Force-displacement Curves Research Articles

Analytical modeling of a device for vibration isolation and energy harvesting using simply-supported bi-stable hybrid symmetric laminate

The bi-stable hybrid symmetric laminate (BHSL) has been investigated for vibration isolation and energy harvesting, by taking advantage of its bi-stable characteristic. A device using simply-supported BHSL is proposed to integrate these two functions. This device is called the quasi-zero-stiffness (QZS) vibration isolator with a piezoelectric element (PE). An equivalent theoretical model is developed based on the restoring force-displacement curve of BHSL. The approximate analytical solutions and direct numerical solutions are obtained by the harmonic balance method and the Runge-Kutta method, respectively. Displacement transmissibility is utilized to quantify the vibration isolation performance of this vibration isolator. The influences of the excitation amplitude, the length of BHSL, the width of BHSL and the load resistance are analyzed. The results show that adjusting these parameters can improve the vibration isolation performance and energy harvesting performance. The QZS vibration isolator with PE achieves the goal of higher power density under a low-frequency and low-amplitude excitation and simultaneously has a good vibration isolation performance.

Research on stress performance of universally wrapped assembled joints of lattice wind power tower with concrete-filled steel tube

With the control parameters of the wall thickness of the ball table and the thickness of the pressure plate of the ball table, four universal wrapped assembled joint models were designed for the research of stress performance via static loading test. The failure mode of the joint, the axial force–displacement curve of the web member, the equivalent stress distribution of the ball table and the pressure plate of the ball table were analyzed, and the ABQAUS finite element software was used for the analysis of parameter expansion of the specimen. The research results show that the failure modes of universally wrapped assembled joints can be divided into the buckling failure of the ball table and the strength failure of the material. The wall thickness of the ball table is the key parameter affecting the failure mode of the joints, and the thickness of the pressure plate of the ball table is the crucial parameter influencing the ultimate bearing capacity of the joints. The maximum equivalent stress of the pressure plate and the ball table at compression zone for all the joints is occurred at the side squeezed by the bolt ball, and the growth rate of the equivalent stress for the ball table at compression zone is more uniform than that at tension zone. According to the finite element analysis results, when the wall thickness of the ball table is greater than 7 mm, the thickness of the pressure plate of the ball table is greater than 16 mm, the growth rate of the ultimate bearing capacity of the joint is significantly decreased, therefore, it is recommended to use the wall thickness of 7 mm and the pressure plate thickness of 16 mm in the actual design of the project.

Experimental and two-scale numerical studies on the behavior of prestressed concrete-steel hybrid wind turbine tower models

Prestressed concrete-steel hybrid (PCSH) wind turbine tower has been recognized as an efficient alternative to traditional steel tube supporting towers for wind farms in harsh sites such as mountain regions. To investigate the global and local mechanical behavior including failure patterns of a full scale PCSH wind turbine towers, an experimental study on a substructure of a scaled PCSH tower is carried out firstly. Then, a material subroutine for three-dimensional (3D) fiber beam elements suitable for implicit analysis on the mechanical behavior of the substructure of the scaled PCSH tower is developed. A two-scale numerical model of the substructure of the scaled PCSH wind turbine tower employing the developed 3D fiber beam elements and solid elements is developed. The accuracy and efficiency of the developed two-scale numerical model for the behavior simulation of the substructure of the scaled PCSH wind turbine tower is illustrated by comparing the numerical results with the experimental measurements. Additional comparison of the simulation results using the developed two-scale numerical model is made with them of a model using sole 3D fiber beam elements and a model using sole solid elements, respectively. Results show that the force–displacement curve determined with the developed two-scale model is close to the test result and coincident well with that of the two models using 3D fiber beam elements and the solid elements. The developed two-scale model can describe the global behavior, the local failure patterns and the stress distribution of the tested specimen accurately with improved simulation efficiency. Finally, the validated two-scale modelling approach is employed to analyze the static behavior, modal parameter, and fatigue of the optimized full-scale PCSH wind turbine tower previously developed by the authors. The simulation results show that the two-scale model can reflect the stress of the PCSH wind turbine tower at the critical position as well as the global mechanical behavior with higher computational efficiency. The fiber beam model can be used for predicting only global, but not local, behavior.

Application of a Genetic Algorithm for the Optimal Calibration of Hysteretic Models

Background: Recent computing improvements have allowed a considerable use of numerical models to predict phenomena concerning various topics. In particular, considering the field of civil engineering, the possibility of having greater computational capabilities has guaranteed to explore both the global and local behaviour of buildings with greater attention and precision so that currently, many software programs allow modelling different structural components with high accuracy. Objective: One of the aspects of interest concerns the calibration of phenomenological laws to model the mechanical behaviour of specific structural members, devices or connections. With this in mind, many efforts have recently been dedicated to solving this problem by implementing computational codes called “Genetic Algorithms”, which provide optimal configurations of parameters following procedures that emulate Darwin’s theory of evolution. However, generally, these algorithms are encoded in C++ formats, which are difficult to be modified basing on the needs of the users. With this in mind, the present work's novelty consists of implementing a Genetic Algorithm that, starting from the knowledge of assigned hysteretic curves, allows their modelling through an appropriate calibration of the parameters of the “hysteretic” uniaxialmaterial element of the OpenSees software. In particular, the originality of the code proposed in this paper is its development in the Matlab environment, which is more easily editable and more flexible to customers' specific needs than traditional C++ compilers, such as MultiCal, a calibration software already available in research. Methods: Genetic Algorithms are instructions through which it is possible to reach the optimal calibration of mathematical models according to a procedure that conceptually refers to the evolutionary process of living species. Results: The proposed GA has been validated against MultiCal tool by calibrating 44 force-displacement hysteretic curves obtained from finite element simulations relating to the cyclic behaviour of connections between circular hollow section profiles and passing-through plates subjected to displacement histories in the axial direction. Conclusion: The results have shown that the proposed algorithm calibrates the known responses with acceptable accuracy, in line with or even better than the outcomes provided by MultiCal.

A double-phase field method for mixed mode crack modelling in 3D elasto-plastic solids with crack-direction-based strain energy decomposition

Crack-direction-based decomposition of elastic strain energy could effectively control the propagation of tensile and shear cracks in a phase field modelling context. The objective of the proposed double-phase field model is to extend the crack-direction-based decomposition strategy from 2D brittle fracture to complex mixed-mode crack modelling in a 3D setting, with plastic deformation incorporated. Both effective (undamaged) stress and plastic strain are split in the crack-orientation-based coordinate system. The decomposed tensile/shear stress contribute to tensile/shear damage evolution, respectively. The plastic contribution is coupled by relating the decomposed tensile/shear plastic strain to the corresponding tensile/shear crack energy release rates. Crack surface normal direction, represented by two orientation variables in 3D spatial domains, is determined by the F-criterion. The proposed model is implemented via ABAQUS subroutines with a staggered scheme for two phase field variables and crack direction. The simulation of a single-edge notch specimen under shear loading demonstrates that the ratio between shear and tensile crack energy release rates plays a significant role in the crack mode and mechanical response. Numerical results of a group of uniaxial tension, simple shear and tension shear specimens show good agreement with the experimental data in terms of the force–displacement curve and crack path, exhibiting the validity of the proposed model for capturing different crack modes. This model has also been proven effective for complex 3D problems via the third Sandia Challenge example.

Dynamic Response and Damage Accumulation of Laminated Composites under Repeated Low-Velocity Impacts.

The mechanical response and damage accumulation of carbon-fiber-reinforced composite laminates subjected to repeated low-velocity impacts were experimentally investigated. The repeated impact tests were conducted on [902/-452/02/452]S quasi-isotropic and [902/02]2S cross-ply composite laminates under 16.8 J impact energy, respectively. For each impact, impact responses such as force-time, force-displacement and energy-time curves were recorded. The trends of peak force, maximum central displacement, energy absorption rate and bending stiffness with the increasing impact number were summarized, and the maximum number of repeated impacts corresponded to the occurrence of penetration events. The results showed that the delamination initiation, fiber breakage and penetration were the three typical characteristics describing the damage evolution of the repeated impacts. The damage accumulation of both the laminates was characterized by employing appropriate damage indices. By contrast, the quasi-isotropic laminates had higher impact resistance and damage tolerance, and their damage accumulation was relatively slower.

Cyclic Buckling Characterization of an Individual MWCNT Using Quantitative In Situ TEM Axial Compression.

Carbon nanotubes (CNTs) are extremely conductive and flexible, making them ideal for applications such as flexible electronics and nanoelectromechanical systems. However, in order to properly apply them in such devices, their long-term durability must be assessed. In the present study, we demonstrate cyclic loading of a thick MWCNT (175 nm) under axial compression, observed in situ under a transmission electron microscope (TEM). The force was applied via controlled displacement, while real-time TEM videos of the deformation process were gathered to produce the morphological data. The in situ observations combined with force-displacement curves revealed the onset of buckling instabilities, and the elastic limits of the tube were assessed. The MWCNT retained its original structure even after 68 loading-unloading cycles, despite observed clues for structural distortions. The stiffness of the tube, calculated after each loading cycle, was in a 0.15 to 0.28 TPa range-comparable to the literature, which further validates the measurement set-up. These in situ tests demonstrate the resilience of CNTs to fatigue which can be correlated with the CNTs' structure. Such correlations can help tailoring CNTs' properties to specific applications.

Seismic behavior of partially grouted masonry shear walls containing openings: Experimental testing

This article presents an experimental study aimed at understanding the effect of openings on the seismic response of partially grouted reinforced masonry (PG-RM) walls. For this purpose, four full-scale PG-RM walls with different opening sizes were built and tested under the combined action of constant axial compression and cyclic lateral loading. All the specimens had the same external dimensions. The effect of openings was assessed in terms of wall hysteresis and force–displacement curves and the quantification of different seismic parameters such as shear capacity, degradation of lateral stiffness, energy dissipated, equivalent viscous damping ratio, and displacement ductility. A 2D Digital Image Correlation (DIC) system was implemented to monitor principal strain fields and cracking patterns during the tests. The paper also includes the assessment of the shear capacity of the tested walls according to three existent approaches developed for in-plane shear panels, which rely on the definition of an effective height of piers.The results indicate that the shear capacity of the walls decreased when the aspect ratio of the piers increased. From DIC analysis results, it was observed that damage extended beyond piers also covering spandrels and that directionality of shear loads played a fundamental role in the damage development. Therefore, the identification of the pier’s effective height and direction of seismic loads should be incorporated into the estimation of the shear capacity. Finally, the performance of the selected shear expressions and different approaches to estimate the effective height of the piers was evaluated. It was concluded that the most accurate approach was to define an effective piers height according to Augenti (2006)’s proposal using the Calderón et al. (2022) shear expression to assess piers’ lateral resistance.

Simulation Techniques for Thin-Walled Circular Tubes

Finite element analysis (FEA) is widely used to investigate the crushing performance of thin-walled tubes, and carry out parametric studies. However, simulation results are not always in good agreements with experimental results especially in terms of deformation modes in published literature. In this paper, a systematic FEA study will be conducted to evaluate two main simulation techniques using indentation triggers and buckling modes to introduce imperfections in FEA. Axial compressive tests were first carried out on three types of thin-walled circular tubes with different geometrical parameters. The finite element models were subsequently developed and used to explore the effects of indentation triggers and buckling modes on the deformation modes and force–displacement curves of thin-walled tubes. The influences of indentation depths and indentation positions on the crushing performance were investigated. Similarly, the effects of the order of buckling modes and scale factors on the crushing characteristics were examined as well. It has been found that for thin-walled circular tubes, a suitable simulation technique with indentation triggers or buckling modes can be employed to precisely mimic the deformation mode and corresponding force–displacement curve. This study is expected to provide some practical techniques and insights into the numerical simulation of circular tubes.

Seismic retrofit of reinforced concrete frames by direct loss-based design

This paper introduces a procedure for the retrofit design of reinforced concrete (RC) frame buildings to achieve the desired target level of earthquake-induced loss for a given seismic hazard profile. The methodology is “direct” because the loss target is specified in the first step of the procedure, and, in principle, no design iterations are required. The target loss level is defined based on designer/client preferences and/or external constraints (e.g., foundation capacity). The proposed procedure relies on a simplified loss assessment enabled by a surrogate model defining the probability distribution of the seismic deformation demands of single degree of freedom (SDoF) systems given different ground-motion intensity levels. Combined with a hazard curve and a building-level damage-to-loss model, such a surrogate model is used to map candidate SDoF force-displacement curves to their earthquake-induced loss by assuming a given retrofit strategy. In this case, the considered retrofit strategy involves changing the frame's local hierarchy of strength to ensure a global plastic structure mechanism. Under such assumptions, a designer can select a design force-displacement curve among those that comply with the chosen loss target. The detailing of the retrofitted frame is carried out according to the direct displacement-based design principles and the Simplified Lateral Mechanism Analysis (SLaMA). The procedure is applied to an under-designed RC frame building retrofitted with concrete jacketing. A benchmark loss estimate is calculated using non-linear time-history analyses for loss assessment purposes. The proposed procedure shows satisfactory compliance with the benchmark loss, emphasising the procedure's effectiveness in practice.

Experimental study on the in-plane response of cast-in-situ reinforced concrete sandwich walls under combined vertical and horizontal load

Cast-in-situ Reinforced Concrete Sandwich Panel (cRCSP) technology represents a viable and increasingly popular solution for the construction sector to face recent crucial challenges, such as great housing demand or environmental sustainability. Recently, cRCSP-based buildings are being widely used also in earthquake-prone countries, like Italy. Nevertheless, so far, the available studies in the literature studies focused on the seismic response of this structural typology are not-exhaustive and, besides, relevant structural technical codes do not provide specific design rules. The present study deals with an experimental campaign carried out on four full-scale cRCSP walls subjected to increasing in-plane cyclic lateral loading. Two wall configurations have been considered different for shape and openings: the first has no openings and a squat profile; the second has a central door-type opening and a square profile. Two levels of uniformly distributed vertical load have been applied and kept constant during the test. Materials, specimens, and test set-up are described. The main experimental outcomes in terms of recorded force-displacement curves and observed damage states are discussed in detail. In particular, different failure modes and seismic performances have been observed.

Mechanical performance of hybrid joints of aluminum sheets and laminated beech veneer plates: an experimental prestudy

Wood-based materials offer a high potential for the lightweight design of modern car bodies. Therefore, this prestudy investigates the static strength of screw-bonded lap joints of 1 mm-thick sheets of EN AW-6016-T4 aluminum alloy and 4.5 mm-thick plates consisting of three 1.5 mm-thick cross-laminated beech veneers. Plates with cover veneers oriented longitudinal (L) or transverse (T) to the uniaxial loading direction and with veneer stacking orders designated as L/T/L and T/L/T were used. Two self-cutting screws and polyurethane-based adhesive were used for hybrid joining. The stacking order and thus the fiber orientation of the cover veneers influenced the fracture behavior, which became evident in the force-displacement curve monitored during uniaxial shear-tensile testing of the joints. Veneer plates with the L/T/L stacking order withstood higher maximum tensile force but pro-vided lower pull-out resistance of the screws than plates with the T/L/T stacking order. However, regardless of the stacking order of the veneers the adhesive layer between the aluminum alloy sheet and the veneer plate mainly determined the maximum tensile force and thus the static strength of the joints, whereas the screws contributed only little.

Assessment of static performance of welded mesh along mesh overlap used at Kiirunavaara mine

Localized failure of mesh, i.e., the mesh was cut or torn by rock blocks as a result of a seismic event, was observed at LKAB’s Kiirunavaara mine. This is especially common along mesh overlap where mesh sheets are joined together. However, the performance of welded mesh along mesh overlap is not well understood. A series of tests was conducted at the laboratory at Luleå University of Technology, Sweden. The tested mesh sheets are made of 5.5 mm diameter wires welded along orthogonal directions spaced on a grid of 75 mm by 75 mm. The mesh sheet(s) was placed on a steel rig and fixed with bolts with spacing of 1.0 m by 1.0 m. A 300 mm loading plate made of concrete was placed underneath the mesh and pull/push load was applied on the mesh through the plate. For comparison purpose, the loading plate was placed at the mesh center following a dice five pattern as well as in the middle between two bolts (overlap position). The force-displacement curves of different test configurations were measured and failure modes of the mesh were observed. Laboratory test results show that the load-carrying and deformation capacity of the mesh is highly dependent on the load spreading and loading position relative to the holding points. When the mesh overlap was loaded, it shows: i) the highest stiffness; ii) the highest rupture load; iii) lower residual load-carrying capacity; and iv) the lowest deformation capacity. Two failure modes were observed in the conducted tests. Heat affected zone failure is the most common one and the second is the tensile failure along wires. Based on the laboratory results, an optimized mesh layout and bolting pattern was suggested for the Swedish underground mines.

High-Yield Characterization of Single Molecule Interactions with DeepTipTM Atomic Force Microscopy Probes.

Single molecule interactions between biotin and streptavidin were characterized with functionalized DeepTipTM probes and used as a model system to develop a comprehensive methodology for the high-yield identification and analysis of single molecular events. The procedure comprises the covalent binding of the target molecule to a surface and of the sensing molecule to the DeepTipTM probe, so that the interaction between both chemical species can be characterized by obtaining force-displacement curves in an atomic force microscope. It is shown that molecular resolution is consistently attained with a percentage of successful events higher than 90% of the total number of recorded curves, and a very low level of unspecific interactions. The combination of both features is a clear indication of the robustness and versatility of the proposed methodology.

Correlation study between the square-cone energy-absorbing structure and the frontal collision behaviour of leading vehicles

Abstract In order to study the influence of square-cone energy-absorbing structures on the mechanical behaviour of the collision performance of the leading vehicle, a parameterization method for rapidly changing the performance of energy-absorbing structures was proposed. Firstly, a finite element simulation model of the collision of the leading vehicle with a square-cone energy-absorbing structure was constructed. Then, the platform force, the slope of the platform force and the initial peak force of the force-displacement curve derived from the energy-absorbing structure were studied for the collision performance of the leading vehicle. Finally, the correlation model of the square-cone energy-absorbing structure and the mechanical behaviour of the collision performance of the leading vehicle was established by the response surface method. The results showed that the increase of the platform force of the energy-absorbing structure can effectively buffer the longitudinal impact of the train and reduce the nodding attitude of the train. The increase of the platform force slope can not only effectively buffer the longitudinal impact and vertical nodding of the train, but also reduce the lateral swing of the train. An increase in the initial peak force to a certain extent may lead to a change in the deformation mode, thereby reducing the energy-absorption efficiency. The correlation model can guide the design of the square-cone energy-absorbing structure and predict the deformation attitude of the leading vehicle.

Experimental and analytical investigation of square-shaped concrete-filled steel tube columns

Square-shaped concrete-filled steel tube (CFST) columns inherit the advantages of conventional steel and concrete columns, and have been used in several super high-rise buildings. This paper presents a calculation model for square-shaped CFST columns. Based on the experimental results of a square-shaped CFST column and the application of a super high-rise building, numerical models are established to simulate the force–displacement curves of the CFST column and the stress–strain curves of square steel tubes and stiffeners, which show consistency with the experimental data. Meanwhile, the load-bearing capacity and ductility of CFST columns can be effectively increased by incorporating tensile plates, diaphragms, shear studs, and stiffeners. Considering the steel ratio, axial compression ratio, and concrete strength, nine finite element models are developed to evaluate the ductility and load-bearing capacity of the columns under the reversed-cyclic lateral load. The seismic and wind resistance properties of the structures are analyzed using a CFST column application.

3D deformation modeling of CrAlN coated tool steel compound during nanoindentation

The finite element method (FEM) nanoindentation simulations of nitride hard coatings are either focused on the coating only or contain an axisymmetric model of the coated compound with isotropic material behavior. Moreover, the material model parameters are optimized at only one particular indentation load. The current work aims to develop a 3D FEM model for studying deformation behavior of a CrAlN PVD coated HS6-5-2C tool steel compound during nanoindentation at varying indentation loads. A machine learning (ML)-based algorithm was used to characterize the coating microstructure. This information allowed to set up a 3D FEM model containing a digital clone of the compound microstructure along with the local orientations of the grains embedded into a larger elastically modelled frame. The material model parameters such as Young's modulus E, yield stress Y, strain hardening coefficient B and strain hardening exponent n for coating, interlayer and substrate were determined by fitting the simulated force-displacement curves to the experimental ones through an iterative optimization approach at four different indentation loads. An overall good agreement between the simulated and experimental force-displacement curves along with physically reasonable material model parameters was achieved. The obtained yield stress of CrAlN coating was comparable to ceramics. Moreover, elastic-plastic deformation in interlayer and elastic deformation in substrate at indentation depth below 10 % of the coating thickness was observed. This necessitates the interlayer and substrate consideration for FEM nanoindentation simulations of PVD coated compounds as in the present study. Therefore, the used modeling approach, based on orthotropic elastic material law for the coating combined with 3D digital clone of the compound microstructure, was successfully implemented and validated for low as well as high indentation loads.

Square tubes with graded wall thickness under oblique crushing

Thin-walled square tubes with graded wall thickness were previously found to be more efficient in terms of energy absorption than square tubes with uniform thickness subjected to axial compression. In this paper, the mechanical performance of square tubes with in-plane graded wall thickness under oblique compression has been investigated for the first time. Three different types of square tube configurations: four walls with uniform wall thickness, single-surface graded wall thickness (SSG) and double-surface graded wall thickness (DSG) were experimentally compressed at loading angles of 0°, 10° and 15°, respectively. Finite element models were subsequently developed to study the effects of wall thickness, graded thickness configuration and loading angle on deformation modes, force–displacement curves and energy absorption. The results show that both SSG and DSG tubes display better specific energy absorption than tubes with uniform thickness and very similar mass under oblique compression. With the increase of the loading angle, the specific energy absorption of all tubes studied decreases except SSG0814 tube. DSG tubes present similar specific energy absorption as that of the corresponding SSG tubes under axial and oblique loadings.

Interfacial shear performance of UHPC-strengthened RC structures using post-installed rebar connections: Experiments and analyses

The reliable bonding effect between the ultra-high performance concrete (UHPC) layer and the existing reinforced concrete (RC) components is always expected when UHPC is used to rehabilitate deteriorated RC structures. The post-installed rebar connection has been demonstrated to possess robust mechanical performance. However, no research to date clarifies how to design the post-installed rebar connection in engineering practice. To this end, this study conducted 34 push-out tests to investigate the interfacial shear performance of UHPC-strengthened RC structures using post-installed rebar connections. The primary variables in the tests included strengthening form, embedded depth of rebar, rebar diameter, rebar spacing, and substrate type. Based on the test results, three different failure modes were identified. The analytical results indicate that the embedded depth of the rebar has a significant influence on the performance of the post-installed connection. A formula was proposed to determine the minimum embedded depth, and its accuracy was validated by the physical experiments. The load-bearing mechanisms were revealed based on the experimentally measured force–displacement curves. The shear capacity of the connection mainly comprises the adhesive effect, rebar shearing, and friction. The connection capacity can be approximated by the rebar shear capacity due to its robust shear resistance. Also, a formula was proposed to estimate the shear capacity of the rebar. The experimental and theoretical results facilitate the design and application of post-installed rebar connections in UHPC-strengthened RC structures.

Pop-in phenomenon at nanoindentation and fracture toughness of two-phase ceramic composites

Material’s resistance to crack propagation corresponds to its fracture toughness. This characteristic can be calculated in laboratory tests, e.g. 3-point bending of notched bars or by indentation test. Spherical, conical, or pyramidal tips can be used during nanoindentation and micro indentation tests, e.g. Vickers, Berkovich, or Cube-Corner tip.The lower level of fracture toughness is a key parameter of ceramic materials and this attribute is not frequently investigated by nanoindentation. If the load force is quite small, an extra increase in penetration depth can occur, which can be described as the pop-in phenomenon.This paper shows the results of nanoindentation tests with the use of cube-corner tips and load levels of 2 mN and 5mN. Five types of ceramic composites Al2O3/ZrO2 with composition ratios of 20, 40, 60, and 80 wt% of Al2O3 content were tested. To estimate the fracture toughness by calculating the crack length force–displacement curves with visible pop-in phenomenon were selected for analysis.