Elasto-plastic Material Model Research Articles

The use of rate-dependent scheme for rate-independent materials: application to a 1D dynamic simple shear elasto-plastic problem

This paper focuses on the usage of a rate-dependent scheme to model rate-independent materials for problems with sharp gradients and/or singularities. In particular, dynamic simple shear of a body characterized by an elastoplastic material model and a non-homogeneous distribution of material properties is analyzed. A 1D representation of the classical elastoplastic model is considered and numerically implemented using a finite difference scheme. It is observed and discussed that rate-dependent scheme helps in material behavior stability post softening for a body experiencing strain localization, which is nearly impossible in the case of rate-independent implementation.

Energy absorbers on the steel plate – rubber laminate after deformable projectile impact

The ability of energy absorption can be used to measure the strength of material against ballistic impact. This paper aims to analyze the rubber plated energy absorption plate that was shot with deformable projectiles. This study was conducted using numerical simulations based on the finite element that have been verified with experimental results. The simulation setting on a steel plate with different hardness with the addition of rubber thickness is prepared as a ballistic test panel. Manufacturing between layers made non fix with the back plate. Panel shot by using 5.56x 45 mm deformable caliber bullet with a distance of 15 m of normal attack angle. The finite element code with Johnson-Cook and Mooney-Rivlin elasto-plastic material models was were employed to perform the simulation study. Simulation results show the energy due to ballistic impact received and absorbed by the panel rises significantly shortly after the collision until reaching a certain number on a single plate where energy will decrease because the projectile successfully penetrated the plate. While on a layered plate, after the projectile succeeded in penetrating the front side plate, the absorption energy reached the maximum number and then remained constant, which caused the projectile not to be able to penetrate the next layer. These findings indicate that the addition of rubber with a layered structure is able to absorb the energy of ballistic impact

Determination of the Shear Modulus of Orthotropic Thin Sheets With the Anticlastic-Plate-Bending Experiment

The shear modulus of orthotropic thin sheets from three advanced high-strength steels (AHSS) is measured using the anticlastic-plate-bending (APB) experiment. In APB, a thin square plate is loaded by point forces at its four corners, paired in opposite directions. It thus assumes the shape of a hyperbolic paraboloid, at least initially. The principal stress directions coincide with the plate diagonals, and the principal stresses are equal and opposite. Hence, at 45 deg to these, a state of pure shear exists. A finite element (FE) study of APB is reported first, using both elastic and elastoplastic material models. This study confirms the theoretical predictions of the stress field that develops in APB. The numerical model is then treated as a virtual experiment. The input shear modulus is recovered through this procedure, thus validating this approach. A major conclusion from this numerical study is that the shear modulus for these three AHSS should be determined before the shear strain exceeds 2 × 10−4 (or 200 με). Subsequently, APB experiments are performed on the three AHSS (DP 980, DP 1180 and MS 1700). The responses recorded in these experiments confirm that over 3 × 10−4 strain (or 300 με) the response differs from the theoretically expected one, due to excessive deflections, yielding, changing contact conditions with the loading rollers and, in general, the breaking of symmetry. But under that limit, the responses recorded are linear, and can be used to determine the shear modulus.

Trapped fluid in contact interface

We study the mechanical contact between a deformable body with a wavy surface and a rigid flat taking into account pressurized fluid trapped in the interface. A finite element model is formulated for a general problem of trapped fluid for frictionless and frictional contact. Using this model we investigate the evolution of the real contact area, maximal frictional traction and global coefficient of friction under increasing external pressure. Elastic and elasto-plastic material models, compressible and incompressible fluid models and different geometrical characteristics of the wavy surface are used. We show that in case of incompressible fluid, due to its pressurization, the real contact area and the global coefficient of friction decrease monotonically with the increasing external pressure. Eventually, the contact opens and the fluid occupies the entire interface resulting in vanishing of static friction. An asymptotic analytical result for the critical trap-opening pressure is found and shown to be independent of the surface slope if it is small. In case of compressible fluids with pressure-dependent bulk modulus we demonstrate a non-monotonous behaviour of the global coefficient of friction due to a competition between non-linear evolution of the contact area and of the fluid pressure. However, for realistic compressibility of solids and fluids, contact-opening cannot be reached at reasonable pressures. On the other hand, in case of elastic-perfectly plastic materials, we again observe fluid permeation into the contact interface. Finally, we study the distribution of frictional tractions during the depletion of the contact area under increasing external pressure. This process leads to emergence of singularity-like peaks in tangential tractions (bounded by the Coulomb’s limit) near the contact edges. We point out the similarity between the processes of trap opening and interfacial crack propagation, and estimate the complex stress intensity factor in the framework of linear elastic fracture mechanics.

Dynamic finite element analysis of shot peening process of 2618-T61 aluminium alloy

Shot peening is one of the surface treatment processes usually used for the improvement of fatigue strength of metallic parts by inducing residual stress field in them. The evaluation of shot peening parameters experimentally is not only very complex but costly as well. An attractive alternative is the explicit dynamics finite element (FE) analysis having the capability of accurately envisaging the shot peening process parameters using a suitable material’s constitutive model and numerical technique. In this study, ANSYS/LS-DYNA software was used to simulate the impact of steel shots of various sizes on 2618-T61 aluminium alloy plate described with strain rate dependent elasto-plastic material model. The impacts were carried out at various incident velocities. The effect of shot velocity and size on the induced compressive residual stress and plastic deformation were investigated. The results demonstrated that increasing the shot velocity and size yielded in an increase in plastic deformation of the aluminium target. However, as observed, the effect of shot velocity and size was small in magnitude on the target's subsurface compressive residual stress.

Viscoelastic material models for more accurate polyethylene wear estimation

Wear debris from ultra-high-molecular-weight polyethylene components used for joint replacement prostheses can cause significant clinical complications, and it is essential to be able to predict implant wear accurately in vitro to prevent unsafe implant designs continuing to clinical trials. The established method to predict wear is simulator testing, but the significant equipment costs, experimental time and equipment availability can be prohibitive. It is possible to predict implant wear using finite element methods, though those reported in the literature simplify the material behaviour of polyethylene and typically use linear or elastoplastic material models. Such models cannot represent the creep or viscoelastic material behaviour and may introduce significant error. However, the magnitude of this error and the importance of this simplification have never been determined. This study compares the volume of predicted wear from a standard elastoplastic model, to a fractional viscoelastic material model. Both models have been fitted to the experimental data. Standard tensile tests in accordance with ISO 527-3 and tensile creep recovery tests were performed to experimentally characterise both (a) the elastoplastic parameters and (b) creep and relaxation behaviour of the ultra-high molecular weight polyethylene. Digital image correlation technique was used in order to measure the strain field. The predicted wear with the two material models was compared for a finite element model of a mobile-bearing unicompartmental knee replacement, and wear predictions were made using Archard’s law. The fractional viscoelastic material model predicted almost ten times as much wear compared to the elastoplastic material representation. This work quantifies, for the first time, the error introduced by use of a simplified material model in polyethylene wear predictions, and shows the importance of representing the viscoelastic behaviour of polyethylene for wear predictions.

Experimental and numerical investigation of ductile fracture of carbon steel structural components

Ductile fracture of steel components cannot be avoided particularly due to large inelastic strain in extreme loading scenarios. Without considering damage model, conventional elasto-plastic constitutive material model cannot lead to accurate finite element (FE) modelling results when damage due to fracture exists. Metal fracture is a complex damage process in which damage onset, material deterioration and final fracture are related to development of material plasticity. Uniaxial tensile fracture and shear fracture are two typical failure modes of structural members. In this study, experimental investigations of monotonic tensile fracture and in-plane shear fracture under different strain rates in quasi-static loading range are presented for low-alloy structural carbon steel. The characteristic steel material properties are obtained insensitive to the chosen strain rate. A semi-empirical process is used to calibrate the damage properties (damage onset and softening criteria) through FE modelling of the coupon samples based on a continuum damage mechanics (CDM) model. Deterioration of the carbon steel properties was found related to the evolution of equivalent plastic strain, and particularly there is a linear relationship for the in-plane shear scenario. The verified damage onset and shear softening are then used for modelling of a welded steel tubular connection experiencing punching shear fracture phenomenon. It is shown that modelling result of the steel connection is significantly improved when the proposed fracture modelling is adopted.

Numerical study of wheel-rail impact contact solutions at an insulated rail joint

This paper presents an analysis of the transient contact solutions of wheel-rail frictional rolling impacts calculated by an explicit finite element model of the wheel-insulated rail joint (IRJ) dynamic interaction. The ability of the model to simulate the dynamic behavior of an IRJ has been validated against a comprehensive field measurement in a recent paper (Yang et al., 2018). In addition to the measured railhead geometry and bi-linear elastoplastic material model used in Yang et al. (2018), this study adopts a nominal railhead geometry and an elastic material model for the simulations to provide an overall understanding of the transient contact behavior of wheel-IRJ impacts. Each simulation calculates the evolution of the contact patch area, stress magnitude and direction, micro-slip distribution, and railhead nodal vibration velocity in the vicinity of the joint during the wheel-IRJ impacts. The simulations apply small computational and output time steps to capture the high-frequency dynamic effects at the wheel-IRJ impact contact. Regular wave patterns that indicate wave generation, propagation and reflection are produced by the simulations; this has rarely been reported in previous research. The simulated waves reflect continuum vibrations excited by wheel-rail frictional rolling and indicate that the simulated impact contact solutions are reliable.

Metamodelling of wheel\u2013rail normal contact in railway crossings with elasto-plastic material behaviour

A metamodel considering material plasticity is presented for computationally efficient prediction of wheel–rail normal contact in railway switches and crossings (S&C). The metamodel is inspired by the contact theory of Hertz, and for a given material, it computes the size of the contact patch and the maximum contact pressure as a function of the normal force and the local curvatures of the bodies in contact. The model is calibrated based on finite element (FE) simulations with an elasto-plastic material model and is demonstrated for rail steel grade R350HT. The error of simplifying the contact geometry is discussed and quantified. For a moderate difference in contact curvature between wheel and rail, the metamodel is able to accurately predict the size of the contact patch and the maximum contact pressure. The accuracy is worse when there is a small difference in contact curvature, where the influence of variation in curvature within the contact patch becomes more significant. However, it is shown that such conditions lead to contact stresses that contribute less to accumulated plastic deformation. The metamodel allows for a vast reduction of computational effort compared to the original FE model as it is given in analytical form.

A computational strategy for the modeling of elasto-plastic materials under impact loadings

This paper presents a numerical strategy for the modeling of elasto-plastic materials under impact loadings. The bi-potential method is efficient in dealing with implicit standard materials constitutive laws, such as frictional contact. The Uzawa algorithm, based on the bi-potential method is applied to deal with the non-linearity of boundary conditions. For the non-linearity associated with materials, a Return Mapping Algorithm is applied to deal with the elasto-plastic constitutive laws. On the basis of the Updated Lagrangian formulation, we adopt a Rotationally Neutralized Objective hypothesis to describe the geometrically non-linear behavior. Equations of motion are integrated with a first order scheme. Three numerical examples are performed to verify the accuracy and to show the applicability of the proposed approach.

Explicit dynamics simulation of shot peening process induced by various types of shots impacts

Shot peening is a cold-working process that induces a small indentation on a metallic surface by impacting shots onto it causing residual compressive stresses which delays the initiation of fatigue cracking. The experimental assessment of shot-peening process parameters is not only very complex but costly as well. The most promising technique is the explicit dynamics finite-element (FE) analysis capable of determining the shot-peening process parameters subject to the selection of a suitable material’s constitutive model and numerical technique. In this work, Ansys/LS-Dyna code was employed to simulate the impact of shots of various sizes made of steel and glass on an aluminium alloy plate defined with strain-rate-sensitive elasto-plastic material model. The impacts were carried out at various incident velocities. The effects of velocity, size, and material of the shots on the compressive residual stress, indentation, and force–time response were investigated. The results showed that impact with the steel shots caused more indentation and larger area of plastic deformation in target material than the glass shots due to higher kinetic energy. Furthermore, increasing the shot velocity and size resulted in an increase in indentation. However, a negligible effect of the shot velocity, size, and material was observed on target’s surface and subsurface residual stress. The obtained results demonstrated that the proposed FE models simulated the shot-peening process in a realistic way. The study can be used to determine and optimise the shot-peening parameters such as shot size, material and velocity, and amount indentation and residual stresses in the aluminium alloy plate.

The damage analysis of the reinforced concrete beam and the prestressed reinforced concrete beam

The paper deals with the finite-element analysis of damage in reinforced concrete beam and prestressed reinforced concrete beam. The steel reinforcement is modeled using non-linear rebar elements and an elastoplastic model of the reinforcement is considered. The initial prestress is defined in the ropes that are used to create the prestressed reinforced concrete beam. These ropes are also modeled using non-linear rebar elements and the elastoplastic material model. Created computational model allows the damage modeling of the reinforced and pre-stressed reinforced concrete beams under static loading.

Methods for Complex Cracked Body Finite Element Assessments

This paper presents approaches developed to allow consistent best practice assessments for complex 2/3D defects in engineering structures subjected to primary loading and secondary thermal stresses. Methods are outlined and discussed with reference to recent two- and three-dimensional cracked body analyses of components which have been undertaken to determine tolerable defect sizes and inform sub-critical crack growth calculations. The analyses considered a range of postulated semi-elliptical, through-wall and fully circumferential defects in pressure systems. Mixed element type meshing strategies with tied contact in combination with multiple node transformation techniques around the defect front were employed during mesh generation. This facilitated highly refined meshes along the defect front which were required to accurately model extensive plastic deformation in the region of interest. Displacement driven thermal loads required detailed assessment with multiple elasto-plastic material models, since lower bound properties do not necessarily provide the most conservative results. The elasto-plastic J-Integral analyses were shown to provide significant benefit over application of the more conservative Failure Assessment Diagram (FAD) approach. The undertaken assessments were validated against analytical solutions and historic inspection evidence and showed good agreement. In summary the adopted modelling techniques released conservatisms and permitted detailed assessment of complex geometries and load cases.

An efficient and robust VUMAT implementation of elastoplastic constitutive laws in Abaqus/Explicit finite element code

This paper describes the development of an efficient and robust numerical algorithm for the implementation of elastoplastic constitutive laws in the commercial non-linear finite element software Abaqus/Explicit through a VUMAT FORTRAN subroutine. In the present paper, while the Abaqus/Explicit uses an explicit time integration scheme, the implicit radial return mapping algorithm is used to compute the plastic strain, the plastic strain rate and the temperature at the end of each increment instead of the widely used forward Euler approach. This more complex process allows us to obtain more precise results with only a slight increase of the total computational time. Corrector term of the radial return scheme is obtained through the implementation of a safe and robust Newton–Raphson algorithm able to converge even when the piecewise defined hardening curve is not derivable everywhere. The complete method of how to implement a user-defined elastoplastic material model using the radial return mapping integration scheme is presented in details with the application to the widely used Johnson–Cook constitutive law. Five benchmark tests including one element tests, necking of a circular bar and 2D and 3D Taylor impact tests show the efficiency and robustness of the proposed algorithm and confirm the improved efficiency in terms of precision, stability and solution CPU time. Finally, three alternative constitutive laws (the TANH, modified TANH and Bäker laws) are presented, implemented through our VUMAT routine and tested.

Load carrying capacity of castellated I-beam in the elastoplastic formulation problem

Developed a method for calculating the load carrying capacity of castellated I-beam with ideal elastoplastic material model in ANSYS Mechanical. The method verified in the test problem of bending a rectangular beam. The ultimate load and ratio of ultimate load to limited load for two different I-beams were calculated. The method can be used for other steel construction.

Numerical analysis of nuclear power plant structure subjected to aircraft crash

An aircraft crashing into a nuclear containment may induce a series of disasters related to containment capacity, including local penetration and perforation of the containment, intensive vibrations, and fire ignited after jet fuel leakage. In this study, structural safety of a reinforced concrete containment vessel (RCCV) has been studied against the direct hit of Airbus A320, Boeing 707-320 and Phantom F4 aircrafts. ABAQUS/explicit finite element code has been used to carry out the three-dimensional numerical simulations. The impact locations identified on the nuclear containment structure are mid height of containment, center of the cylindrical portion, junction of dome and cylinder, and over the cylindrical portion close to the foundation level. The loading of the aircraft has been assigned through the corresponding reaction-time response curve. The concrete damaged plasticity model was predicted to simulate the behavior of concrete while the behavior of steel reinforcement was incorporated using elastoplastic material model. Dynamic loading conditions were considered using dynamic increase factor. The mid height of containment and center of cylindrical portion have been found to experience most severe deformation against each aircraft crash. It has also been found that compression damage in concrete is not critical at none of the impact locations.

Strength reduction method in Barodesy

Strength reduction analysis are very common in geotechnical engineering to define a factor of safety of structures, e.g. slopes. Usually, the Mohr-Coulomb strength parameters friction angle φ′ and cohesion c′ are reduced until limit equilibrium is reached. This method is only applicable to material models which utilize a Mohr-Coulomb or similar (e.g. Drucker-Prager) failure criterion. In this article a strength reduction method for the barodetic material model is introduced and the results of slope stability calculations compared with the results with an elasto-plastic material model (Mohr-Coulomb) and with the results of an analytical analysis according to Bishop are presented. The strength reduction method for barodesy has been implemented in the Finite Element code Abaqus.

Finite element based contact analysis of radio frequency MEMs switch membrane surfaces

Finite element simulations were performed to determine the contact behavior of radio frequency (RF) micro-electro-mechanical (MEM) switch contact surfaces under monotonic and cyclic loading conditions. Atomic force microscopy (AFM) was used to capture the topography of RF-MEM switch membranes and later they were analyzed for multi-scale regular as well as fractal structures. Frictionless, non-adhesive contact 3D finite element analysis was carried out at different length scales to investigate the contact behavior of the regular-fractal surface using an elasto-plastic material model. Dominant micro-scale regular patterns were found to significantly change the contact behavior. Contact areas mainly cluster around the regular pattern. The contribution from the fractal structure is not significant. Under cyclic loading conditions, plastic deformation in the 1st loading/unloading cycle smooth the surface. The subsequent repetitive loading/unloading cycles undergo elastic contact without changing the morphology of the contacting surfaces. The work is expected to shed light on the quality of the switch surface contact as well as the optimum design of RF MEM switch surfaces.

Fatigue lifetime prediction of adhesively bonded joints: An investigation of the influence of material model and multiaxiality

In the present work the influence of material model and multiaxiality on the fatigue lifetime predictions of scarf and single-lap joints under uniaxial tension-tension cyclic loading is investigated. Lifetime predictions, from 103 to 106 cycles, were performed using a stress-life approach taking into account for the effect of multiaxiality by means of hydrostatic pressure (p) and von Mises stress (q). These stresses were calculated employing 2D-FEA with linear-elastic and elastoplastic (von Mises and Drucker-Prager) material models. Effective stresses were obtained using the theory of critical distances. Findings showed that material model affected significantly the multiaxiality distribution of the single lap joint (SLJ), especially at singularity regions. For scarf joints, this effect was noticeable for higher stresses. With the exception of the SLJ, by excluding the singularity regions close to the free edges, the value of multiaxiality was nearly constant and decreased with increasing bondline angles (higher shear effects). With regards to lifetime predictions, overall accuracy for the scarf joint was higher than for the SLJ. Linear-elastic material models provided satisfactory accuracy for the scarf joint, but not for the SLJ. Elastoplastic material models were able to improve predictions and to provide suitable accuracy for both joint configurations.

Fatigue analysis of railway wheel using a multiaxial strain‐based critical‐plane index

AbstractA fatigue damage model to assess the development of subsurface fatigue cracks in railway wheels is presented in this paper. A 3‐dimensional finite element model (FEM) is constructed to simulate repeated cycles of contact loading between a railway wheel and a rail. The computational approach includes a hard‐contact over‐closure relationship and an elastoplastic material model with isotropic and kinematic hardening.Results from the simulation are used in a multiaxial critical‐plane fatigue damage analysis. The employed strain‐based critical‐plane fatigue damage approach is based on Fatemi‐Socie fatigue index that takes into account the non‐proportional and out‐of‐phase nature of the multiaxial state of stress occurs when a railway wheel rolls on a rail. It predicts fatigue‐induced micro‐crack nucleation at a depth of about 3.7 mm beneath the wheel tread, as well as the crack plane growth orientation which indicates the possible failure pattern. Additionally, the influence of various factors such as contribution of normal stresses, higher wheel load, and material model have been investigated.