Effects Of Material Nonlinearity Research Articles

Dynamic flexoelectric instabilities in nematic liquid crystals.

Electrohydrodynamic phenomena in liquid crystals constitute an old but still very active research area. The reason is that these phenomena play the key role in various applications of liquid crystals and due to the general interest of the physical community in out-of-equilibrium systems. Nematic liquid crystals (NLCs) are ideally representative for such investigations. Our article aims to study theoretically the linear NLCs dynamics. We include into consideration orientation elastic energy, hydrodynamic motion, external alternating electric field, electric conductivity, and flexoelectric polarization. We analyze the linear stability of the NLC film, determining dynamics of perturbations with respect to the homogeneous initial state of the NLC. For the purpose we compute eigenvalues of the evolution matrix for a period of the external alternating electric field. These eigenvalues determine the amplification factors for the modes during the period. The instability occurs when the principal eigenvalue of the evolution matrix becomes unity by its absolute value. The condition determines the threshold (critical field) for the instability of the uniform state. It turns out that one might expect various types of the instability, only partially known and investigated in the literature. Particularly, we find that the flexoelectric instability may lead to two-dimensionally space-modulated patterns exhibiting time oscillations. This type of the structures was somehow overlooked in the previous works. We formulate conditions needed for the scenario to be realized. We hope that the results of our work will open the door to a broad range of further studies. Of especial importance would be a comprehensive understanding of the role of various material parameters and nonlinear effects which is a key step for the rational design of NLCs exhibiting the predicted in this publication multidimensional oscillating in time patterns.

Evaluation of Material Integrity Using Higher-Order Harmonic Generation in Propagating Shear Horizontal Ultrasonic Waves.

Material nonlinearity is explored for the assessment of structural integrity. Crack-wave interactions are of particular interest. The major focus is on higher-order harmonics, generated in propagating shear horizontal (SH) waves. These harmonics are generated due to global material nonlinearity and local effects such as fatigue cracks. The theoretical background of the proposed method is explained. The method is examined using numerical simulations and experimental tests. The former involves the Local Interaction Simulation Approach (LISA), implemented for the nonlinear shear horizontal wavefield. The latter is based on a high-frequency shear excitation approach. Experimental tests are conducted using a series of beam specimens with fatigue cracks. Low-profile, surface-bonded piezoceramic shear actuators are used for excitation. The excitation frequency is selected to minimize the number of generated modes in the examined specimens. Nonlinear ultrasonic responses are collected using a non-contact laser vibrometer. The results show that higher-order harmonic generation-based on shear horizontal wave propagation-can be used for crack detection in the presence of global material nonlinearity.

Simultaneous effects of material and geometric nonlinearities on nonlinear vibration of nanobeam with surface energy effects

Simultaneous effects of material and geometric nonlinearities on nonlinear vibration of nanobeam with surface energy effects

Artificial neural network-based sequential approximate optimization of metal sheet architecture and forming process

Abstract This paper introduces a sequential approximate optimization method that combines the finite element method (FEM), dynamic differential evolution (DDE), and artificial neural network (ANN) surrogate models. The developed method is applied to address two optimization problems. The first involves metamaterial design optimization for metal sheet architecture with binary design variables. The second pertains to optimizing process parameters in multi-stage metal forming, where the discrete nature arises owing to changing tool geometries across stages. This process is highly nonlinear, accumulating contact, geometric, and material nonlinear effects discretely through forming stages. The efficacy of the proposed optimization method, utilizing ANN surrogate models, is compared with traditionally used polynomial response surface (PRS) surrogate models, primarily based on low-order polynomials. Efficient learning of ANN surrogate models is facilitated through the FEM and Python integration framework. Initial data for surrogate model training is collected via Latin hypercube sampling and FEM simulations. DDE is employed for sequential approximate optimization, optimizing ANN or PRS surrogate models to determine optimal design variables. PRS surrogate models encounter challenges in dealing with nonlinear changes in sequential approximate optimization concerning discrete characteristics such as binary design variables and discrete nonlinear behavior found in multi-stage metal forming processes. Owing to the discrete nature, PRS surrogate models require more data and iterations for optimal design variables. In contrast, ANN surrogate models adeptly predict nonlinear behavior through the activation function's characteristics. In the optimization problem of Metal Sheet Architecture for design target C, the ANN surrogate model required an average of 4.6 times fewer iterations to satisfy stopping criteria compared to the PRS surrogate model. Furthermore, in the optimization of multi-stage deep drawing processes, the ANN surrogate model required an average of 6.1 times fewer iterations to satisfy stopping criteria compared to the PRS surrogate model. As a result, the sequential global optimization method utilizing ANN surrogate models achieves optimal design variables with fewer iterations than PRS surrogate models. Further confirmation of the method's efficiency is provided by comparing Pearson correlation coefficients and locus plots.

Analytical Study of Nonlinear Flexural Vibration of a Beam with Geometric, Material and Combined Nonlinearities

This article explores the nonlinear vibration of beams with different types of nonlinearities. The beam vibration was modeled using Hamilton’s principle, and the equation of motion was solved using method of multiple time scales. Three models were developed assuming (a) geometric nonlinearity, (b) material nonlinearity and (c) combined geometric and material nonlinearity. The material nonlinearity also included both third and fourth nonlinear elasticity terms. The frequency response equation of these models were further evaluated quantitatively and qualitatively. The models capture the hardening effect, i.e., increase in resonant frequency as a function of forcing amplitude for geometric nonlinearity, and the softening effect, i.e., decrease in resonant frequency for material nonlinearity. The model is applied on the first three bending modes of the cantilever beam. The effect of the fourth-order material nonlinearity was smaller compared to the third-order term in the first mode, whereas it is significantly larger in second and third mode. The combined nonlinearity models shows a discontinuous frequency shift, which was resolved by utilizing a set of transition assumptions. This results in a smooth transition between the material and geometric zones in amplitude. These parametric models allow us to fine tune the nonlinear response of the system by changing the physical properties such as geometry, linear and nonlinear elastic properties.

Effects of Initial Small-Scale Material Nonlinearity on the Pre-Yield and Pre-Buckling Response of an Externally Pressurized Ring

The effects of initial small-scale material nonlinearity on the pre-yield and pre-buckling response of externally pressurized metallic (plane strain) perfect rings (very long cylindrical shells) is investigated. The cylindrically curved 16-node element, based on an assumed quadratic displacement field (in surface-parallel coordinates) and the assumption of linear distribution of displacements through thickness (LDT), is employed to obtain the discretized system equations. The effect of initial small-scale material nonlinearity (assumed hypo-elastic) on the deformation and stress in the pre-yield and pre-buckling regime of a very long relatively thin metallic cylindrical shell (plane strain ring) is numerically investigated. These numerical results demonstrate that the enhanced responses for metallic rings due to initial small-scale nonlinearity are significant enough to not miss attentions from designers and operators of submersibles alike.

Effects of non-linearity and thixotropy in linear amplitude sweep testing for the evaluation of self-healing of bituminous binders

Linear amplitude sweep tests have been demonstrated to have good potential in being used for the evaluation of self-healing properties of neat and polymer-modified bituminous binders. Past research works, however, have neglected the effects of material non-linearity and thixotropy. This implies that the whole material integrity loss is attributed to damage and all restoration to self-healing, thus resulting in the possible overestimate of both damage and self-healing when evaluating the fatigue performance of materials. In the study described in this paper, specific experimental and analytical methods were adopted with the purpose of separating non-linearity and thixotropy in LAS healing tests. Non-linearity was assessed by means of multiple strain sweep tests carried out to determine the material non-linear viscoelastic moduli at specific testing temperatures. Thixotropy was considered by coupling self-healing LAS testing with a purposely defined test in which loading was applied to the undamaged material after a rest period equal to that applied in self-healing tests. Obtained results were processed by means of an analytical approach based on the simplified viscoelastic continuum damage model. Quantification of self-healing included the determination of material integrity and damage parameters recovered after the rest period. Such parameters, calculated by excluding time-dependent and non-linear biasing effects, can be used as straightforward indicators of the self-healing potential of neat and polymer-modified bituminous binders. Moreover, obtained results substantiate the concept that time–temperature superposition is still applicable when non-linearity is incorporated into the simplified viscoelastic continuum damage model.

A Bilayer Method for Measuring Toughness and Strength of Dental Ceramics

The ever-increasing usage of ceramic materials in restorative dentistry necessitates a simple and effective method to evaluate flexural strength σF and fracture toughness KC. We propose a novel method to determine these quantities using a bilayer specimen composed of a brittle plate adhesively bonded onto a transparent polycarbonate substrate. When this bilayer structure is placed under spherical indentation, tunneling radial cracks initiate and propagate in the lower surface of the brittle layer. The failure analysis is based on previous theoretical relationships, which correlate σF with the indentation force P and layer thickness d, and KC with P and mean length of radial cracks. This work examines the accuracy and limitations of this approach using a wide range of contemporary dental ceramic materials. The effect of layer thickness, indenter radius, load level, and length and number of radial cracks are carefully examined. The accuracy of the predicted σF and KC is similar to those obtained with other concurrent test methods, such as biaxial flexure and 3-point bending (σF), and bending specimens with crack-initiation flaws (KC). The benefits of the present approach include treatment for small and thin plates, elimination of the need to introduce a precrack, and avoidance of dealing with local material nonlinearity effects for the KC measurements. Finally, the bilayer configuration resembles occlusal loading of a ceramic restoration (brittle layer) bonded to a posterior tooth (compliant substrate).

Effects of Material and Geometric Nonlinearities on Seismic Soil-Pile Interaction in Liquefiable Soils

Effects of Material and Geometric Nonlinearities on Seismic Soil-Pile Interaction in Liquefiable Soils

Vacuum insulated glazing (VIG) units under wind load—part 1: global deformation and stresses on the outer glass surfaces

This paper presents the first part of a study on the effect of wind loads on Vacuum Insulated Glass (VIG) units. The study provides background information on VIG and relevant Standards, explains the numerical modelling process, and discusses the implications of the results in relation to European and North American codes and Standards. The focus of the study is on vertical windows and façade installations in low-rise buildings (< 25 m) commonly found in residential buildings. The mechanical behaviour of VIG was analysed using the Finite Element Method (FEM) with respect to various design parameters such as glass pane size, glass thickness, surface pressure magnitude, and edge boundary conditions. The study analysed global deformation as well as the stresses on the outer glass surfaces. The VIG features such as pillar geometry and contact dynamics, and material non-linear effects, were explicitly modelled. In addition, monolithic glass plates were also modelled, and the FEM results of the monolithic cases were in reasonable agreement with an analytical solution obtained from linear thin plate theory. These results highlight the limit of linear behaviour in monolithic plate bending. The centre-of-pane deflection of the VIG was in good agreement with the FEM and analytical solutions of the equivalent thickness monolithic pane, for sample sizes below 800 × 800 mm. However, for larger glass sizes, a deviation was found, and the VIG exhibited a higher plate stiffness than the equivalent thickness monolithic pane. The simulations also showed that the stresses in the glass panes are highly dependent on the edge of glass boundary condition. Finally, the results demonstrated that with appropriate design choices, the VIG can satisfy the Standards requirements for wind load and glass design in both Europe and North America.

I-section stainless steel portal frames: Loading tests and numerical modelling

Austenitic stainless steel is an attractive structural material due to its high ductility, appropriate toughness, significant strain hardening and good fire resistance. Also the laser welding technology for fabrication of structural stainless steel profiles has recently become increasingly popular. However, there is still only a limited amount of experimental data on laser-welded stainless steel members. And loading tests of whole structures made of these sections have still not been published. Therefore, loading tests were performed on two austenitic stainless steel frames made of laser-welded I-sections. The frames had pinned columns and were loaded both vertically and horizontally. The objective of the loading tests was to capture the effects of material nonlinearity on the global sway behaviour of the stainless steel frames. In fact, material nonlinearity leads to a gradual loss of stiffness, which results in higher deformations and thus a higher second-order effect. The resulting load-displacement diagrams of the experiment are tabulated, allowing their further use. A numerical model of the studied frames was developed and validated on the basis of the performed experiments. Based on the elastic buckling load factor and the modified elastic buckling load factor, a large influence of material nonlinearity on second-order effect has been demonstrated.

Addressing geometric and material nonlinearities in fluid-structure interaction with the ALE-SSM framework

A novel methodology was introduced for integrating skeleton-based structural models (SSMs) with an Arbitrary Lagrangian-Eulerian (ALE) formulation to perform fluid–structure interaction (FSI) simulations (i.e., ALE-SSM). In ALE-SSM, the structural domain consists of force-based line elements, which are favored in modeling solid structures because of their computational efficiency. This paper enhances ALE-SSM to account for geometrically nonlinear and inelastic material responses of the structural domain. Geometric nonlinearity is introduced in two stages: (1) at the basic coordinate system of the force-based elements, where second-order effects stemming from the transverse element deformations are accounted for in the element flexibility matrix; and (2) at the global coordinate system, where a corotational formulation is used to perform the geometric transformation from the basic to the global coordinate system. The proposed approach for modeling geometric nonlinearity in ALE-SSM is evaluated with benchmark problems involving large deformations of beam structures positioned parallel and perpendicular to one-phase flows. Next, ALE-SSM is employed to define a new benchmark study that evaluates the effects of geometric and material nonlinearities in FSI simulations with force-based elements.

Review of Wind-Induced Effects Estimation through Nonlinear Analysis of Tall Buildings, High-Rise Structures, Flexible Bridges and Transmission Lines

The nonlinear effects exhibited by structures under the action of wind loads have gradually stepped into the vision of wind-resistant researchers. By summarizing the prominent wind-induced nonlinear problems of four types of wind-sensitive structures, namely tall buildings, high-rise structures, flexible bridges, and transmission lines, the occurrence mechanism of their nonlinear effects is revealed, providing cutting-edge research progress in theoretical studies, experimental methods and vibration control. Aerodynamic admittance provides insights into the aerodynamic nonlinearity (AN) between the wind pressure spectrum and wind speed spectrum of tall building surfaces. The equivalent nonlinear equation method is used to solve nonlinear vibration equations with generalized van-der-Pol-type aerodynamic damping terms. The elastic–plastic finite element method and multiscale modeling method are widely employed to analyze the effects of geometric nonlinearity (GN) and material nonlinearity (MN) at local nodes on the wind-induced response of latticed tall structures. The AN in blunt sections of bridges arises from the amplitude dependence of the aerodynamic derivative and the higher-order term of the self-excited force. Volterra series aerodynamic models are more suitable for the nonlinear aerodynamic modeling of bridges than the polynomial models studied more in the past. The improved Lindstedt–Poincare perturbation method, which considers the strong GN in the response of ice-covered transmission lines, offers high accuracy. The complex numerical calculations and nonlinear analyses involved in wind-induced nonlinear effects continue to consume significant computational resources and time, especially for complex wind field conditions and flexible and variable structural forms. It is necessary to further develop analytical, modeling and identification tools to facilitate the modeling of nonlinear features in the future.

Effect of Material Non-linearities on the Transient Dynamic Behavior of the Beni-Bahdel Dam in the Presence of the Dam-foundation Interaction

The current paper's goal is to investigate how dynamic interaction phenomena and material nonlinearities affect the dynamic behavior of a concrete gravity multi-arch dam in terms of maximum displacements, natural stresses, principal stresses, and Von Mises stresses when subjected to seismic excitation. Utilizing ANSYS APDL software, linear and nonlinear transient analysis using the finite element method was employed to analyze the interaction between the dam and its rock foundation. As a case study for this work, the multi-arch Beni-Bahdel dam was selected, and the seismic excitation used data from a simulated earthquake. The direct method is employed to model the interaction between the multi arch dam and the rock foundation using two approaches; the fixed base approach and the mass foundation approach. Six finite element models were performed using ANSYS code, “linear dam-fixed support”, “nonlinear dam-fixed support”, “linear dam-linear rock foundation” “nonlinear dam-linear rock foundation”, “nonlinear dam-nonlinear rock foundation” and “linear dam-nonlinear rock foundation”. The bilinear kinematic hardening model is employed to represent the nonlinearity of both dam body and rock foundation. The results obtained are compared to understand the effect of both material nonlinearities and interaction phenomenon on the dynamic behavior of the studied dam. In contrast to the nonlinearity of the rock foundation material, it is concluded that the nonlinearity of the concrete dam material has a significant impact on the behavior of the system.

Experimental investigation on the square and rectangular hollow section stainless steel portal frames

Cold-rolled hollow sections are the most commonly used stainless steel sections in the construction industry, because the production of this type of profile is the most cost-effective in smaller volumes. However, very little experimental research has been carried out so far on whole structures made of these sections. Therefore, experiments on stainless steel frames were carried out. In total, 5 portal frames made of austenitic stainless steel SHS/RHS were tested. These tests are described in detail, including the layout of auxiliary elements and measuring devices. The aim of the experiments was to capture the effects of material nonlinearity on the global behaviour of the stainless steel frames. The load–displacement diagrams are presented in tables, enabling their use for the validation of numerical models. Tensile coupon tests were carried out and parameters for common material models were determined. Numerical models of the studied frames were developed and validated using the experiments performed. These numerical simulations have been shown to be able to capture the general load–displacement response in a global, in-plane mode. Linear buckling analysis was carried out. Resulting elastic critical load factors indicated a high susceptibility of the frames to second order effects. In addition, modified elastic critical load factors were determined, showing the large influence of material nonlinearity on second order effects.

Effects of material non-linearity on the structural performance of sandwich beams made of recycled PET foam core and PET fiber composite facings: Experimental and analytical studies

This paper presents the results of experimental and analytical studies on sandwich beams subjected to three-point bending beyond their limit of proportionality. The sandwich beams were composed of polyethylene terephthalate (PET) fiber-reinforced polymer (FRP) composite facings and recycled PET (R-PET) foam core made from post-consumer plastic bottles. The study tested three R-PET core densities (70, 80, and 100 kg/m3) and compared the results to a control group with 100 kg/m3 core density and glass FRP facings. The beam geometry and testing set-up were consistent throughout the study, with 12 beams tested in total. The results showed that all specimens exhibited non-linear load–deflection behavior, resulting in developing a non-linear analytical model using decreasing secant elastic and shear moduli under increasing loads. The proposed model was validated, and a parametric analysis was performed to evaluate its mechanical performance under different conditions, including variations in span length and the thickness of the core and facing components. Additionally, the study created a novel failure mode map to predict the failure mechanism of the sandwich panels based on core density and the PET FRP facing thickness to span length ratio, considering the non-linear behavior of both components. As a result, this study provides valuable insights into using recycled materials in construction, contributing to reducing plastic waste and mitigating environmental impact.

Fibre reinforcement and stacking sequence influence on the through-thickness compression behaviour of polymer composites

A combined experimental and numerical study was performed to investigate the influence of multi-axial stress states and reinforcement type on the constitutive response of fibre reinforced epoxy polymers. The constitutive behaviour of unidirectional and cross-ply layups of carbon and glass fibre reinforced epoxy resin, IM7/8552 and S2/8552 respectively, was investigated. Prismatic short block specimens at different off-axis angles were tested under quasi-static through-thickness compression. The experiments were simulated with an enhanced non-linear material model based on shear localisation planes and pressure dependency, which represents the elastic and plastic experimental behaviour better than other formulations. The results show that the overall constitutive response is highly dependent on the fibre reinforcement type and multi-axial stress state on the mesoscale. In order to obtain an accurate description of the material behaviour, measurement aspects such as determining the correct orthotropic elastic constants, especially the Poisson’s ratios, are highlighted. Furthermore, particular focus is also drawn on important modelling aspects such as material non-linearity and pressure effects.

A two-scale thermo-mechanically coupled constitutive model for grain size- and rate-dependent deformation of nano-crystalline NiTi shape memory alloy

In this paper, a two-scale thermo-mechanically coupled constitutive model is established to predict the grain size (GS)- and rate-dependent deformation of nano-crystalline super-elastic NiTi shape memory alloy (SMA). At the mesoscopic scale, the polycrystalline representative volume element (RVE) is considered as an aggregation of individual grains. Owing to the relatively large volume fraction (VF) of grain boundary in nano-crystalline NiTi SMA, an individual grain is further considered as a composite containing the grain interior (GI) and grain boundary (GB) phases. For the GI phase, a crystal plasticity-based model accounting for the internal heat generation is developed through the fundamental laws of irreversible thermodynamics. The constraint of GB phase on the martensite transformation in the GI phase is considered by introducing a scaling law between the transformation hardening modulus (THM) and GS. Owing to its un-transformable nature and relatively high yielding stress, the GB phase is assumed to behavior constitutively linear thermo-elasticity. To evaluate the thermo-mechanical interactions among the grains, GI phase and GB phase, and obtain the overall response of the polycrystalline RVE, a double inclusion self-consistent homogenization scheme involving the material nonlinearity and thermo-mechanical coupling effect is developed in an incremental form. At the macroscopic scale, the overall thermo-mechanical responses for the specimen of nano-crystalline NiTi SMA are obtained by solving the equations of force balance, deformation compatibility, and thermodynamic equilibrium through an approximation method. Finally, considering the specific texture measured in experiments, the proposed model is validated by predicting the GS- and rate-dependent deformation of nano-crystalline NiTi SMA sheet. Furthermore, the anisotropic thermo-mechanical responses of the sheet caused by the texture are predicted and discussed.

An investigation into the transferability of dynamic elastomer dampers’ properties between different damper sizes using FEM

Elastomer dampers are used in drive systems to systematically adjust the systems’ vibration behavior. Selecting the right damper therefore requires model-based prediction of the system’s vibrations. Modelling elastomer dampers in the system context involves a high degree of complexity, since non-linear material effects in elastomers, such as the dependence of material properties on loading speed and history, make it difficult to predict the material behavior. This complexity hinders the model parameters of elastomer dampers to be determined from physical parameters such as material composition and geometric quantities. Instead, abstract models must be used that represent the material behavior phenomenologically and that are parameterized via experimental investigations on each individual damper. The diversity of variants as well as customly produced dampers mean that manufacturers and industrial applicators of elastomer dampers are confronted with disproportionately large numbers of required experiments.The aim of this work is to reduce the number of required experiments by inferring the behavior of various different elastomer dampers from experiments on a single damper. For this purpose, it is assumed that separating the influence of the damper’s geometry and the influence of the material is possible, while the geometries’ influence can be predicted by abstracting parts of the phenomenological model via a simple FE model. The method is exemplarily demonstrated by predicting the transmission behavior of two torsional loaded elastomer couplings from experiments on a test specimen. The method is validated by comparing predicted and measured dynamic stiffness of the investigated couplings.

Experimental and numerical analysis of hyperelastic plates using Mooney-Rivlin strain energy function and meshless collocation method

In this research, the flexural behavior of a hyperelastic plate made of silicone under uniformly distributed loading was investigated. The displacements and strains were formulated using the first-order shear deformation plate theory (FSDPT). The right Cauchy-Green tensor and Mooney-Rivlin strain energy function were employed to formulate hyperelastic silicone plate governing equations. The strong-form of the governing equations of the silicone plate using Mooney-Rivlin strain energy function and Euler-Lagrange relations were derived for the first time. In the governing equations, the effects of geometrical and material nonlinearity effects were considered simultaneously. The meshless collocation method (MCM) and thin-plate spline radial basis function were utilized to discretize the governing equations. The arc-length continuation algorithm was also used for analyzing the system of non-linear equations. MCM results were compared to those of the experimental test to validate the results of the meshless method. For this purpose, a square silicone plate with simply supported boundary conditions under uniformly distributed loading was investigated via the digital image correlation (DIC) technique. According to the obtained results, the MCM based on radial basis function is an adequate method for non-linear analysis of hyperelastic plates with Mooney-Rivlin strain energy function under uniformly distributed loading.