Elasto-plastic Material Model Research Articles

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.

Estimation of the effective yield properties of human trabecular bone using nonlinear micro-finite element analyses.

Micro-finite element ([Formula: see text]FE) analyses are often used to determine the apparent mechanical properties of trabecular bone volumes. Yet, these apparent properties depend strongly on the applied boundary conditions (BCs) for the limited size of volumes that can be obtained from human bones. To attenuate the influence of the BCs, we computed the yield properties of samples loaded via a surrounding layer of trabecular bone ("embedded configuration"). Thirteen cubic volumes (10.6mm side length) were collected from [Formula: see text]CT reconstructions of human vertebrae and femora and converted into [Formula: see text]FE models. An isotropic elasto-plastic material model was chosen for bone tissue, and nonlinear [Formula: see text]FE analyses of six uniaxial, shear, and multi-axial load cases were simulated to determine the yield properties of a subregion (5.3mm side length) of each volume. Three BCs were tested. Kinematic uniform BCs (KUBCs: each boundary node is constrained with uniform displacements) and periodicity-compatible mixed uniform BCs (PMUBCs: each boundary node is constrained with a uniform combination of displacements and tractions mimicking the periodic BCs for an orthotropic material) were directly applied to the subregions, while the embedded configuration was achieved by applying PMUBCs on the larger volumes instead. Yield stresses and strains, and element damage at yield were finally compared across BCs. Our findings indicate that yield strains do not depend on the BCs. However, KUBCs significantly overestimate yield stresses obtained in the embedded configuration (+43.1 ± 27.9%). PMUBCs underestimate (-10.0 ± 11.2%), but not significantly, yield stresses in the embedded situation. Similarly, KUBCs lead to higher damage levels than PMUBCs (+51.0 ± 16.9%) and embedded configurations (+48.4 ± 15.0%). PMUBCs are better suited for reproducing the loading conditions in subregions of the trabecular bone and deliver a fair estimation of their effective (asymptotic) yield properties.

Enodimenzijski model elastoplastičnega materiala s poškodbo za hitro ugotovitev lastnosti materiala

Enodimenzijski model elastoplastičnega materiala s poškodbo za hitro ugotovitev lastnosti materiala

Verification of Ram-Press Pipe Bending Process using Elasto-Plastic FEM Model

Abstract In this paper selected aspects of numerical modelling of bending pipes process are described. Elasto-plastic material model was used in COMSOL FEM environment. The results of numerical analyses of two kinds of steel were presented. The correctness of the proposed model was verified based on comparison shapes of deformed pipe profile obtained at the ending step of bending both from numerical simulations and experiment.

Numerical study of reinforced and prestressed concrete components under biaxial tensile stresses

The focus of this study was the numerical investigation of reinforced and prestressed concrete components under biaxial tensile stresses in ANSYS in order to display the state of stress in a containment wall. Solid elements were used for concrete, whereas beam elements were used for reinforcing steel. The description and representation of the nonlinear material behavior and the fundamental phenomena of the damage of the concrete was implemented by using an elastoplastic material model. As crack width, crack spacing, and the deformation behavior of components largely depend on the bond behavior, a node‐to‐node contact between reinforcement and concrete was used. Therefore, a specific bond model was implemented. In the longitudinal reinforcement direction, the bond model implemented defines the bond resistance as a function of the relative displacements between concrete and reinforcement.

Dynamic numerical simulation of plastic deformation and residual stress in shot peening of aluminium alloy

Shot peening is a cold surface treatment employed to induce residual stress field in a metallic component beneficial for increasing its fatigue strength. The experimental investigation of parameters involved in shot peening process is very complex as well as costly. The most attractive alternative is the explicit dynamics finite element (FE) analysis capable of determining the shot peening process parameters subject to the selection of a proper 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 an aluminium alloy plate described with strain rate dependent elasto-plastic material model. The impacts were carried out at various incident velocities. The influence of shot velocity and size on the plastic deformation, compressive residual stress and force-time response were investigated. The results exhibited that increasing the shot velocity and size resulted in an increase in plastic deformation of the aluminium target. However, a little effect of the shot velocity and size was observed on the magnitude of target´s subsurface compressive residual stress. The obtained results were close to the published ones, and the numerical models demonstrated the capability of the method to capture the pattern of residual stress and plastic deformation observed experimentally in aluminium alloys. The study can be quite helpful in determining and selecting the optimal shot peening parameters to achieve specific level of plastic deformation and compressive residual stress in the aluminium alloy parts especially compressor blades.

Low-speed bending impact behavior of adhesively bonded single-lap joints

This study addresses the low-speed impact behavior of adhesively bonded single-lap joints. An explicit dynamic finite element analysis was conducted in order to determine the damage initiation and propagation in the adhesive layers of adhesive single-lap joints under a bending impact load. A cohesive zone model was implemented to predict probable failure initiation and propagation along adhesive–adherend interfaces whereas an elasto-plastic material model was used for the adhesive zone between upper and lower adhesive interfaces as well as the adherends. The effect of the plastic deformation ability of adherend material on the damage mechanism of the adhesive layer was also studied for two aluminum materials Al 2024-T3 and Al 5754-0 having different strength and plastic deformation ability. The effects of impact energy (3 and 11 J) and the overlap length (25 and 40 mm) were also investigated. The predicted contact force-time, contact force-central displacement variations, the damage initiation and propagation mechanism were verified with experimental ones. The SEM and macroscope photographs of the adhesive fracture surfaces were similar to those of the explicit dynamic finite element analysis.

Selecting the objective function during the inverse identification of the parameters of a material model of concrete

Selecting the correct objective function is the critical precondition for a successful optimization task. The validity of this condition is also required when optimization algorithms are needed for the inverse identification of the unknown parameters of nonlinear material models of concrete, where experimentally measured load-displacement curves can be conveniently applied. In such cases, the objective function expressions can be formulated as the difference between the functional values of the curves or via comparing the characteristic features, which comprise the area under the curve and also the maximum functional value. The proposed article brings a study of the influence of the different formulations of the objectives functions to achieving optimum in the inverse analysis using genetic algorithm. The numerical part of the study was performed in the ANSYS computational system with use of multiPlas library of elasto-plastic material models from which the model based on formulations of Menetrey and Willam was chosen.

A plasticity model for predicting the rheological behavior of paperboard

The sorption of water into the paperboard exposes a container to reversible and irreversible deformations under relative humidity variations. In this study, an elasto-plastic material model is used to demonstrate how through-thickness dry solids content gradients can generate permanent in-plane strains in paperboard. The measurements presented in this paper indicate that in consecutive loading-unloading cycles, the yield stress either remains roughly constant or decreases, and an additional permanent set of strain is obtained even when the maximum tension of repetitions stays constant. Two modified approaches concerning elasto-plastic hardening behavior based on the measurements of this work and the observations of previous studies are introduced. The simulated results exhibit some shared features of the frequently observed shrinkage behavior of paperboard exposed to cyclic relative humidity changes. The results suggest that with the use of a suitable hardening approach, the plastic deformations arising from through-thickness dry solids content gradients may be considered as a time-independent component for simulations of phenomena such as moisture-accelerated creep and release of dried-in stresses.

Simulation of thick adhesive layers at finite strains utilizing an associated flow rule in a thermodynamically consistent framework

AbstractThe application of elastoplastic material models is commonly used for the modelling of adhesive layers with high strength adhesives as realized with polyurethane or epoxy resin. To fulfill thermodynamic consistency often restrictions on the choice of material parameters are requested. One of them is the introduction of a non‐associated flow rule, which always ensures positive dissipation. Nevertheless, this assumption is a non‐essential criterion, which will be addressed in this work. Continuing along this argumentation, the constitutive relations for the material is modified based on an associated flow rule. The applied model for the simulation of the adhesives is based on a small strain theory. A yield surface including two stress invariants, the hydrostatic pressure as well as the deviator stress state, set the elastic limit of the material response. Linear as well as exponential hardening is incorporated and material softening that arises subsequently is also included by substituting effective invariants in the yield function. This material model as proposed from literature was extended to finite strain application with the concept of generalized stress‐strain‐measure, which was realized in a previous work. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An anisotropic elasto-plastic material model for injection-molded long fiber-reinforced thermoplastics accounting for local fiber orientation distributions

This paper presents an anisotropic elasto-plastic material model for injection-molded long fiber-reinforced thermoplastics. It considers local heterogeneities which are attributed to process-induced variations of fiber orientation distributions and fiber volume fractions. These inhomogeneities have an effect on the mechanical properties and need to be considered in structural computations. In the material model, this is realized through a two-step homogenization procedure. First, an anisotropic stiffness tensor is approximated using mean field homogenization. Second, the plastic behavior is described using Hill’s transversely isotropic yield criterion averaged over the three principal directions of the fiber orientation. The advantage in combining these two approaches is a micro-mechanically based, yet fast numerical calculation of the composite material behavior within an explicit finite element code. The anisotropic material model is calibrated by simulating tensile tests on specimens taken in different directions from an injection-molded plate of fiber reinforced thermoplastic. The spatial variation of fiber orientation distribution and fiber volume fraction throughout the plate is determined from numerical mold filling simulations and is compared with computer tomography scans at different positions. A validation of the model is performed through simulating position-dependent tensile tests on smooth and notched specimens as well as a punch test which is well reproduced.

Viscous regularization for cohesive zone modeling under constant displacement: An application to hydrogen embrittlement simulation

The convergence problem during the cohesive zone modeling of hydrogen embrittlement in constant displacement scenario is attributed to the numerical instability which is studied analytically in the present work. The property of numerical stability is directly associated with the number of solutions for the controlling equations from the failure initiation point. It is shown that all the cases with a non-unique solution are numerically unstable thereby having convergence problem. Linear elastic and elasto-plastic material models are considered in the derivation, and the convergence properties for both models are proved essentially the same. The viscous regularization proposed by Gao and Bower (2004) proves effective in solving the convergence problem with good accuracy under constant displacement, provided that the viscosity is small enough. This is further supported by a pipeline engineering case study where the viscosity regularized cohesive zone approach is applied to the hydrogen embrittlement simulation. The stabilizing mechanism of the viscous regularization is attributed to its capacity to enforce a single solution by modifying the controlling equations. The influence of viscous regularization on symmetry modeling is also discussed.

The concept of virtual material testing and its application to sheet metal forming simulations

A crystal plasticity based full-field microstructure simulation approach is used to virtually determine mechanical properties of sheet metals. Microstructural features like the specific grain morphology and the crystallographic texture are taken into account to predict the plastic anisotropy. A special focus is on the determination of the Lankford coefficients and on the yield surface under plane stress conditions. Compared to experimental procedures, virtual material testing allows to generate significantly more data points on the yield surface. This data is used to calibrate anisotropic elasto-plastic material models which are commonly used for sheet metal forming simulations. A numerical study is carried out to analyze the influence of the chosen points on the yield surface on the calibration procedure.

Experimental and numerical study of Kuru granite under confined compression and indentation

The paper presents an experimental and numerical investigation on the response of Kuru granite rock under confining compression and static indentation. Triaxial compression tests were executed at different levels of confining pressure. Indirect tensile tests were carried out with Brazilian disks, and quasi-static indentation tests with a spherical indenter were conducted. An elasto-plastic material model with piecewise yield function, plastic hardening/softening, coupled damage and non-associated plastic flow is presented and calibrated using the experimental test results. Finite element simulations of the triaxial compression tests and static indentation are performed. The influence of the material model features (e.g., the yield function and non-associativity) is discussed, and the effect of confining pressure during indentation is evaluated. It was found that, within the investigated pressure range, the dilatancy angle of the rock linearly decreased with pressure. With a saturating yield function, the simulated force-penetration curve is in good agreement with the experimental curve for the loading phase, but the simulated stiffness during unloading and the subsequent residual penetration are overestimated. The numerical simulation showed that the peak force of indentation increased approximately 11% with a confining pressure of 150MPa compared to the unconfined case. The shape of the equivalent stress field near the free surface of the rock is affected by the confining pressure as well.

Determination of the elasto-plastic material characteristics of Norway spruce and European beech wood by experimental and numerical analyses

Abstract Experimental and numerical analyses are presented concerning of compression tests parallel and perpendicular to the grain, three-point bending, and double-shear joints in compliance with the relevant test standards (ASTM D2395, BS 373, EN 383 and EN 26891). Woods of Norway spruce (Picea abies L. Karst.) and European beech (Fagus sylvatica L.) were tested to describe their non-linear behavior. Elasto-plastic material models were the basis for the finite-element (FE) analyses with the input of own experimental data and those of the literature. The elasto-plastic material model with non-linear isotropic hardening was applied based on the Hill yield criterion in regions of uniaxial compression. The material characteristics were first optimized and validated by means of basic 3D FE models under the same conditions as applied for the experiments. Afterwards, the validated material models were implemented into the solver with more complex numerical analyses of wooden dowel joints. Concurrently, the digital image correlation (DIC) served for verification of the numerical wooden joint models. A good agreement (with a relative error up to 16%) was found between numerically predicted and experimentally measured data. The differences may be mainly attributed to some natural characteristics of wood which were not considered in the proposed material models. The proposed elasto-plastic material models are capable of predicting the wood’s ultimate strength, and therefore could contribute to a more reliable design of wood structures and their performance.

Phase-field modeling of brittle and ductile fracture in shells with isogeometric NURBS-based solid-shell elements

In this paper, we investigate fracture in shells with a phase-field modeling approach. The shell model is based on solid-shell kinematics with small rotations and displacements and is discretized using quadratic Non-Uniform Rational B-Spline basis functions. Membrane and shear locking is alleviated through the Assumed Natural Strain approach. The solid-shell formulation is combined with a brittle phase-field model for elastic materials, as well as with a ductile fracture model for elasto-plastic materials exhibiting J2 plasticity with isotropic hardening. Several examples demonstrate the ability of the proposed framework to capture crack initiation, propagation, merging and branching phenomena as well as crack bulging effects in shells under different states of loading.

Coupled diffusion-deformation multiphase field model for elastoplastic materials applied to the growth of Cu6Sn5

A coupled diffusion-deformation, multiphase field model for elastoplastic materials is presented. The equations governing the evolution of the phase fields and the molar concentration field are derived in a thermodynamically consistent way using microforce balance laws. As an example of its capabilities, the model is used to study the growth of the intermetallic compound (IMC) Cu6Sn5 during room-temperature aging. This IMC is of great importance in, e.g., soldering of electronic components. The model accounts for grain boundary diffusion between IMC grains and plastic deformation of the microstructure. A plasticity model with hardening, based on an evolving dislocation density, is used for the Cu and Sn phases. Results from the numerical simulations suggest that the thickness of the IMC layer increases linearly with time and that the morphology of the IMC gradually changes from scallop-like to planar, consistent with previous experimental findings. The model predicts that plastic deformation occurs in both the Cu and the Sn layers. Furthermore, the mean value of the biaxial stress in the Sn layer is found to saturate at a level of −8 MPa to −10 MPa during aging. This is in good agreement with experimental data.

Some experience in numerical modelling of unsaturated slope instabilities

In the past couple years, the region of South-East Europe is subjected to gust rainfall events activating many landslides which cause significant material and human losses. To revaluate the existing risk maps and set new standards some old case histories are revaluated. This paper presents two case histories of landslide instabilities subjected to excess climatic perturbations, gust rainfall, namely the «Stanjevci» cut-slope near the railway line in North-East of Slovenia; and the «Ramina» a natural landslide in urban area near the city of Veles in Central Macedonia. They are briefly described later to be analysed using coupled thermo-mechanical calculations. They are subjected to specific short and gusting rainfall considered as possible trigger. Hence, van Genuchten’s hydraulic model is used in combination with elastoplastic material models. The results are summarized with critical comments regarding the mathematical formulation used to describe atmospheric-soil interaction and the influence of different aspects on the accuracy is discussed briefly.