Force-displacement Curves Research Articles

Experimental and numerical analysis of a novel 3D re-entrant auxetic structure

The energy absorption performance during collisions and crushing is one of the critical parameters in the design of vehicle structures. Therefore, researchers are continually trying to improve the energy-absorbing properties of the crash box to reduce the force transmitted to the occupant during an accident. In this research, a novel three-dimensional re-entrant auxetic structure has been proposed to improve energy-absorbing performances. Criteria for evaluating energy absorption including the initial peak crushing force, energy absorption, mean crushing force, crushing force efficiency, and specific energy absorption, were obtained through numerical and experimental methods. The structure showed auxetic behavior in two transverse directions during compressive loading and absorbed more energy. The force-displacement curve showed low initial peak crushing force, and the structure collapsed uniformly during compressive loading. The effects of the angle of the diagonal strut with the vertical axis, the thickness of the struts, and the ratio of horizontal strut length to diagonal strut length on the energy absorption properties of the structure were studied, too.

Cylindrical metastructure simulating yielding with elastic deformation: Theoretical and experimental studies

This paper investigates a cylindrical shell metastructure which has a plateau in its force-displacement curve due to geometric nonlinearity. The metastructure is based on bistable inclined beams with an out-of-plane curvature connected in series. An approximate explicit expression was deduced for this kind of beam relating its horizontal stiffness and force with its vertical deformation. Based on the expression, axial interaction of the series-connected beams was shown to always create a stable plateau in force-displacement curve of the structure. A series of tests were conducted to validate this behavior. The tests confirm that the structure with different geometric details can stably achieve plateau in its force-displacement curve in both the monotonic and cyclic load. Metastructure based on the proposed mechanism can be very simple and light-weighted, making them useful in shock absorption and vibration control. • This paper proposes a cylindrical metastructure that consistently shows a plateau in its force-displacement curve due to geometric nonlinearity • The underlying mechanism to generate the force plateau was demonstrated based on an explicit approximate solution was deduced for inclined bistable beam deduced • A series of tests were conducted to validate behaviour of the metastructure

Numerical analysis of micropillar compression behaviour and stress-strain curve estimation verified on glass fused silica

Microcompression testing became an incredibly popular approach to investigating the mechanical response of micro-scale volumes. Among many objectives, the determination of stress-strain relations from experimental force-displacement data is complicated, as compression micropillars are better considered as components a rather than samples, and an experimental force-displacement curve cannot be simply transferred to an accurate stress-strain curve. In this work the microcompression behaviour of fused silica – an amorphous, isotropic material – was investigated to quantitative the extent to which this novel approach can be used to achieve accurate stress-strain relations. Finite element simulations, assuming isotropic hyperelastic behaviour applied for an amorphous material, was essential in assessing the method, while also making comparison to experiments. Symmetric micropillars as well with imperfections were considered, combined with different friction coefficients to provide effects from e.g. slope of contact plane, inclined micropillar height, taper angle, or foot transition. For symmetric micropillars buckling phenomenon additionally occurred due to the predominant elastic deformation. Failure due to fracture was excluded in this approach. Based on the numerical simulations a sufficiently reliable, accurate, and verified approach was achieved providing the determination of stress-strain curves from experimental data and was also experimentally confirmed by a micropillar experiments. It is expected that the approach is also valid for other isotropic amorphous materials. • New approach for the determination of stress-strain curves from micropillar under compression. • Comprehensive numerical analysis for perfect and imperfect micropillars. • Micropillars with typical imperfections can still be treated to obtain valid stress-strain curves.

Load-carrying and energy-absorbing performance of honeycombs with different cross sections under cyclic loading

Honeycombs, characterized by advantages including large compressive deformation and controllable deformation, have been widely used in energy-absorbing components. The loading process of honeycombs is generally influenced by recovery after unloading in application environments. Expounding the load-carrying and energy-absorbing performance of honeycombs under cyclic loading is critical for the practical engineering application of honeycombs. Honeycombs with four different cross sections were selected to compare their deformation process and load-carrying performance under cyclic loading by conducting quasi-static compression tests and displacement-controlled cyclic loading and unloading tests. On this basis, influences of the cyclic loading on the energy-absorbing performance of honeycombs were revealed. It is shown that cyclic loading does not change the four-stage characteristics of the displacement-force curve of honeycombs while to some extent influences the load-carrying capacity of honeycombs. Under cyclic loading, the honeycombs have larger plateau force and plateau force efficiency and exhibit better stable load-carrying capacity and uniformity. Moreover, evaluation of the energy-absorbing performance of honeycombs based on the total energy absorption index has some limitations, which takes the energy absorption of structures in each stage into account. In view of this, the effective energy absorption was proposed to accurately evaluate the energy-absorbing performance of honeycombs. It is found that honeycombs exhibit better energy-absorbing performance under cyclic loading. The research achievements provide theoretical support for application of honeycombs in fields including mines and underground spaces.

Degradation and failure analysis of bolted joints under transverse loading

There are a huge number of bolted joints used in engineering applications. However, unreasonable design and use may lead to degradation and failure of the connected structure. Herein, finite element analysis method is used to investigate the influence of various factors on the mechanical properties of bolted joints. To simulate the actual assembly and loading process, different analysis steps were considered, given as: tightening step, initial lose step and the loading step. In the loading step, transverse load is applied to obtain the force-displacement curve. Structural parameters, i.e. clamping force, effective clamp length and assembly clearance, and coefficients of friction of all the contact surfaces are considered in the finite element analysis. The results showed that the performance of the bolted joint under transverse loading exhibits different stages, and this agrees well with the results of our previous experimental results. Through the analysis of the force-displacement curves, the characterization parameters for the mechanical properties of the bolted joint can be extracted, such as curve form, tangential stiffness, slip distance, transverse load threshold, etc. The characterization and evaluation of the mechanical properties integrates the process from design to service, which helps to provide reference for the reliability design and performance improvement of bolted joints.

Numerical study on the stiffness and ultimate strength of cold-formed steel C-shaped connectors under pull-out failure

ABSTRACT In this paper, cold-formed steel C-shaped connectors, as one of the most commonly used components in steel wall/framing systems, were investigated under the pull-out failure modes using a detailed numerical study. Finite element models were validated using the data obtained from an experimental program; and the results were compared with the current design equations. Finally, a new pull-out strength equation was proposed based on the critical parameters affecting the behaviour of C-shaped connectors. In addition, initial bending stiffness of C-shaped connectors was studied using a simplified analytical approach; and the results obtained from the proposed new stiffness equation were compared with the initial slope of experimental and numerical force-displacement curves. These comparisons confirm the accuracy of the new strength and stiffness equations in order to apply to the analytical methods such as component-based method in future works.

Simulation of compound anchor intrusion in dry sand by a hybrid FEM+SPH method

The intrusion of deformable compound anchors in dry sand is simulated by coupling the Finite Element Method (FEM) with Smoothed Particle Hydrodynamics (SPH). This novel approach can calculate granular flows at lower computational cost than SPH alone. The SPH and FEM domains interact through reaction forces calculated from balance equations and are assigned the same soil constitutive model (Drucker–Prager) and the same constitutive parameters (measured or calibrated). Experimental force–displacement curves are reproduced for penetration depths of 8 mm or more (respectively, 20 mm or more) for spike-shaped (respectively, fan-shaped) anchors with 1 to 6 blades. As the number of blades increases, simulations reveal that the granular flow under the anchor deviates from the vertical and that the horizontal granular flow transitions from orthoradial to radial. We interpret the strain field distribution as the result of soil arching, i.e., the transfer of stress from a yielding mass of soil onto adjoining stationary soil masses. Arching is fully active when the radial distance between blade end points is less than a critical length. In that case, the normal stress that acts on the compound anchor at a given depth reaches the normal stress that acts on a disk-shaped anchor of same radius. A single-blade anchor produces soil deformation and failure similar to Prandtl’s foundation sliding model. Multiblade anchors produce a complex failure mechanism that combines sliding and arching.

Tensile Characteristics and Fracture Mode of Frozen Fractured Rock Mass Based on Brazilian Splitting Test

Frozen fractured rock mass is often encountered during the implementation of geotechnical engineering in cold regions. The tensile strength parameters of frozen rock play an important role in the construction of rock slopes involving tensile failure. In order to study the tensile characteristics of a frozen fractured rock mass in a cold region, original rock specimens were mined and processed in the Yulong Copper Mine, and artificial, frozen fractured marble specimens were made. The effects of different ice-filled crack angles, lengths, and widths on the force–displacement curve and the tensile strength of frozen rock were studied by laboratory Brazilian splitting experiments and RFPA3D, and the evolution law of the tensile strength of frozen rock was revealed. At the same time, wing crack initiation and cracking mode after tensile failure were analyzed by high-speed camera; the whole process of the Brazilian splitting of frozen rock was reconstructed, and the development of microcrack initiation in frozen rock was analyzed. The following conclusions were drawn from the test results: the frozen rock specimens have typical brittle-failure characteristics. The tensile strength of frozen rock decreases gradually with the increase in the width and length of ice-filled cracks, and decreases first and then increases with the increase in the angle of the ice-filled crack. The ice-filled crack incurs damage first, and then the wing cracks start from the tip of the ice-filled crack and extend continuously. The tensile strength of frozen rock is significantly affected by the angle and length of ice-filled cracks.

Investigation of deformation mechanics and forming limit of thin-walled metallic bipolar plates

The present study is conducted on forming of the metallic bipolar plates made of 316 stainless steel sheet with a parallel serpentine flow field. The plastic deformation of straight and curved microchannels, forming limit criteria, and deformation mechanics during the process are investigated partially to present a reliable model for estimating fracture initiation. For this purpose, experimental stamping tests are employed to fabricate metallic bipolar plates and the process is simulated by finite element software. The validity of simulation results is examined by comparing thickness distribution and force-displacement curves reflecting 4.76% and 3.85% error rates, respectively. According to experimental observations, fracture starts at a channel depth of 0.610 mm. Hence, for determining the forming limit and predicting the fracture during the process, the deformation mechanic is studied at different points of the microchannels. Results of stress states analysis indicate that the stress state of plane-strain tension up to biaxial tension governs this process. Despite the presence of different loading paths during the process, the critical element in each channel is deformed under plane-strain tension. Therefore, a fracture model is developed based on thinning percentage and equivalent strain to predict the instability of metallic bipolar plates. According to the results, both the equivalent strain and thinning percentage criteria with critical limits of 0.56 and 33.45%, respectively, are considered as an allowable range of plastic deformation during the conventional stamping process of bipolar plates. Results indicate that maximum thinning in all directions is lower than 33.45% by using the modified stamping process.

Safety Study of High-Speed Collisions between Trains and Live Intruder.

To investigate the safety of train collisions with live intruders under high-speed operation, a new 3D finite element laminated model of live intruder filling was constructed based on reconstruction using physical 3D scanning, with three outer layers of the model simulating the skin, three inner layers simulating bone, and internal filling simulating internal organs. The model was simulated in LS-DYNA with pendulum side collision, and the force-time and force-displacement curves of the collision between the pendulum and the living intruder were obtained, which were consistent with the curve trend of the results of the cadaver pendulum collision test by Viano in 1989, and the accuracy of the finite element model of the intruder was verified. Through the simulation calculation of high-speed collision between the train and two kinds of living intrusions, the maximum acceleration of the train body, the maximum lifting of the wheel pair, the deformation of the cowcatcher, and the maximum central load on the cowcatcher during the collision can be obtained. The results of the study show that at a collision speed of 110 km/h and different collision positions, the collision risk factor between the train and heavier organisms is relatively high, and the risk arising from frontal collisions is generally greater than that of offset collisions; despite this, all the indicators such as the maximum acceleration of the train, the maximum lift of the wheel pairs, the reduction in the length of the cowcatcher discharge per 5 m of space, and the maximum central load borne by the cowcatcher discharge are lower than the EN15227 standard. Additionally, the safety of the train is not affected and the components can work reliably.

Axial loading mechanism analyses and evaluation methods of CCFT short columns with gap defects

The gap defect has proved to be a common quality issue in concrete-filled tubular (CFT) structures, which offers distinct unfavourable effects on their mechanics properties. To determine out the guidelines of gap defect affecting the axial loading performance of circular CFT (CCFT) short columns, this paper develops an array of refined numerical models of the axially-compressed CCFT short columns with spherical-cap gaps (CCFT-SG) and circumferential gaps (CCFT-CG), whose accuracy is verified by existing experiments. The typical axial force versus longitudinal displacement (N-Δ) curves, the contact stress, the longitudinal stress distribution and the failure modes are respectively given focus to reveal the intrinsic axial loading mechanism of the CCFT short columns, taking the existence of the gap defect into consideration. Based on these analyses, various design methods using confinement regionalization and circumferential expansion thoughts are proposed and adopted to evaluate the load bearing capacities of the axially-compressed CCFT-SG and CCFT-CG short columns. The results declare that the appearance of the gap defects dramatically weakens or delays the contact behaviour between the infilled concrete and the hollow tube, which accelerates the local bulging of the tube, reduces the longitudinal stress of the core concrete, and therefore the axial resistance of the CCFT short column is distinctly influenced. The design approaches delivered in this paper can assess the axial resistances of the CCFT short columns with gap defects accurately according to the test validation. The research may provide a theoretical basis and a reliable way for evaluating and treating the actual CFT structures with gap defects.

Measurement of bone damage caused by quasi-static compressive loading-unloading to explore dental implants stability: Simultaneous use of in-vitro tests, μ-CT images, and digital volume correlation

Primary stability of dental implants is the initial mechanical engagement of the implant with its adjacent bone. Implantation and the subsequent loading may cause mechanical damage in the peripheral bone, which ultimately reduces the stability of the implant. This study aimed at evaluating primary stability of dental implants through applying stepwise compressive displacement-controlled, loading-unloading cycles to obtain overall stiffness and dissipated energy of the bone-implant structure; and quantifying induced plastic strains in surrounding bone using digital volume correlation (DVC) method, through comparing μCT images in different loading steps. To this end, dental implants were inserted into the cylindrical trabecular bones, then the bone-implant structure was undergone step-wise loading-unloading cycles, and μCT images were taken in some particular steps, then comparison was made between undeformed and deformed configurations using DVC to quantify plastic strain within the trabecular bone. Comparing stiffness reduction and dissipated energy values in different loading steps, obtained from the force-displacement curve in each loading step, revealed that the maximum displacement of 0.16 mm can be deemed as a safe threshold above which damages in peri-implant bone started to increase considerably (p < 0.05). In addition, it was found here that peri-implant bone strain linearly increased with decreasing bone-implant stiffness (p < 0.05). Moreover, strain concentration in peri-implant bone region showed that the plastic strain in trabecular bone spread up to a distance of about 2.5 mm away from the implant surface. Research of this kind can be used to optimize the design of dental implants, with the ultimate goal of improving their stability, also to validate in-silico models, e.g., micro-finite element models, which can help gain a deeper understanding of bone-implant construct behavior.

Numerical simulation and analysis of fully-grouted sleeve connection and two special points at elevated temperatures

Fire is one of the main objects of study at the cutting edge of the research on disaster prevention and mitigation in structures. In the event of a fire, the mechanical properties of the structural material will be significantly reduced, resulting in serious consequences. This paper simulates the tensile properties of sleeve grouting members at five different temperatures, to contribute to the research here. The simulated member stress-strain curves fit well with the corresponding experimental results. The paper introduces constitutive models of concrete, steel, and sleeve. Beyond that, a feasible finite element model of the grouted sleeve is proposed. Two special points’ (yield point, ultimate point) coordinate formulas which are related to different temperatures (25–1000 °C) are presented. It indicates the regularity of fully-grouted sleeve tensile force-displacement curves in various temperatures. Meanwhile, the research content provides the basis for further research on reinforcing bars spliced by grout-filled coupling sleeves.

Ex vivo postimplantation biomechanical properties of a press-fit cementless femoral stem with transfixation pin for canine total hip replacement.

To compare ex vivo postimplantation biomechanical characteristics of 3 implants for canine total hip replacement: a cementless press-fit femoral stem with a pin in the femoral neck (p-pfFS), a press-fit cementless femoral stem without this pin (pfFS), and a cemented femoral stem (cFS). 18 cadaveric femurs from 9 dogs. Femurs were assigned randomly to 3 groups, and biomechanical testing was performed by measuring vertical displacement during cyclic loading and resistance to failure with compression parallel to the longitudinal axis of the femur. Force-displacement curves were assessed for failure tests, and work necessary for failure was calculated. No significant differences were observed in vertical displacement during cyclic loading (P = .263) or work necessary for failure (P = .079). Loads to failure for cFS and p-pfFS implants were significantly greater than that for the pfFS, but no significant difference in load to failure was observed between cFS and p-pfFS implants (P = .48). Cementless femoral stems with a transfixation pin offer significantly greater immediate resistance to failure to compressive loads parallel to the longitudinal axis of the femur than standard cementless stems, and a level of stability comparable to that of cemented stems. p-pfFS implants may be valuable in total hip replacement, potentially reducing the risk of fracture during the early postoperative period prior to osteointegration.

Multiscale hierarchical and heterogeneous mechanical response of additively manufactured novel Al alloy investigated by high-resolution nanoindentation mapping

Smart alloying and microstructural engineering mitigate challenges associated with laser-powder bed fusion additive manufacturing (L-PBFAM). A novel Al–Ni–Ti–Zr alloy utilized grain refinement by heterogeneous nucleation and eutectic solidification to achieve superior performance-printability synergy. Conventional mechanical testing cannot delineate complex micromechanics of such alloys. This study combined multiscale nanomechanical and microstructural mapping to illustrate mechanical signatures associated with hierarchical heat distribution and rapid solidification of L-PBFAM. The disproportionate hardening effect imparted by Al3(Ti,Zr) precipitates in the pool boundaries and the semi-solid zone was successfully demonstrated. Nanomechanical response associated with heterogeneity in particle volume fraction and coherency across melt pool was interpreted from nanoindentation force–displacement curves. The hardness map effectively delineated the weakest and strongest sections in the pool with microscopic accuracy. The presented approach serves as a high throughput methodology to establish the chemistry-processing-microstructure-properties correlation of newly designed alloys for L-PBFAM.

A mixed mode phase-field model of ductile fracture

We present the first mixed mode phase-field model of ductile fracture. The contribution of crack opening and shearing deformations to the propagation of a crack is expressed by introducing two phase fields. Constitutive relations are then introduced to couple and distinguish these phase fields. Special attention is given to the maximum shear stress and its effect on the development of fractures. The proposed model is validated by tensile testing experiments found in the literature on Al 2024 T-351. Model predictions of the crack path and load-displacement response are compared to a plane-strain tension experiment, a round bar tension experiment and a notched round bar tension experiment. The model is shown to accurately capture the slant and cup-cone crack paths as well as force-displacement curves.

Investigation of penetration behavior of combined geometry shells at quasi-static and intermediate strain rates: An experimental and numerical study

In this study, the penetration/perforation behavior of a core material with previously determined static and dynamic crushing characteristics was investigated both experimentally and numerically. Penetration/perforation problems occur due to shrapnel effect when sandwich structures containing energy-absorbing core materials by crushing are exposed to blast loads. The penetration behavior of combined geometry shells consisting of a hemispherical cap and a cylindrical segment was investigated experimentally using blunt, conical and hemispherical penetrator tips. The quasi-static penetration tests were performed in a universal test machine, and the intermediate strain rate penetration tests were performed in a drop weight test device. The numerical models of penetration tests were implemented in LS-DYNA at the test strain rates as well as at the higher strain rates. Results showed that different penetrator geometries induced damage forms of symmetrical tearing, petaling, plugging and inversely formed hemispherical domed cone. The increase in the thickness of core geometry resulted in a decent increase in force–displacement curves, as average of force levels increased around 140%, 200% and 220% for blunt, conical and hemispherical tip penetrators, respectively. Numerical results indicated very good correlation with experimental work and enabled to investigate effect of strain rate and micro-inertia over numerical models at elevated penetrator velocities. Penetration behavior was found to be affected from micro-inertia effects up to a threshold displacement of 4 mm for thicker and 5 mm for thinner core units and strain rate effects were found to be dominant beyond that point.

Objectivity in quasi-brittle structural failure via adaptive formulation and mesh refinement

In this work, the combined implementation of Adaptive Formulation Refinement (AFR) and Adaptive Mesh Refinement (AMR) strategies is proposed for the efficient and mesh objective evaluation of quasi-brittle fracture.A critical issue when computing localized structural failure is the spurious mesh bias dependence of the crack trajectories and collapse mechanisms that ensues when adopting the standard displacement-based finite element (FE) formulation. This problem is resolved by the introduction of the mixed strain/displacement FE formulation, which allows for local convergence, producing mesh objective results.On the one hand, the proposed AFR approach allows to adaptively switch between the standard and mixed FE formulations during the numerical simulation depending on the level of accuracy required in different regions of the domain. Within this framework, the more accurate mixed formulation is activated only in the areas where the crack onset and evolution take place, while the standard formulation is adopted for the rest of the structure.On the other hand, the adopted octree-based AMR strategy allows to adaptively refine only certain areas of the domain, also in function of the level of accuracy required. Using this methodology, it is possible to start the simulation with an initially relatively coarse mesh and adaptively introduce several levels of mesh refinement only in the regions of interest, where cracks appear and propagate. This approach guarantees the necessary mesh resolution to capture the fracture phenomenon accurately while further increasing the computational efficiency of the simulation. The subsequent adaptive coarsening of the FE mesh is also allowed.Structural failure and fracture propagation are reproduced via a local isotropic damage model. For this reason, a refinement/coarsening criterion defined in function of the equivalent effective stress is conveniently adopted with both AFR and AMR strategies.To assess the capabilities of the proposed method, a set of numerical simulations featuring benchmark problems and experiments is included. Results show the mesh objectivity and cost-efficiency of the approach combining AFR and AMR in fracture problems. The proposed model is able to reproduce experimental crack paths, collapse mechanisms and force–displacement curves with accuracy and without spurious mesh bias dependence.The paper includes a comparative assessment of the performance of the proposed method and the standard FE formulation exclusively, showing the superior performance of the AFR methodology and its mesh objectivity. Convergence of the computed results when introducing different levels of AMR is also verified. Computational efficiency of the AFR and AMR techniques is specifically assessed. The combination of AFR and AMR approaches allows to provide accurate and mesh objective results in quasi-brittle fracture problems with very significant savings in computational cost.

Force-displacement relationships for NiTi alloy helical springs by using ANSYS: Superelasticity and shape memory effect

Abstract Shape memory alloys are smart materials which have remarkable properties that promoted their use in a large variety of innovative applications. In this work, the shape memory effect and superelastic behavior of nickel-titanium helical spring was studied based on the finite element method. The three-dimensional constitutive model proposed by Auricchio has been used through the built-in library of ANSYS® Workbench 2020 R2 to simulate the superelastic effect and one-way shape memory effect which are exhibited by nickel-titanium alloy. Considering the first effect, the associated force-displacement curves were calculated as function of displacement amplitude. The influence of changing isothermal body temperature on the loading-unloading hysteretic response was studied. Convergence of the numerical model was assessed by comparison with experimental data taken from the literature. For the second effect, force-displacement curves that are associated to a complete one-way thermomechanical cycle were evaluated for different configurations of helical springs. Explicit correlations that can be applied for the purpose of helical spring's design were derived.

Adhesive depth-sensing indentation tests: Slopes of the force–displacement curves

Depth-sensing indentation experiments are a very important tool for estimating mechanical properties of modern materials. A review of various aspects of contact problems that used as the theoretical basis for interpretation of depth-sensing nanoindentation experiments is presented. Usually, analytical treatment of the indentation tests is based on analysis of the slopes of the force–displacement curves according to the non-adhesive Hertz contact theory. However, molecular adhesion is crucially important for many physical processes at the micro/nano-scales. Here, depth-sensing indentation techniques are reviewed and analyzed using the recent results obtained for adhesive contact problems. Fundamental relations for adhesive nanoindentation tests are derived for both frictionless and no-slip boundary conditions within the contact region. It is argued that the adhesive effects may be very important for treatment of the nanoindentation tests because the slopes of the force–displacement curves may considerably differ from the slopes derived using the non-adhesive contact theory.