Nonlinear Material Model Research Articles

Numerical and experimental investigations on quasistatic pulse generation of ultrasonic guided waves in fiber reinforced composite pipes

The quasistatic pulse (QSP) generation of ultrasonic guided waves in composite pipes can exhibit many features that are useful for early-stage material characterization and structural health monitoring. The intrinsic relationship between the QSP generation and the weak elastic nonlinearity of solids is complex. It has yet promised for developing the nonlinear ultrasonic guided wave technique that combines its advantages of high sensitivity to microdamage and low ultrasonic attenuation in composite materials. This study presents a systematic investigation of the QSP generation in fiber reinforced composite pipes. Using a three-dimensional finite element simulation with a nonlinear material model, the temporal waveform, mode conversion effect, cumulative effect, generation efficiency, and duration effect of QSP generation are revealed. The nonlinear QSP signals in laminated composite pipes are confirmed as the fastest wave mode that only has axial displacement. The shape of QSP depends on the group velocity difference between the QSP and the primary wave. The magnitude of QSP is related to the excitation level, frequency, and tone-burst duration of the primary wave. Experiments are conducted using carbon fiber reinforced composite pipes and the signals are measured using a laser vibrometer scanning system for verifying the QSP generation. The experimental results are consistent with the numerical findings. A relative nonlinear acoustic parameter based on the QSP generation is proposed and used to evaluate the early-stage thermal fatigue damage in the pipes. The measured nonlinear acoustic parameter demonstrates high sensitivity to the damage, indicating considerable potential for industrial applications.

Comparison and analysis of ProTaper, ProTaper Next, and ProTaper Gold using finite element analysis

Aim: The aim of this study is to compare three endodontic files: ProTaper Universal (PTU), ProTaper Next (PTN), and ProTaper Gold (PTG) under bending forces using finite element analysis. Methods: This study utilizes finite element analysis conducted with ANSYS software. 3D models of the three endodontic files were prepared using ANSYS. A non-linear material model was applied, idealizing the stress-strain curve for Nickel-Titanium alloy (NiTi), the material of these endodontic files. Static and transient analyses were performed to identify three different material phases: austenitic phase, transition phase, and martensitic phase. Results: Finite element analysis reveals that the PTU file exhibited a maximum von Mises stress magnitude of 1249.7 MPa, PTN showed a maximum von Mises stress magnitude of 798.16 MPa, whereas the PTG file showed a minimum von Mises stress magnitude of 465.68 MPa. PTN showed more bending compared to the other file models for the same load magnitude. PTN remained in the austenitic phase until a tip displacement of 7.3657 mm, while PTU reached a maximum displacement of 4.5633 mm in the austenitic phase. Conclusion: The study concludes that the PTU file is the most rigid among the three file models. PTU generates higher stress magnitudes compared to the other files; thus, it is more likely to fracture under lesser bending forces. The study also concludes that PTG exhibits higher displacement with the lowest von-Mises stresses, making it the most flexible file among the three models.

Finite element analysis of concrete slab exposed to high velocity pressure wave – simplified vs. smoothed-particle hydrodynamics (SPH) method

Many structures are required to sustain the structural resistance also under extreme loading conditions, for example impacts of high-velocity objects (airplane crash into nuclear power plant), impacts of projectiles (defence structures), or while exposed to high velocity pressure wave caused e.g. by explosion of various chemicals in industry, nature gas, or also conventional weapons. Numerical analyses of these phenomena are feasible while utilizing explicit approach of the finite element method (FEM), available in commercially accessible software LS-Dyna. In order to predict the behaviour of the structure properly, advanced nonlinear material models are required to be considered, which are often mathematically described by numerous input parameters. Several approaches to model the exposure to blast load exist, from simplified, where the blast wave is considered as timedependent pressure based on empirical equations, to more advanced ones, where the propagation of the pressure wave itself through the surrounding environment is being modelled Arbitrary Lagrangian Eulerian, (ALE method), or so called smoothed-particle hydrodynamics (SPH) method, which might be used to model the blast itself. In this paper, FEM analyses of a simply supported concrete slab with basalt fibre reinforced polymer (BFRP) bars exposed to close range explosion of TNT charge are presented. 3D numerical models are analysed utilizing explicit solver of LS-Dyna. Karagozian and Case (K&C) nonlinear material model for concrete is used, which is suitable when high strain rates are present in the quasi brittle materials. Two variants of the blast loads modelling are compared. The simplified empirical approach, which is less demanding on computational power, and feasible for utilization in case of simple structure geometry, and more demanding method using SPH method to model the TNT detonation and interaction with the exposed concrete slab. The results of these numerical analyses are compared with experimental data based on available literature, and properly discussed.

Transient analysis of trusses considering nonlinear elastic and viscoelastic material models

Transient analysis of trusses considering nonlinear elastic and viscoelastic material models

Analytical Performance Assessment of Deteriorated Prestressed Concrete Beams

In this paper, a new approach is developed to numerically evaluate the structural performance of deteriorated prestressed concrete beams using the finite element analysis application RCAHEST (Reinforced Concrete Analysis in Higher Evaluation System Technology). A prestressing steel element was modified to represent the interaction between deteriorated concrete and prestressing steel. Considering the corrosion effects—as shown by the reduction of the prestressing steel section and loss of bond—a nonlinear material model was proposed for deteriorated prestressed concrete behavior. The modified damage index is intended to provide a numerical method for quantifying the structural performance of deteriorated prestressed concrete beams. The analytical procedure developed for the performance evaluation of deteriorated beams was validated by comparison with the credible test results, thereby enabling a more reliable and rational prestressed concrete beams design process.

Mechanical characterization of visually graded boards from turkish fir and black pine by nondestructive and destructive tests

For the mechanical characterization of Turkish fir and black pine, 400 board specimens with 22 mm× 50 mm × 420 mm were visually graded according to TS 1265 standard. Nondestructive tests were here upon performed using the stress wave method. After specimens were intentionally tested under flatwise bending to research the applicability as an alternative to tension and edgewise bending tests in European strength grading system. According to analyses of variance, the mean values of MOR and MOE differed in four groups at a p<0,05 significance level for visually graded boards. High correlations were found between MOR-MOE (R2=0,837) for fir and MOR-MOE (R2=0,776) for black pine. In addition, correlations of MOR-Knot rate for fir and black pine were respectively R2=0,669 and R2=0,660 showing the effectiveness of flatwise bending tests with the visual grading standard. For nondestructive tests, the mean values of the dynamic modulus of elasticity were very close in between fir and black pine grades while the usage of defect-free density performed better than the density of the whole specimen. Higher strength classes were found for black pine boards (Class 1= C40, Class 2= C27 and Class 3= C22) compared to fir boards (Class 1= C24, Class 2= C22 and Class 3= C18), respectively. Moreover, a simplified nonlinear material model was proposed for numerical modelling, and the results were found in good agreement in terms of the bending stiffness, strength, and deformation capacity of boards especially for class 1 and class 2 in both softwood species.

Phase-field simulation of fracture in Polymethyl Methacrylate

Significant interest and developments in phase-field fracture modeling have emerged. It approximates fracture continuously using a length-scale parameter, accurately simulating fracture initiation and crack propagation in brittle materials like Polymethyl Methacrylate (PMMA) with nonlinear elasticity. This study proposes a phase-field approach for simulating PMMA fracture behavior using ABAQUS with a nonlinear elastic material model (UMAT) and a three-layered element composition (UEL). The staggered approach sequentially solves displacements and phase-field variables. Numerical results are validated against experiments considering various geometries, stress concentrators, and pre-cracks. The computational approach accurately predicts fracture initiation and crack growth in complex patterns and diverse loading conditions.

Solver‐free classical computational homogenization for nonlinear periodic heterogeneous media

AbstractModeling the behavior of composite materials is an important application of computational homogenization methods. Classical computational homogenization (CCH), based on asymptotic analysis, is such a method. In CCH, equilibrium equations are separated into two length scales and solved numerically. Solving the fine‐scale equilibrium equations at every coarse‐scale Gauss point, in every iteration of a Newton–Raphson loop, is often too computationally expensive for real engineering applications. In this study, we propose a modified CCH approach that avoids solving the fine‐scale equilibrium equations. The proposed method, which we call solver‐free CCH, works by pre‐computing a set of eigenstrain influence function tensors based on data from a small number of numerical experiments. Then, during the online stage of the computation, these eigenstrain influence tensors are used in the fine‐scale problem to evaluate and homogenize strains and stresses. This article begins by formulating the solver‐free CCH approach for small‐deformation problems involving composites with nonlinear constituent phase material models, including computation of the eigenstrain influence tensors and their application within the online stage. To verify the proposed approach, we consider loading cases outside the training set used to derive the eigenstrain influence tensors. The combinational efficiency and accuracy of the solver‐free CCH in comparison to the conventional CCH is studied on a multilayer composite plate in three point bending (3pt‐bend) and open hole tension.

Soil-structure interaction of nuclear power plant

Nuclear power plants are special facilities with large foundation designs, located in areas with good geology. However, in areas where seismic loads need to be considered, analyzing the soilstructure interaction of nuclear power plants is essential. Nonlinear analyses of soil-structure interaction can be performed in the time domain or frequency domain. Time domain analysis has the advantage of easily incorporating nonlinear material models or geometric nonlinearity. However, this method is limited by the boundary conditions of the geological region near the structure, as current analysis methods assume vertically propagating seismic waves towards the structure. This assumption is made to limit the errors that finite element methods can introduce at the boundaries. This paper presents a new computational method that combines finite element method and boundary element method, in which the propagation of seismic waves towards the structure can be considered at a predetermined angle. The paper analyzes the impact of wave propagation on the response spectrum of the Kashiwazaki-Kariwa Nuclear Power Plant Unit 7. The results of the analysis show that the new computational method can consider the influence of the angle of incoming wave on the soil-structure interaction analysis.

Significance of construction sequence and the initial behaviour in concrete-faced rockfill dams

ABSTRACT Finite Element Model simulations are widely used to validate experimental and field observations. Out of these, modelling and comparing the stability of dams under various loading conditions presents significant challenges for researchers and practitioners, none more than the concrete-faced rockfill dams that are present in Australia (e.g. Cethana dam) and around the globe. A review shows that the construction sequence of such dams has not been incorporated in the initial configuration of concrete-faced rockfill dams. In this research, static analysis has been conducted for 2D and 3D finite element models of the Kotmale concrete-faced rockfill dam (CFRD) with and without the construction stage. Both 2D and 3D analysis of the case study dam using MIDAS FEA NX software and static analysis have been conducted. A linear elastic material model and a nonlinear material model (Duncan and Chang EB Model) were used to model the rockfill material. The resulting deformations were compared with the in-situ measurements to identify the accuracy of the developed cases. Results show that construction stage inclusion and the nonlinear material model agree well with the in-situ measurements, warranting the need for such advancements in Finite Element Analysis. Such an inclusion can model future settlement behaviour reasonably well, which can lead to the development of appropriate management measures.

Failure behavior of an adaptive concrete beam with integrated fluidic actuators: non-linear three-dimensional finite element analysis

In the present study, the adaptive behavior of a concrete beam with integrated fluidic actuators was numerically investigated through three-dimensional (3D) non-linear finite element (FE) analysis. The employed numerical approach for the mechanical behavior of concrete is based on the microplane theory, implemented in the in-house software MAcroscopic Space Analysis (MASA). Different cases were analyzed and the results compared with experimental tests available in the literature. First, a reference concrete beam without actuators was numerically analyzed in order to calibrate and validate the employed non-linear microplane material model. Thereafter, the validated model was used for the non-linear analysis of the concrete beam with integrated fluidic actuators, with respect to different load cases. The obtained results confirm the capability of the model to reproduce the deformational behavior of the beam for all analyzed cases. A fundamental aspect is the realistic modeling of the actuators and related applied pressure. The use of a non-linear material model allows to realistically capture the possible cracking and consequent failure of the beam. It is worth mentioning that a full model validation should be extended to the long-term behavior of actuated structural elements. In future perspective, the well-established numerical framework for concrete, based on coupled 3D hygro-thermo-mechanical model, can be used to 1) investigate the performance of adaptive structural components, with respect to more complex loading conditions, e.g., cyclic; 2) perform durability analysis under exposure to different combinations of mechanical and/or environmental loading conditions.

Calculation Method for Traffic Load-Induced Permanent Deformation in Soils under Flexible Pavements

Rutting is one of the most common types of distress in flexible pavement structures. There are two fundamental methods of designing pavement structures: conventional empirical methods and analytical approaches. Many analytical and empirical design procedures assume that rutting is mostly of asphalt origin and can be reduced by limiting the vertical deformation or stress at the top of the subgrade, but they do not quantify the rutting depth itself. Mechanistic–empirical models to predict the permanent deformations of unbound pavement layers have been well investigated and are rather common in North America; however, they are not widely utilized in the rest of the world. To date, there is no generally accepted, widely recognized, and documented procedure for calculating permanent deformations and thus for determining the rutting depth in flexible pavement courses originating from the unbound granular layers. This paper presents a layered calculation method with which the deformation of soil layers (base, subbase, and subgrade courses) under flexible pavements due to repeated traffic load can be determined. In the first step, the cyclic strain amplitude is calculated using a nonlinear material model that is based on particle size distribution parameters (d50 and CU) and dependent on the mean normal stress, relative density, and actual strain level. In the second step, the HCA (High Cycle Accumulation) model is used to calculate the residual settlement of each sublayer as a function of the number of cycles. It is shown that the developed model is suitable for describing different types of subgrades and pavement cross-sections. It is also demonstrated with finite element calculations that the developed model describes both the elastic and plastic strains sufficiently accurately. The developed model can predict the settlement and rutting of pavement structures with sufficient accuracy based on easily available particle size distribution parameters without the need for complex laboratory and finite element tests.

A Numerical Analysis Model of Composite Pneumatic Formwork Considering the Stiffness Contribution of Polyurethane Layer

Pneumatic formwork is a kind of inflated fabric-polyurethane composite formwork formed by spraying polyurethane on the interior surface of the membrane. A numerical analysis model of composite pneumatic formwork considering the stiffness contribution of polyurethane is proposed to predict the structural response. The analysis model simulates the component of fabric and polyurethane with membrane elements and shell elements respectively, and Tie constraint of surface to surface is defined at the interface. A nonlinear material model for fabric is adopted considering the influence of stress ratio and loading history, and the constitutive relation of polyurethane is described in the foaming plane with different properties for tension and compression. Newton-Raphson incremental iterative method is used to solve the involved nonlinear problems. The simulation accuracy of the proposed analysis model is verified by comparing its predictions with test results about the loaddeformation response of an inflated membrane structure and the corresponding composite pneumatic formwork under horizontal loading. The numerical model is further used to investigate the influence of the thickness of polyurethane layer on the improvement of overall structural stiffness of a larger pneumatic formwork under horizontal fresh gale, and the polyurethane is proved to be beneficial for the shape-control of pneumatic formwork.

The application of an isotropic crushable foam model to predict the femoral fracture risk.

For biomechanical simulations of orthopaedic interventions, it is imperative to implement a material model that can realistically reproduce the nonlinear behavior of the bone structure. However, a proper material model that adequately combines the trabecular and cortical bone response is not yet widely identified. The current paper aims to investigate the possibility of using an isotropic crushable foam (ICF) model dependent on local bone mineral density (BMD) for simulating the femoral fracture risk. The elastoplastic properties of fifty-nine human femoral trabecular cadaveric bone samples were determined and combined with existing cortical bone properties to characterize two forms of the ICF model, a continuous and discontinuous model. Subsequently, the appropriateness of this combined material model was evaluated by simulating femoral fracture experiments, and a comparison with earlier published results of a softening Von-Mises (sVM) material model was made. The obtained mechanical properties of the trabecular bone specimens were comparable to previous findings. Furthermore, the ultimate failure load predicted by the simulations of femoral fractures was on average 79% and 90% for the continuous and discontinuous forms of the ICF model and 82% of the experimental value for the sVM material model. Also, the fracture locations predicted by ICF models were comparable to the experiments. In conclusion, a nonlinear material model dependent on BMD was characterized for human femoral bone. Our findings indicate that the ICF model could predict the femoral bone strength and reproduce the variable fracture locations in the experiments.

High-performance unsymmetric 8-node hexahedral element in modeling nearly-incompressible soft tissues

In biomechanics problems, the biological soft tissues are usually treated as anisotropic nearly incompressible hyperelastic materials, but such complicated nonlinear material models often cause challenging problems of severe volumetric locking and instabilities in numerical simulations. In this paper, the recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with different test and analytical trial functions (ATFs) is modified for the analysis of the anisotropic nearly-incompressible hyperelastic soft tissues. Unlike the original formulation, the linear analytical general solutions for anisotropic elasticity and the consistent tangent modulus are firstly employed for formulating the trial functions, and are used to construct the incremental displacement fields that result in the incremental deformation gradient. The total deformation gradient is obtained by multiplying the incremental deformation gradient by the deformation gradient, after which the Cauchy stresses can be directly calculated from a total-form constitutive equation relating to the deformation gradient. Numerical tests, including commonly used benchmarks and cardiac examples, demonstrate attractive properties of the proposed finite element formulation in modeling nearly-incompressible anisotropic hyperelastic materials. It is free of various locking and quite insensitive to mesh distortions, and provides high accuracy with faster convergence rates when compared with other existing models.

Numerical analysis, experimental tests and non-linear analytical models in the study of bent timber beams reinforced with FRP strips

The paper presents selected methods for modelling bent timber beams strengthened with fibre-reinforced polymers (FRP). The assumptions are described, and the main analytical models representing the non-linear bending behaviour of wood are shown. Based on the models presented, analytical approaches considering reinforcement in the tension zone are proposed. The problem of determining the appropriate material parameters of the wood used in analytical calculations and numerical models is discussed. The main numerical methods used in timber analyses are presented. The Hill yield criterion and the generalised Hill yield criterion are discussed in more detail. A method for retrospective estimation of material properties of wood taking into account non-linear material models and fitting the generalised Hill yield criterion is described. Experimental bending tests of technical-scale beams reinforced with composites are presented. The numerical analysis was carried out and discussed. The generalised Hill yield criterion was applied to represent the behaviour of the wood, distinguishing the different yield stresses in compression and tension. The suitability of using non-linear models and advanced strength criteria in the numerical analysis of timber elements is discussed.

Non-Linear Material Model of Ferrite to Calculate Core Losses With Full Frequency and Excitation Scaling

A material model for ferrite is presented, enabling an accurate calculation of the core losses from 100 kHz to 1000 kHz with a single set of scalar parameters over a decade of excitation current. It is based on the modelling of different material effects such as quantum tunnelling conduction between ferrite grains and atomic level magnetisation. The implications of the satisfying results of this approach on core loss modelling techniques at high frequencies are discussed.

Finite Element Investigation of Angle Ring Confinement for Clustered Large-size Stud Shear Connector in Full-Depth Precast Concrete Bridge Deck Panel

Full-Depth Precast Concrete (FDPC) bridge deck panel system, consisting of concrete deck and steel girders, has been used widely for highway and bridge construction due to rapid construction and replacement as well as in terms of economics. This system could integrate with clusters of large size headed-stud shear connectors for more significant connection, although larger composite actions were experienced. Therefore, a new angle steel ring confinement was introduced and tested by push-off samples for the most effective shear transfer. The Finite Element Analysis (FEA) of the push-off model with an in-depth investigation of non-linear concrete properties, boundary parameters, and different geometries of angle ring confinement was developed in this study. The FE models were verified with the push-off test in terms of loads, displacements, and failure stages. Nonlinear concrete material models: Concrete Damage (CD) and Drucker Prager (DP) were identified the different abilities either for predicting initial cracks, or determining maximum resistance and critical failure, respectively. The thickness of the angle and the sizes of hook bars were investigated for the most effective aspects of the angle ring confinement. The results showed comparable stiffness and load resistance for various aspects. However, compatible geometries, either 5 mm thick angles with DB12 hook bars or 10 mm angles with DB25 hook bars, were suggested. The final non-linear FEA model was reliable for comparative studies to FDPC push-off with different confinement configurations.

Developing failure criteria for laceration injury of dermal tissue

Despite its importance, there is a poor understanding of human injury tolerance to trauma generally, and more specifically understanding of the mechanics of skin penetration or laceration. The objective of this analysis is to determine the failure criteria that will allow the evaluation of the laceration risk of blunt-tipped edges within a computational modeling environment. An axisymmetric tissue finite element model was set up in Abaqus 2021 to match the experimental set-up from a previous study. The model simulated the pressing of penetrometer geometries into dermal tissue, and stress and strain outputs were evaluated at the experimental failure force. Two separate nonlinear hyperelastic material models were calibrated for the dermis to data from the literature (high and low stiffness models). For both the high-stiffness and low-stiffness skin models, the failure force appears to occur near a local maximum in the principal strain. All failures occurred after the maximum strain near or at the top surface is or above 59%, with mid-thickness strain at a similar level. The strain energy density is concentrated near the edge tip for each configuration, indicating highly localized material damage at the point of loading, and increases rapidly prior to the approximate failure force. As the edge is further compressed into the tissue, the stress triaxiality near the edge contacting point decreases towards zero. This study has identified general failure criteria for skin laceration which can be implemented in a computational model. A higher risk for laceration would be indicated with strain energy density larger than 60 mJ/mm3, dermal strain larger than 55%, and stress triaxiality below 0.1. These findings were largely insensitive to the dermal stiffness and broadly applicable across different indenter geometries. It is expected that this framework may be implemented to evaluate hazardous forces for product edges, interactions with robots, and interfaces with medical and drug delivery devices.

Equibiaxial Planar Tension Test Method and the Simulation Analysis for Hyperelastic EAP Membrane

The equibiaxial planar tension test is an important method for determining the mechanical properties of hyperplastic membranes, and it is also critical to designing an effective equibiaxial tension test rig to meet experimental accuracy requirements. However, any analysis addressing the accuracy of this test is not reported in the literature. In this paper, an equibiaxial planar tension apparatus is proposed for conducting single-corner-point tension tests on hyperelastic electroactive polymer (EAP) membranes. The experimental data were compared with those obtained from two-corner-point-fixed tension tests and fitted with nonlinear material models, and the model’s parameters were also evaluated. Finally, the widely-used finite element software ABAQUS was employed to simulate equibiaxial planar tension methods and investigate the impact of clamping mode and point number on test accuracy as well as the uniformity of overall deformation. The test results indicate that the stress-strain curves for the two tensions remain consistent across small stretch ratios. However, as the stretch ratio increases (about λ > 2.25 ) in two-corner-point-fixed tension, stress shielding may lead to a degradation of strain uniformity and result in greater stresses than single-corner-point tension. Additionally, both the three-parameter Yeoh model and the four-parameter Ogden model can provide an accurate description of the EAP membrane material. The simulation results indicate that the axial strain variation amplitudes remain below 5% within a region spanning approximately 80% of the specimen’s overall length from its center to edge and even below 1% within a region spanning 85% in the single-corner-point tension; stress inaccuracies increase with stretch ratio, while the calculated error is about 2.1% when λ = 4 in the single-corner-point tension test, which has the smallest stress error among the tests; when the number of tension points is increased, the overall deformation becomes more sufficient, and the test accuracy improves as well. The conclusions drawn from this paper will be beneficial in designing equibiaxial planar tension test rigs and analyzing their accuracy and uniformity of deformation.