model takes into account elastoplastic properties of materials and non-linear contacts with friction. The proposed joint consists of an aluminum tapered blade root, two steel retainers with similar tapered surfaces, and two steel bolts that join the retainers around the root. Pre-tightening the bolts allows fixing the blade in an unloaded state in the socket and prevents its unwanted turns. Such a tightening is taken into account in the finite element analysis by means of determining, in compliance with special rules, the axial force of the pretension of the bolts. With the help of a hydraulic press acting on the lower surface of the airfoil root, the effect of the centrifugal load on the conical joint from the side of the blade airfoil is simulated. Nonlinear static analysis of the elastoplastic behavior of the structure allows determining the destructive loads that cause the bolts to break with the subsequent disconnection of the fasteners and the blade to fly out of the seat. The graphs of the equivalent von Mises stresses indicate that the maximum stresses are reached in the working part of the bolts, which fully corresponds to the nature of the destruction of the structure upon reaching the maximum equivalent load on it. The experimental study confirms the correctness of the determination of contact stresses at the tapered socket location. Correspondence of the results of the static analysis with the results of the full-scale experiment makes it possible to draw a conclusion about the correctness of the conducted finite element modelling. This allows using the developed formulation of the problem to determine the strength of rotor structures with conical connections of blades without performing preliminary experimental studies. In addition, the developed technique can be extended to a larger range of conical and cylindrical joints due to the simplicity of the approach and the versatility of the formulation of the nonlinear finite-element problem which models structures with preloaded or tensioned elements.

On the importance of accurate elasto-plastic material properties in simulating plate osteosynthesis failure.

Background: Plate osteosynthesis is a widely used technique for bone fracture fixation; however, complications such as plate bending remain a significant clinical concern. A better understanding of the failure mechanisms behind plate osteosynthesis is crucial for improving treatment outcomes. This study aimed to develop finite element (FE) models to predict plate bending failure and validate these against in vitro experiments using literature-based and experimentally determined implant material properties. Methods: Plate fixations of seven cadaveric tibia shaft fractures were tested to failure in a biomechanical setup with various implant configurations. FE models of the bone-implant constructs were developed from computed tomography (CT) scans. Elasto-plastic implant material properties were assigned using either literature data or the experimentally derived data. The predictive capability of these two FE modelling approaches was assessed based on the experimental ground truth. Results: The FE simulations provided quantitatively correct prediction of the in vitro cadaveric experiments in terms of construct stiffness [concordance correlation coefficient (CCC) = 0.97, standard error of estimate (SEE) = 23.66, relative standard error (RSE) = 10.3%], yield load (CCC = 0.97, SEE = 41.21N, RSE = 7.7%), and maximum force (CCC = 0.96, SEE = 35.04, RSE = 9.3%), when including the experimentally determined material properties. Literature-based properties led to inferior accuracies for both stiffness (CCC = 0.92, SEE = 27.62, RSE = 19.6%), yield load (CCC = 0.83, SEE = 46.53N, RSE = 21.4%), and maximum force (CCC = 0.86, SEE = 57.71, RSE = 14.4%). Conclusion: The validated FE model allows for accurate prediction of plate osteosynthesis construct behaviour beyond the elastic regime but only when using experimentally determined implant material properties. Literature-based material properties led to inferior predictability. These validated models have the potential to be utilized for assessing the loads leading to plastic deformation in vivo, as well as aiding in preoperative planning and postoperative rehabilitation protocols.

Identification of elastoplastic properties of materials with gradient residual stresses using a co-simulation method and nanoindentation experiments

Nanoindentation technology has many advantages in the acquisition of elastoplastic properties of certain small-scale materials (coatings, films, etc.) due to its small size and non-destructive properties. However, because of the microscopic scale involved, test results are also more susceptible to disturbances by internal residual stress of the specimen. To address these issues, this paper develops a co-simulation method for combining the optimization algorithm with finite element simulation in order to obtain the true elastoplastic properties of unknown materials using nanoindentation testing. This method is suitable for any surface treated materials, and the reliability of the method is also verified by the case of laminar plasma quenched rail.

Critical Review of Nanoindentation-Based Numerical Methods for Evaluating Elastoplastic Material Properties

It is well known that the elastoplastic properties of materials are important indicators to characterize their mechanical behaviors and are of guiding significance in the field of materials science and engineering. In recent years, the rapidly developing nanoindentation technique has been widely used to evaluate various intrinsic information regarding the elastoplastic properties and hardness of various materials such as metals, ceramics, and composites due to its high resolution, versatility, and applicability. However, the nanoindentation process of indenting materials on the nanoscale provides the measurement results, such as load-displacement curves and contact stiffness, which is challenging to analyze and interpret, especially if contained in a large amount of data. Many numerical methods, such as dimensionless analysis, machine learning, and the finite element model, have been recently proposed with the indentation techniques to further reveal the mechanical behavior of materials during nanoindentation and provide important information for material design, property optimization, and engineering applications. In addition, with the continuous development of science and technology, automation and high-throughput processing of nanoindentation experiments have become a future trend, further improving testing efficiency and data accuracy. This paper critically reviewed various numerical methods for evaluating elastoplastic constitutive properties of materials based on nanoindentation technology, which aims to provide a comprehensive understanding of the application and development trend of the nanoindentation technique and to provide guidance and reference for further research and applications.

Dimensionless Analysis to Determine Elastoplastic Properties of Thin Films by Indentation

By assuming the elastoplastic properties of thin-film materials, a reverse analysis method is proposed by deriving a dimensionless function for the indentation process. The substrate effect is taken into account by assuming a perfect interface between thin-film and substrate materials. In order to obtain the applied load–penetration depth (P-h) curves, the indentation process is numerically modeled as an axisymmetric problem with a rigid-body Berkovich indenter on the semi-infinite substrate when performing finite element (FE) simulations. As a typical soft film/hard substrate problem, the elastic substrate is assumed and the power–law model is used to describe the constitutive properties of thin-film materials. Varying elastic modulus (10–50 GPa), yield strength (60–300 MPa), and hardening exponent (0.1–0.5) characterize different elastoplastic mechanical properties of thin-film materials with film thickness of 10–30 μm. Owing to the good trending P-h curves with the maximum indentation depth up to the 2/3 film thickness for different elastoplastic thin-film materials, a dimensionless function is derived and validated based on the predictions by reliable FE simulations. The proposed dimensionless function elegantly elucidates the essential relationship between the elastoplastic mechanical properties of the thin-film material and indentation responses (e.g., loading and unloading variables). The elastoplastic constitutive curves predicted by the proposed reverse method are confirmed to be in good agreement with the stress-strain curves of materials by FE simulations with the randomly selected elastoplastic mechanical properties and film thicknesses. This study provides a theoretical guidance to understand the explicit relationship between elastoplastic mechanical properties of the thin-film material and indentation responses.

Determine the unique constitutive properties of elastoplastic materials from their plastic zone evolution under nanoindentation

The evolution of the plastic zone underneath the indenter is challenging to be described during nanoindentation, which is recently known to be crucial to establish a constitutive model that features the plastic properties of the substrate materials based on their indentation responses. Using molecular dynamics and axisymmetric finite element (FE) simulations in this study, we show that the plastic zone shape in the elastoplastic materials is hemispherical in a broad range of length scales under a three-sided pyramid-shaped Berkovich indenter. By considering the critical factors of the applied load–penetration depth (P–h) curve, dimensional analysis is performed to derive dimensionless functions regarding the radius of the hemispherical plastic zone. For the loading and unloading stages in extensive FE simulations, a set of polynomial functions are proposed by associating the instantaneous and residual plastic zone radii with constitutive parameters. In addition to Young's modulus and the hardening exponent, the ratio of the representative stress to the reduced modulus is found to be crucial for predicting the plastic deformation. Lastly, the proposed dimensionless function reveals that the plastic zone radii are drastically different for three representative materials with identical P–h curves as confirmed by three independent methods. This result suggests that the proposed plastic zone radius in the dimensionless analysis helps to overcome the challenging uniqueness issue for decades to determine the unique elastoplastic properties of materials based on nanoindentation responses.

An Inverse Method for Measuring Elastoplastic Properties of Metallic Materials Using Bayesian Model and Residual Imprint from Spherical Indentation.

In this paper, an inverse method is proposed for measuring the elastoplastic properties of metallic materials using a spherical indentation experiment. In the new method, the elastoplastic parameters are correlated with sub-space coordinates of indentation imprints using proper orthogonal decomposition (POD), and inverse identification of material properties is solved using a statistical Bayesian framework. The advantage of the method is that model parameters in the numerical optimization process are treated as the stochastic variables, and potential uncertainties can be considered. The posterior results obtained from the measuring method can provide valuable probabilistic information of the estimated elastoplastic properties. The proposed method is verified by the application on 2099-T83 Al-Li alloys. Results indicate that posterior distribution of material parameters exhibits more than one peak region when indentation load is not large enough. In addition, using the weighting imprints under different loads can facilitate the uniqueness in identification of elastoplastic parameters. The influence of the weighting coefficient on posterior identification results is analyzed. The elastoplastic properties identified by indentation and tensile experiment show good agreement. Results indicate that the established measuring method is effective and reliable.

Strains Comparisons of Unbound Base/Subbase Layer Using Three Elasto-Plastic Models under Repeated Loads

The constitutive model is the crucial part for the finite element analyses. To study the elasto-plastic properties of unbound granular materials (UGMs) under repeated vehicular loads, an elasto-plastic constitutive model called revised spatially mobilized plane (SMP) was proposed and validated. In this study, the revised SMP model was used for the plastic strain analyses of a typical three-layer pavement structure. To make comparisons, the Mohr-Coulomb and Druck-Prager models were employed for the numerical computation. The results show that plastic tensile and compressive strains in the horizontal and vertical directions appear on the top surface of UGM using the revised SMP model, but no plastic strains are produced by the Mohr-Coulomb and Druck-Prager models. The distribution of plastic strains in the revised SMP model had a good relationship with the actual loading areas under the vehicular loading, which related to the rutting. With the Mohr-Coulomb and Druck-Prage models, a great plastic strain was produced during the first several loading cycles and hardly increased in the following loading cycles, while the plastic strain in the revised SMP model presented an obvious increasing tendency with increased loading cycles. The predicted permanent deformations of the revised SMP, Mohr-Coulomb and Druck-Prage models were 0.557 mm, 0.78 mm and 0.155 mm, respectively. Our work reveals that the Mohr-Coulomb model may over-predict and Druck-Prage model may under-predict the rutting of pavement in early loading stage and the results proved that the revised SMP model had advantages in the description of the plastic strain of UMG under repeated loads.

Stress-Shot-Peened Leaf Springs Material Analysis through Nano- and Micro-Indentations.

Heat-treated and shot-peened lightweight steels with demanding requirements for durability are applied in high-performance automotive leaf springs. Due to their heat-treatment they exhibit degraded properties in the surface-near area compared to the core. This area, which may extend until 300 μm from the surface to the core, experiences the highest bending stresses at operation. The microstructure in the surface and sub-surface layers determines the mechanical performance as well as the wear resistance. The present study refers to the material properties of a stress shot-peened 51CrV4 steel at various depths from the surface. The effect of the manufacturing process has been captured both by Vickers micro-hardness measurements and nanoindentation. The latter combined with a Fine Element Method (FEM)-based algorithm enables the determination of variations in the material’s stress–strain curves over the affected layers, which translate to internal stress changes. The nanoindentation technique has been applied here successfully for the first time ever on leaf springs. The combination of microstructural analysis, microhardness and nanoindentation captures the changes of the treated material, offering insights on the material characteristics, and yielding accurate elastoplastic material properties for local, layered-based analysis of the components’ mechanical performance at operational loading scenarios, i.e., in the framework of stress shot-peening simulation models.

Importance of dynamics in the finite element prediction of plastic damage of polyethylene acetabular liners under edge loading conditions

After hip replacement, in cases where there is instability at the joint, contact between the femoral head and the acetabular liner can move from the bearing surface to the liner rim, generating edge loading conditions. This has been linked to polyethylene liner fracture and led to the development of a regulatory testing standard (ISO 14242:4) to replicate these conditions. Performing computational modelling alongside simulator testing can provide insight into the complex damage mechanisms present in hard-on-soft bearings under edge loading. The aim of this work was to evaluate the need for inertia and elastoplastic material properties to predict kinematics (likelihood of edge loading) and plastic strain accumulation (as a damage indicator).While a static, rigid model was sufficient to predict kinematics for experimental test planning, the inclusion of inertia, alongside elastoplastic material, was required for prediction of plastic strain behaviour. The delay in device realignment during heel strike, caused by inertia, substantially increased the force experienced during rim loading (e.g. 600 N static rigid, ∼1800 N dynamic elastoplastic, in one case). The accumulation of plastic strain is influenced by factors including cup orientation, swing phase force balance, the moving mass, and the design of the device itself. Evaluation of future liner designs could employ dynamic elastoplastic models to investigate the effect of design feature changes on bearing resilience under edge loading.

Numerical study of random material properties within a soil specimen

Material properties derived from laboratory soil tests often assume that the property is uniform throughout the specimen. For some exceptional soils, this may hold true, but for many others it is obviously false. We have been performing cyclic and irregular torsional simple shear (TOSS) tests on hollow cylinder samples for decades and were intrigued by the idea of how to model inherently non-uniform specimens. As an added corollary, we wanted to understand the influence of imperfections (voids, inclusions) on the measured stress-strain behaviour in these tests. This paper examines two general classes of problems: (a) uniform specimens with inclusions of voids or imperfections, and (b) non-uniform specimens with random distributions of material properties within the specimen. Finite element modelling was performed on a TOSS specimen (ID = 4cm, OD = 6cm, L = 14cm) using a set of over 500 different elastoplastic material properties within the specimen. Various distributions (Normal, Log-normal, Bimodal) of stiffness and strength properties were examined. The results were examined as torque vs. twist curves since those values are typically measured in the TOSS laboratory test before being converted (with assumptions of uniformity) to shear stress-shear strain hysteresis. The Bimodal distributions were used to represent soils with distinct hard and soft zones. Additionally, distributions with some degree of spatial correlation were also examined.

A FEM-Based 2D Model for Simulation and Qualitative Assessment of Shot-Peening Processes.

Shot peening is one of the most favored surface treatment processes mostly applied on large-scale engineering components to enhance their fatigue performance. Due to the stochastic nature and the mutual interactions of process parameters and the partially contradictory effects caused on the component’s surface (increase in residual stress, work-hardening, and increase in roughness), there is demand for capable and user-friendly simulation models to support the responsible engineers in developing optimal shot-peening processes. The present paper contains a user-friendly Finite Element Method-based 2D model covering all major process parameters. Its novelty and scientific breakthrough lie in its capability to consider various size distributions and elastoplastic material properties of the shots. Therewith, the model is capable to provide insight into the influence of every individual process parameter and their interactions. Despite certain restrictions arising from its 2D nature, the model can be accurately applied for qualitative or comparative studies and processes’ assessments to select the most promising one(s) for the further experimental investigations. The model is applied to a high-strength steel grade used for automotive leaf springs considering real shot size distributions. The results reveal that the increase in shot velocity and the impact angle increase the extent of the residual stresses but also the surface roughness. The usage of elastoplastic material properties for the shots has been proved crucial to obtain physically reasonable results regarding the component’s behavior.

Identification of elastoplastic properties of rods from torsion test using meshless methods and a metaheuristic

In the paper, we consider a numerical simulation of torsional experiment and identification of elastoplastic properties of materials in such a test. The former is a direct problem. We consider a nonlinear boundary value problem, which is solved by means of the method of fundamental solutions and global radial basis function collocation method. The latter is an inverse problem, in which elastoplastic properties of materials are unknown. In order to solve it, we treat it as an optimization problem. We define an error between the measurements from torsional experiment and the results of simulations. To identify the parameters, we apply the virus optimization algorithm. The results show very good accuracy of the proposed approach.

Application of Artificial Intelligence to Solve an Elasto-Plastic Impact Problem

<div class="section abstract"><div class="htmlview paragraph">Artificial intelligence (AI) is dramatically changing multiple industries. AI’s potential to transform Computer-Aided Engineering (CAE) cannot be overlooked. Conventionally, Finite Element Analysis (FEA) is the simulation of any given physical phenomenon to obtain an approximate solution to a group of problems governed by Partial Differential Equations (PDE). Implementation of AI methods in this area combines human intelligence with numerical solutions to make them more efficient. This paper attempts to develop a Deep Neural Network (DNN) model to solve an elasto-plastic impact problem of a symmetric short crush tube made of three materials impacted by a moving wall. A structured learning database was established to train and validate the model using finite element simulations. Tube size, gauge and elasto-plastic material properties were used as input attributes or features. The maximum axial displacement of the tube is the target label to predict. The dataset was analyzed to understand relations among the design features such as section size, gauge, and elasto-plastic material properties. The DNN model architecture and the hyper-parameters tuned to improve the model fit. The trained model was then evaluated with an unseen dataset to assess its prediction accuracy in real-world settings. The output of the DNN model was compared with the finite element simulation results. The established model shows a reasonable co-relation. Thus, this paper offers an alternative or a supplemental tool to conventional FEA methods to accelerate and augment design decision making. This paper offers an alternative or a supplemental tool to conventional FEA methods to accelerate and augment design decision making, and briefs an overall process to set up the Machine Learning (ML) model using TensorFlow and Python libraries. Finally, recommendations are made to propose potential research areas.</div></div>

Nonlinear vibrations of a circular plate reinforced by ribs

The behavior of a circular elastoplastic plate, consisting of a shell and reinforced ribs of a quadran-gular cross-section and under the action of dynamic loads, has been investigated. The rib sections are considered to be constant. The relationship between deformations and displacements is taken geometrically nonlinear, and between stresses and deformations in the form of Hooke’s law. Refined equations of the Timoshenko type are taken as resolving ones. It is believed that the vibrations of the plate are excited by a dynamic load acting on the surface of the plate. The solution of the differential equations for the vibrations of the plate, taking into account the elastoplastic properties of the shell materials and the reinforced ribs, is carried out by the finite difference method. The elastic and elastoplastic models are used to calculate the deflections of the central point and forces depending on the location of the ribs. In particular, it has been established that: when the plate is reinforced with one rib, the smallest deflection of the center point can be achieved when the rib is located in the middle of the radius; the proposed model and calculation method allow achieving the desired deflection value by varying the number of ribs.

Elastoplastic Properties of Polylactide Composites with Finely Divided Fillers

By using the modular-deformation method of calculations, we established the influence of finely divided filler (talc) and additional heat treatment on the elastoplastic properties of polylactide materials. We detected the changes in the modulus of deformation, elasticity modulus, and thermomechanical characteristics of polylactide composites. The maximum values of the moduli and melting point were observed for thermally treated specimens with a talc content of 2 wt.%. We determined the fractions of the elastic, plastic, and highly elastic components in the total deformation of polylactide materials and showed that the fraction of the plastic component decreases after thermal treatment and as a result of introduction of the filler. It was also discovered that the level of hardness and structure factor of the obtained materials noticeably increase as a result of the introduction of talc and additional thermal treatment.

Elastoplastic buckling of FGM beams in thermal environment

The elastoplastic buckling behaviors of functionally graded material (FGM) beams under axial compression loading are studied in consideration of temperature dependence of material properties. Firstly, elastoplastic material properties are obtained on the basis of bilinear hardening model and temperature dependence, meanwhile the elastoplastic constitutive equations of the FGM are established as well. Then introducing the Hamilton principle, the elastoplastic buckling behaviors of FGM beams are transformed into solving the eigenvalues in symplectic space. At the same time, the buckling critical loads corresponding to the generalized eigenvalues of the canonical equations can be calculated by the bifurcation conditions. Finally, the elastoplastic buckling characteristics and solution process of them are revealed by the symplectic method and effects of material gradient, geometrical parameters of structure and ambient temperature on the critical loads of elastoplastic buckling are discussed in detail.