Linear Material Model Research Articles

Multi-Step Relaxation Characterization and Viscoelastic Modeling to Predict the Long-Term Behavior of Bitumen-Free Road Pavements Based on Polymeric Resin and Thixotropic Filler.

Asphalt pavements are fundamental to modern transportation infrastructure, requiring elasticity, firmness, and longevity. However, traditional asphalt, based on bitumen, faces several limitations. To improve pavement performance, polymer resins are being used to substitute bitumen and improve requirements. Therefore, a deep understanding of the material behavior is required. This study presents the analysis of the relaxation behavior of a poly(methyl methacrylate)-based pavement and the influence of mineral fillers. An approach using a linear elastic-viscoelastic material model was selected based on evidence and validated across the linear and nonlinear deformation range. The results reveal no influence of the mineral fillers on the relaxation behavior. The presented modification of the linear elastic and viscoelastic modeling reveals accurate results to predict long-term pavement performance. This approach offers a practical method for forecasting asphalt behavior. Further research is needed to incorporate deformation behavior into the model.

Comparison of a quasi Newton method using Broyden’s update formula and an adjoint method for determining local magnetic material properties of electrical steel sheets

PurposePerforming accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various manufacturing steps, e.g. heat treatment or cutting techniques, the magnetic material properties can strongly vary locally, and the assumption of homogenized global material parameters is no longer feasible. This paper aims to present the general methodology and two different solution strategies for determining the local magnetic material properties using reference and simulation data.Design/methodology/approachThe general methodology combines methods based on measurement, numerical simulation and solving an inverse problem. Therefore, a sensor-actuator system is used to characterize electrical steel sheets locally. Based on the measurement data and results from the finite element simulation, the inverse problem is solved with two different solution strategies. The first one is a quasi Newton method (QNM) using Broyden's update formula to approximate the Jacobian and the second is an adjoint method. For comparison of both methods regarding convergence and efficiency, an artificial example with a linear material model is considered.FindingsThe QNM and the adjoint method show similar convergence behavior for two different cutting-edge effects. Furthermore, considering a priori information improved the convergence rate. However, no impact on the stability and the remaining error is observed.Originality/valueThe presented methodology enables a fast and simple determination of the local magnetic material properties of electrical steel sheets without the need for a large number of samples or special preparation procedures.

A computational approach to modeling flow-induced large deformation of thin-walled compliant vessels

We present a computational method capable of modeling 3D flow-induced deformation of thin, highly compliant, hyperelastic vessels conveying viscous, inertial fluid. The method can uniformly consider vessel extension and collapse. Very large inflation, transient deformation, complex flow features as well as highly complex buckling shapes are well resolved by this method. The methodology combines finite volume and spectral methods for fluid motion, finite element method for structural mechanics of the vessel wall, and the immersed boundary method for two-way coupling between the wall and fluid. A hybrid of the continuous forcing and the ghost node methodologies capitalizing on the strengths of each is developed. The method avoids the surface instability encountered with the continuous forcing methods, as well as the need for domain remeshing as required in the iterative and partitioned approaches. The vessel wall can follow linear or nonlinear (strain softening and hardening) material models, and the fluid inertia can vary over a wide range. We demonstrate the versatility of the method by considering vessel inflation and collapse with large, complex, and transient deformation. Remarkable differences in vessel inflation at low versus moderate inertia are observed; this includes steady versus oscillatory motion, emergence of flow recirculation and pressure wave reflection which are well resolved. For the collapsing vessels, well-defined shapes with different buckling modes as well as highly complex buckling with fine surface folds are predicted. Additionally, a second-order correction to the well-known law of Laplace is developed and used to validate our computational results for vessel inflation.

Topology Optimization and Efficiency Evaluation of Short-Fiber-Reinforced Composite Structures Considering Anisotropy

The current study aims to develop a methodology for obtaining topology-optimal structures made of short fiber-reinforced polymers. Each iteration of topology optimization involves two consecutive steps: the first is a simulation of the injection molding process for obtaining the fiber orientation tensor, and the second is a structural analysis with anisotropic material properties. Accounting for the molding process during the internal iterations of topology optimization makes it possible to enhance the weight efficiency of structures—a crucial aspect, especially in aerospace. Anisotropy is considered through the fiber orientation tensor, which is modeled by solving the plastic molding equations for non-Newtonian fluids and then introduced as a variable in the stiffness matrix during the structural analysis. Structural analysis using a linear anisotropic material model was employed within the topology optimization. For verification, a non-linear elasto-plastic material model was used based on an exponential-and-linear hardening law. The evaluation of weight efficiency in structures composed of short-reinforced composite materials using a dimensionless criterion is addressed. Experimental verification was performed to confirm the validity of the developed methodology. The evidence illustrates that considering anisotropy leads to stiffer structures, and structural elements should be oriented in the direction of maximal stiffness. The load-carrying factor is expressed in terms of failure criteria. The presented multidisciplinary methodology can be used to improve the quality of the design of structures made of short fiber-reinforced composites (SFRC), where high stiffness, high strength, and minimum mass are the primary required structural characteristics.

Topology optimization for maximizing buckling strength using a linear material model

Buckling resistance has gained significant attention in topology optimization due to its profound implications for structural designs. Despite considerable research on buckling-constrained topology optimization, maximizing the critical buckling load factor (BLF) still remains a challenging topic. In this study, an innovative algorithm that utilizes a linear material interpolation scheme is introduced to maximize the buckling resistance of structures. The linear material model offers several advantages, such as obviating the need to select the penalization schemes and penalty values, facilitating straightforward sensitivity analysis, and removing the ambiguous physical meaning of penalization for the stress stiffness matrix. The accuracy of the linear material model for buckling analysis is systematically examined, and the avoidance of stress singularities in low-density regions is investigated. The effectiveness and efficiency of the proposed approach are supported by four buckling optimization design examples, which also demonstrate substantial improvements compared to the existing algorithms.

Examination of compressive and flexural behaviors of acrylonitrile-butadiene-styrene filled with hemp fiber particles

Effects of the addition of hemp fiber particles on the compressive and flexural behaviors of an industrially important amorphous thermoplastic, Acrylonitrile-Butadiene-Styrene (ABS), were investigated for the first time in this study. Particles with a size of 67–500 μm were first extracted from 10% NaOH alkaline-treated hemp fibers, and then incorporated into ABS at three various weight ratios (1wt%, 5wt% and 10wt%). Compression and three-point bending tests results revealed that both the compressive and flexural modulus of ABS increase with increasing particle content, but its compressive post-yield and flexural strengths decrease as enhancing particle content. The test results also showed that increasing particle content results in a significant improvement in the compressive modulus of ABS, but a slight enhancement in its flexural modulus. The notch-impact test results revealed that the impact strength of ABS is adversely affected by the incorporation of hemp fiber particles. The FT-IR (Fourier Transform Infrared Spectroscopy) analysis results indicated that mechanical bonding is formed between matrix and natural particles rather than chemical bonding. The SEM (Scanning Electron Microscopy) results put forth that the observed decrease in both the compressive post-yield and flexural strength is mainly due to the lack of strong mechanical bonding between ABS and particles. The three-point bending test data of the materials were satisfactorily reproduced using the linear Drucker-Prager material model in Abaqus engineering software.

Identification of the extended standard linear solid material model by means of experimental dynamical measurements

A novel algebraic procedure for the non-parametric identification of the material model by means of dynamical test measurements is proposed. An extended Standard Linear Solid (SLS) material model is taken into account to model the material linear visco-elastic behavior. It consists of the series arrangement of fractional Kelvin model elements adopting real parameters and integer and non-integer order time differential operators, and of hysteretic Kelvin model elements adopting complex parameters and integer order time differential operators. Hysteretic Kelvin model elements are introduced to take account of the material hysteretic behavior. The material E(j⋅ω) complex modulus, is analytically modeled as the ratio of pseudo polynomials (non-integer power terms) in the j⋅ω Fourier variable. A multi-step, iterative, material model identification technique is here proposed to identify the unknown polynomial coefficients and the non-integer exponent values starting from E(j⋅ω) material discrete estimates from input-output dynamical measurements made on a beam specimen at different ω frequency values. Computational, nonphysical SLS elements resulting from the application of the identification procedure can be found and eliminated, so that a low order optimal model result. Some results obtained by applying the proposed identification technique with real experimental measurements are shown and discussed.

Numerical modeling of the erosion of alumina particulate reinforced epoxy-matrix composites: Material removal mechanisms including reinforcement fracture

Sacrificial composite coating layers are used to protect surfaces from solid particle erosion due to the high-speed impact of particles. Epoxy-based coatings are easily reapplied and are sometimes mixed together with a reinforcing phase consisting of ceramic particles in an attempt to lower the erosion rate. Previous experiments have indicated that different erosion mechanisms can occur depending on, amongst other things, the relative sizes of the reinforcement and abrasive particles. In the present work, a coupled finite element/smoothed particle hydrodynamics (FE/SPH) decomposition method was used to model the erosion of an epoxy-matrix composite reinforced with relatively large 0.5 mm alumina (Al2O3) spheres, by irregularly shaped 152 μm silicon carbide (SiC) abrasives. 5600 overlapping impacts of SiC particles were modeled on carefully chosen representative volumes of the particulate reinforced composite. A Johnson–Holmquist material model (JH-2) with dynamic tensile strength was used to model the particulate phase, while the epoxy was modeled using a piecewise linear plasticity material model coupled with a Cowper-Symonds strain and strain rate hardening relationship. Realistic abrasive particle morphologies were modeled, based on measurements of the abrasive powder used in the verifying experiments. The erosion rates at both perpendicular and oblique incidence were successfully predicted to within ∼10% of those measured. Both the model and experiments showed that the erosion resistance of the composite was higher than the epoxy at oblique incidence; however, at perpendicular incidence, even though the erosion rate of the reinforcements (0.67 ± 0.04 mm3/g) was lower than that of the epoxy (1.27 ± 0.1 mm3/g), the erosion rate of the composite was slightly higher (∼1.38 ± 0.16 mm3/g) than that of the epoxy. It was shown that this occurred because, as the epoxy eroded in a typically ductile fashion with cutting and ploughing mechanisms, the reinforcements fractured leading to an approximately level eroded surface at any instant. The model was able to capture these material removal mechanisms which were also confirmed using non-contact profilometry of the eroded surfaces.

A new hyperelastic lookup table for RT-DC.

Real-time deformability cytometry (RT-DC) is an established method that quantifies features like size, shape, and stiffness for whole cell populations on a single-cell level in real-time. A lookup table (LUT) disentangles the experimentally derived steady-state cell deformation and the projected area to extract the cell stiffness in the form of the Young's modulus. So far, two lookup tables exist but are limited to simple linear material models and cylindrical channel geometries. Here, we present two new lookup tables for RT-DC based on a neo-Hookean hyperelastic material numerically derived by simulations based on the finite element method in square and cylindrical channel geometries. At the same time, we quantify the influence of the shear-thinning behavior of the surrounding medium on the stationary deformation of cells in RT-DC and discuss the applicability and impact of the proposed LUTs regarding past and future RT-DC data analysis. Additionally, we provide insights about the cell strain and stresses, as well as the influence resulting from the rotational symmetric assumption on the cell deformation and volume estimation. The new lookup tables and the numerical cell shapes are made freely available.

Experimental and Numerical Investigation of the In-Plane Compression of Corrugated Paperboard Panels

Finite element analysis (FEA) has been proven as a useful design tool to model corrugated paperboard boxes, and is capable of accurately predicting load capacity. The in-plane deformation, however, is usually significantly underpredicted. To investigate this discrepancy, a panel compression test jig, that implemented simply supported boundary conditions, was built to test individual panels. The panels were then modelled using non-linear FEA with a linear material model. The results show that the in-plane deformation was still underpredicted, but a general improvement was seen. Three discrepancies were identified. The first was that the panels showed an initial region of low stiffness that was not present in the FEA results. This was attributed to imperfections in the panels and jig. Secondly, the experimental results reported a lower stiffness than the FEA. Applying an initial imperfection in the shape of the first buckling mode shape was found to reduce the FEA stiffness. Thirdly, the panels showed a decrease in stiffness near failure, which was not seen in the FEA. A bi-linear material model was investigated and holds the potential to improve the results. Box compression tests were performed on a Regular Slotted Container (RSC) with the same dimensions as the tested panel. The box displaced 13.1 mm compared to 3.5 mm for the panel. There was an initial region of low stiffness, which accounted for 7 mm of displacement compared to 0.5 mm for the panels. Thus, box complexities such as horizontal creases should be included in finite element (FE) models to accurately predict the in-plane deformation, while a bi-linear (or any other non-linear) material model may be useful for panel compression.

Topological design of strain sensing nanocomposites

High-performance piezoresistive nanocomposites have attracted extensive attention because of their significant potential as next-generation sensing devices for a broad range of applications, such as monitoring structural integrity and human performance. While various piezoresistive nanocomposites have been successfully developed using different material compositions and manufacturing techniques, current development procedures typically involve empirical trial and error that can be laborious, inefficient, and, most importantly, unpredictable. Therefore, this paper proposed and validated a topological design-based methodology to strategically manipulate the piezoresistive effect of nanocomposites to achieve a wide range of strain sensitivities without changing the material system. In particular, patterned nanocomposite thin films with stress-concentrating and stress-releasing topologies were designed. The strain sensing properties of the different topology nanocomposites were characterized and compared via electromechanical experiments. Those results were compared to both linear and nonlinear piezoresistive material model numerical simulations. Both the experimental and simulation results indicated that the stress-concentrating topologies could enhance strain sensitivity, whereas the stress-releasing topologies could significantly suppress bulk film piezoresistivity.

Investigation of Structural Performance of Historical Amasya Hundi Hatun Bridge

Abstract Bridges have been built by many civilizations throughout history to connect the two banks of a river. There have been numerous historical bridges built in Anatolian geography because the area has served as a bridge to various civilizations. This study performed a structural evaluation of the Hundi Hatun Bridge in Amasya, Turkey. First, a 3D model of the bridge was created in a digital environment, and then static and dynamic analyses were performed with software using the ANSYS Workbench finite element method. The bridge demonstrated sufficient dimensions under static loads and in the modal analysis, although the arches were subject to translational movement in the flow direction of the river. In addition, linear and nonlinear material models were used to perform dynamic analyses, including bridge seismic analyses. The linear material model indicated that the bridge is safe, while the nonlinear material model revealed that damage may occur, especially at the abutments and peak regions of the bridge. Moreover, the bridge arch flatness was determined to be a very important parameter. The results of this study can be used to guide future restoration efforts.

Natural Frequencies of Beams with Axial Material Gradation Resting on Two Parameter Elastic Foundation

Free vibration analysis is carried out on axially inhomogeneous beams resting on Winkler-Pasternak elastic foundation. The material properties of the beam like Young’s modulus, modulus of rigidity and material density are considered to be varying along the length direction following constant, linear and exponential material models. The beam is subjected to different combinations of clamped and simply supported boundary conditions. The formulation is based on Timoshenko beam theory and energy method along with Hamilton’s principle is used to derive the governing equations. The effect of material gradation and the 2 parameters of elastic foundation on the natural frequencies are studied in detail. The present results are validated by comparing them with established ones and satisfactory matching is observed.
 HIGHLIGHTS
 
 Free vibration behavior of axially functionally graded beams in investigated
 Three different material models and three boundary conditions are considered
 Effect of two parameter elastic foundation is considered
 Timoshenko beam theory and Rayleigh Ritz method are employed
 It is found that the stiffness of elastic foundation significantly affects the natural frequency of the beam
 
 GRAPHICAL ABSTRACT

Investigations on Stresses and Displacements of Annular Rotating Disc using FEA

Engineering components that can be modeled as a rotating disc include the rotor of a turbine engine, saw blades, grinding wheels, and computer magnetic recording disks etc. The rotating disc is subjected to centrifugal force which tends to pull the disc in radial direction, introduces large stresses and displacements on the disc. Further the disc is mounted on a shaft by interference fit. The stresses and displacements of the rotating disc are estimated for potential boundary conditions by building a finite element model using ANSYS. The disc is meshed using SOLID45 elements by taking the rotating disc to be 3D cyclic symmetric model. The contact simulation is done for shaft and disc using surface to surface contacts in ANSYS. The linear isotropic material model is used.
 The model creation for the given dimension with the required material properties is done by APDL (Ansys Parametric Design Language) macro. The user inputs the dimensions of the disc in the macro, which takes care of the model preparation, mesh generation, applying boundary conditions, solution and post processing for the load case. This gives flexibility to change the parameters and material properties according to user specification and saves time for finite element model preparation.

Finite element derived femoral strength is a better predictor of hip fracture risk than aBMD in the AGES Reykjavik study cohort.

Hip fractures associated with a high economic burden, loss of independence, and a high rate of post-fracture mortality, are a major health concern for modern societies. Areal bone mineral density is the current clinical metric of choice when assessing an individual's future risk of fracture. However, this metric has been shown to lack sensitivity and specificity in the targeted selection of individuals for preventive interventions. Although femoral strength derived from computed tomography based finite element models has been proposed as an alternative based on its superior femoral strength prediction ex vivo, such predictions have only shown marginal or no improvement for assessing hip fracture risk. This study compares finite element derived femoral strength to aBMD as a metric for hip fracture risk assessment in subjects (N=601) from the AGES Reykjavik Study cohort and analyses the dependence of femoral strength predictions and classification accuracy on the material model and femoral loading alignment. We found hip fracture classification based on finite element derived femoral strength to be significantly improved compared to aBMD. Finite element models with non-linear material models performed better at classifying hip fractures compared to finite element models with linear material models and loading alignments with low internal rotation and adduction, which do not correspond to weak femur alignments, were found to be most suitable for hip fracture classification.

Modeling a Symmetrically-Notched Continuum Neurosurgical Robot With Non-Constant Curvature and Superelastic Property

A neurosurgical robot with 3-dimensional (3D) distal manipulation can increase instrument workspace for reaching peripheral regions of intracranial lesions to achieve complete lesion removal and minimal brain manipulation in a keyhole procedure. In this work, we designed a Nitinol-based symmetrically notched continuum robot based on the neurosurgical clinical constraints. A mechanics model is developed for the robot using a second order differential equation that exploits the shearing force formulation based upon the Euler <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-$</tex-math></inline-formula> Bernoulli moment-curvature equation. It affords non-constant curvature analysis, and integrates the piecewise linear material model with three stages that closely approximates the nonlinear superelastic property of Nitinol. A solution was introduced to this complex mechanics model based on the fourth order Runge-Kutta method with variable transformation, and an iterative approach. Comparison with the experimental data using our proposed model shows its high modeling accuracy in terms of the bending angle and tip position for a single symmetric notch bending as well as 2D bending motion of the robot. The significantly improved accuracy over previous models justifies the added complexity of our modeling approach and could better guide the determination of the notch parameters during robot design.

Mechanical buckling can pattern the light-diffracting cuticle of Hibiscus trionum.

Many species have cuticular striations that play a range of roles, from pollinator attraction to surface wettability. In Hibiscus trionum, the striations span multiple cells at the base of the petal to form a pattern that produces a type of iridescence. It is postulated, using theoretical models, that the pattern of striations could result from mechanical instabilities. By combining the application of mechanical stress with high-resolution imaging, we demonstrate that the cuticle buckles to create a striated pattern. Through mechanical modeling and cryo-SEM fractures, we show that the cuticle behaves like a bilayer system with a stiff film on a compliant substrate. The pattern of buckling aligns with the direction of the stress to create a larger-scale pattern. Our findings contribute to the understanding of the formation of tissue-wide patterns in living organisms.

Behaviour and design of duplex stainless steel CHS stub columns at elevated temperature

AbstractThis paper investigates the behaviour and design of duplex stainless steel stub columns with a circular hollow cross‐section (CHS) at elevated temperature. A numerical model is developed to supplement the limited number of test results available in the literature. Following validation, the numerical approach is employed to gain an understanding of the critical behavioural characteristics which have not previously been studied. In addition, the paper considers and extends the continuous strength method (CSM) to include duplex stainless steel for CHS stub columns in fire. This approach employs a base curve linking the cross‐sectional resistance to the deformation capacity and is implemented herein using an elastic, linear hardening material model. The cross‐sectional resistances obtained from the CSM are compared with those from the numerical analysis, as well as with the standardised procedures in the European, American and Australia/New Zealand design standards. It is demonstrated that the proposed design method can lead to more accurate and less scattered strength predictions compared with current design codes.

Finite Element Stress Analysis of PEEK, Glass Fiber and Zirconia Post-Core Sys-tems in Maxillary Central Incisor

Objective: This study aims to analyze structural strength features (such as deformation and stress distributions) of polyether ether ketone (PEEK), glass fiber and zirconia post-core systems utilized in maxillary central incisor roots by means of finite element analysis (FEA).&#x0D; Material and Method: The main geometry of maxillary central incisor considered in this study was obtained using an intraoral scanner. Other sub-components were modelled in a parametric computer aided design software based on the data obtained from the literature. Glass fiber, PEEK and zirconia were defined as post materials. 100 N force was applied with 45° angle on the palatal surface of veneered tooth in the FEA set up. The FEA was solved with linear material model and static linear loading assumptions through a commercial FEA code. Visuals and numerical results related to equivalent stress (Von Mises) and deformation distributions were interpreted.&#x0D; Results: Maximum equivalent stress value of 32.76 MPa was calculated at the PEEK post-core. The maximum values for glass fiber and zirconia posts were 0.80 MPa and 21.17 MPa, respectively. Maximum equivalent stress values at the tooth roots in the glass fiber, zirconia and PEEK posts were 72.79 MPa, 69.01 MPa and 58.22 MPa respectively.&#x0D; Conclusion: The stress magnitude experienced at the PEEK post-cores on the root was lower than glass fiber post and zirconia post. Regarding to this, although, it may be concluded that PEEK may reduce the complications that require tooth extraction in clinical practice, further researches are suggested including clinical trials.

Load effects in reinforced concrete beam bridges affected by alkali–silica reaction—Constitutive modelling including expansion, cracking, creep and crushing

Material modelling, from the micro to the macro level, of concrete affected by alkali–silica reaction (ASR) has been devoted a lot of research. However, the application of the material models in structural analyses of reinforced concrete (RC) structures, showing the structural implications/consequences of ASR, has got little attention in the literature. This paper aims to show the relevance of the constitutive model on the calculated load effects—induced by ASR—in statically indeterminate beam structures. For the purpose of the study, a three-span RC beam, inspired by a real bridge in Norway, is analysed. The RC beam is modelled using Euler–Bernoulli beam theory, and numerical solutions are obtained with the finite element method. The effects of ASR on the concrete are accounted for in an expansion based (macro) constitutive model, which also accounts for cracking, creep and compressive non-linearity. In this way, ASR gives an imposed deformation similar to thermal dilation and shrinkage, for which structural effects have been widely studied. As imposed strain gradients tend to cause higher load effects than uniform strains, the effect of ASR gradients, owing to e.g. a moisture gradient, is addressed.It is shown that linear structural analyses (using a linear material model), give conservative results (the greatest load effects) when an ASR strain gradient is imposed. Among the non-linear material effects investigated, it is shown that stress dependent ASR expansion and concrete cracking are important to consider. The stress dependency of the ASR expansion is shown to have a smoothing effect on the imposed ASR strain field, and as a result, reduces the load effects induced by ASR, while cracking results in crack/plastic hinges releasing the stresses in the system.