Force-displacement Response Research Articles

Simulation and experimental verification of an original full-scale bamboo truss

This study examines experimentally and numerically the performance of a full-scale bamboo truss footbridge. The truss is built of multi-culm bamboo axial members with bolted steel connections, joined together via steel gusset plates. The study proposes a hierarchical simulation approach with the aid of existing and new material/structural member experimental test results. Specifically, it models first the non-linear (bilinear) behaviour of the multi-culm bamboo structural members, and then using the structural member model as building block, it creates a non-linear model of the entire truss structure. The proposed numerical simulations return realistic force–displacement response of the truss structure. The axial deformation of truss members is mostly due to bolt deformation and embedment, since the bamboo culms are significantly stiffer than the bolted connections. The simulated yielding and damage modes occur at similar locations in the truss structure as those observed experimentally. The simulated sequence of damage modes is affected by the natural variability of bamboo culms. Overall, the developed simulations are promising towards predicting via a hierarchical systematic modelling approach, the non-linear response of the bamboo structures, after modelling the behaviour of its multi-culm bamboo structural members.

Battered minipile response to low-frequency cyclic lateral loading in very dense sand

This experimental study investigates the response of vertical and battered minipiles to two-way symmetrical low-frequency (0.1 Hz) cyclic lateral loading. Laboratory (1-g) tests were performed on scaled-down minipiles in very dense cohesionless soil, for batter angles of 0°, 25° and 45°. The cyclic loading is classified into two categories: multi-amplitude and long-term single amplitude, where force-controlled load was applied at a constant frequency. The minipiles were instrumented with optic fibres, and strain profiles were obtained at each loading stage, in both compression and tension stroke. The results are presented in terms of hysteresis loops, variation of normalised stiffness, minipile strain and bending moments under cyclic loading. In the multi-amplitude loading category, backbone curves show a stiffer force–displacement response in tension stroke than in compression stroke. For the single-amplitude category, the area of the hysteresis loop is largest for 45° battered minipiles with the lowest accumulated deformation. The normalised stiffness at the end of 50 cycles is highest for 25° minipiles with a value slightly greater than one. The strain profiles along the minipiles show stabilisation of measured strain before the number of cycle reaches 50, for all three battered conditions. A multi-surface hardening constitutive model is used to explain the effect of shearing and cyclic loading, with increasing loading amplitude on 25° battered minipiles. These test results are indicative of better performance capability of 25° battered minipiles, in terms of secant stiffness, compared to the vertical and 45° battered cases.

Fracture behaviour and toughening mechanisms of dry and wet collagen

The growing interest to the use of collagen films for biomedical applications motivates the analysis of their fracture behaviour in different environments. Studies revealed the decreased mechanical strength and stiffness as well as increased plasticity in water compared to collagen specimens tested in air. However, the fracture behaviour of pure collagen films in both air and water has not been reported so far. In this paper, the entire process of mode-I loading of single-edge notched tension (SENT) specimens was recorded and analysed. In case of in-air (dry) specimens, cracks propagated rapidly in a brittle fashion while large plastic deformations were observed in aqua prior to failure due to crack opening and a blunting mechanism in wet specimens. The fracture-toughness parameters for pure collagen in air and in aqua were estimated using linear-elastic (KI and GI) and elasto-plastic (JI) fracture-mechanics approaches, respectively, following the force-displacement response and deformational behaviour. GIC and JI were 1365 ± 112 J/m2 and 2500 ± 440 J/m2, respectively. Scanning electron microscopy was used to observe the structural changes linked to collagen fibrils in the crack-tip area and the fracture surface. For in-air specimens, the former mostly exhibited extrinsic toughening (usually at micro scale) acting behind the crack-tip, while in-aqua intrinsic toughening acting ahead of a crack tip was found. Fractography of in-air specimens showed no occurrence of voids while multiple micro-voids were found for in-aqua specimens. Statement of significanceThe fracture toughness and crack propagation of both mineralised (bone, dentine) and non-mineralised (skin) tissues has been extensively investigated over the past decades. Though these tissues are rich in collagen, the fracture properties of pure collagen have not been quantified yet at macroscale. Considering the applications of collagen films in tissue regeneration, it is essential to perform investigations of their fracture behaviour in both dry and wet conditions. Determining the effect of environment on the fracture behaviour of collagen and understanding its toughening mechanism are essential for prevention of failures during application. Moreover, this would give an insight for fabrication of tougher collagen-based biomaterials for biomedical uses.

Fracture resistance of Ceramic-Polymer hybrid materials using microscopic finite element analysis and experimental validation

The objective of this paper is to elucidate the response to contact stresses of Polymer Infiltrated Ceramic Network (PICN) using the microscopic viscoplastic finite elements, validated by clinically relevant in vitro tests. A feldspathic ceramic material, namely Vita Mark II, is an interconnected structure infiltrated with the polymer (PMMA). Axisymmetric finite element microstructure models are reconstructed from two-dimensional images of a PICN microstructure. Viscoplastic finite element analysis (FEA) with various degrees of microscopic damages occurring over contact is performed. The force-displacement responses obtained from FEA are validated with Hertzian contact tests. Finite element results for force-displacement, stresses and strains in each phase are discussed. We hypothesize that the resistance to fracture of PICN can be further improved by microstructural tailoring. The experimental evidence suggests that a composite material is both more resistant to displacement under load and more resistant to crack initiation and propagation, as hypothesized. Further parametric study on the effects of various volume fractions of two phases in PICN is done to provide some insight on increased contact damage resistance of PICN as well as potential optimization of microstructures.

On simulating impact fracture in high-strength concrete using GraFEA

In this work, we use a recently-formulated Graph-based Finite-Element Analysis (GraFEA) framework developed for modeling deformation and non-local fracture in quasi-brittle materials to simulate the fracture response of high-strength concrete (HSC) samples under impact loads. By fitting the material parameters in the theory to match a macroscopic force–displacement response obtained from a three-point bending experiment conducted under quasi-static conditions, we show that the GraFEA computational method is able to independently validate the experimentally-determined impulse response, obtained from impact experiments conducted under various initial impact speeds imposed by a drop-weight on HSC samples that are 6 to 7 orders of magnitude higher than the quasistatic tests. Furthermore, the GraFEA-based FEM simulations are also able to reproduce experimental crack propagation speeds in a HSC sample under different initial impact speeds to good accord.

Failure behavior of prismatic Li-ion battery cells under abuse loading condition - A combined experimental and computational study

Li-ion jelly rolls and prismatic battery cells were quasi-statically loaded by three different indenters: (1) Hemispherical nose punch, (2) Flat end punch, and (3) Round edge wedge. Force and displacement during indentation were measured. For the cells, voltage drop was also recorded to monitor short circuiting. The deformation/failure modes of specimens were examined and the critical force at initiation of short circuit was analyzed for the cells. Substantial differences occurred depending upon indenter shape; also loading orientation for the wedge. In all cases, short circuiting of the entire cell initiated by formation of the first jelly roll crack. Based on test loading and boundary conditions, finite element (FE) models were developed using explicit FEA code LS-DYNA. The model predictions demonstrated good agreement in terms of force-displacement responses and structural failure modes at both jelly roll and prismatic cell levels. With the validated numerical model, the original battery cell design was modified in order to alter the deformation and failure modes of the jelly roll. Three design modifications were considered: (1) Include a thin mica sheet between the first and second jelly roll layers; (2) Use thinner, but higher stiffness/strength steel to replace the aluminum alloy enclosure material; and (3) Change the enclosure material where indenter contact occurs from an aluminum alloy sheet to an aluminum alloy sandwich structure. All three indentation conditions were simulated and results were compared to the original design. The outcomes were sensitive to indenter shape, where round end wedge indentation benefitted the most. The findings have potential for improving prismatic battery cell safety by incorporating them into future designs.

Research on Transverse Restraint System of Cable-stayed Bridge under Ultra High Performance Concrete Deck Pavement

In order to explore the optimal lateral restraint system for long-span cable-stayed bridges under ultra-high performance concrete deck pavement. This paper takes a UHPC deck pavement cable-stayed bridge as an example, selects four different lateral restraint systems, calculates the stress of each key section of the cable-stayed bridge under the action of an earthquake, and then selects the optimal lateral Constraint system. The research results show that when ultra-high performance concrete is used as the bridge deck pavement, the increase in the quality of the bridge deck system will have a greater adverse effect on the seismic performance of the bridge. Compare the internal force response and displacement response at each key section of the bridge under four different lateral restraint systems under earthquake action. Compared with the other three systems, the internal force response and displacement response value of the horizontal cable system is smaller, and the energy dissipation and shock absorption effect is better. For cable-stayed bridges using ultra-high performance concrete as the deck pavement, in the selection of the lateral restraint system, a restraint system of cables is set between the towers and beams, which can better reduce the impact of the increase in the quality of the bridge deck on the seismic performance of the bridge, is the most reasonable horizontal restraint method. Considering the internal force and displacement response of the bridge structure and the safety of the support under the earthquake, the parameter selection of the cable support is k = 135000 kN / m and S = 0.4 m.

Modelling lead-rubber seismic isolation bearings using the unified mechanics theory

Lead-rubber seismic isolation bearings (LRB) have been installed in a number of essential and critical structures, like hospitals, universities and bridges, in order to provide them with period lengthening and the capacity of dissipating a considerable amount of energy to mitigate the effects of strong ground motions. Therefore, studying the damage mechanics of this kind of devices is fundamental to understand and accurately describe their thermo-mechanical behavior, so that seismically isolated structures can be designed more safely. Hitherto, the hysteretic behavior of LRB has been modeled using 1) Newtonian mechanics and empirical curve fitting degradation functions, or 2) heat conduction theories and idealized bilinear curves which include degradation effects. The reason for using models that are essentially phenomenological or that contain some adjusted parameters is the fact that Newton’s universal laws of motion lack the term to account for degradation and energy loss of a system. In this paper, the Unified Mechanics Theory – which integrates laws of Thermodynamics and Newtonian mechanics – is used to model the force-displacement response of LRB. Indeed, there is no need for curve fitting techniques to describe their damage behavior because degradation is calculated at every point using entropy generation along the Thermodynamics State Index (TSI) axis. A finite element model of a lead-rubber bearing was constructed in ABAQUS, where a user material subroutine UMAT was implemented to define the Unified Mechanics Theory equations and the viscoplastic constitutive model for lead. Finite element analysis results were compared with experimental test data.

On bending crashworthiness of smooth-shell lattice-filled structures

Thin-walled structures are widely used in engineering applications. In order to improve the mechanical properties of thin-walled structures, porous structures are usually filled into thin-walled tubes. However, the widely used porous structures have the disadvantages of randomness, heterogeneity and anisotropy. Recently, a novel porous structure called as smooth-shell lattice has gain attention for its high energy absorption capacity. The crashworthiness of thin-walled tube may be highly improved if it is filled by smooth-shell lattice. However, there are few researches on studying the crashworthiness of the smooth-shell lattice-filled structures. To this end, the bending crashworthiness of the smooth-shell lattice-filled structure is investigated jointly using experiment, numerical simulation and empirical formula in this study. The smooth-shell lattice of this study is constructed based on the triply periodic minimal surface (TPMS). Three kinds of TPMS-based smooth-shell lattices are considered in our study. The influence of the design parameters such as the shell thickness of lattice, unit-cell size of lattice and thickness of tube on the crashworthiness is studied. In order to obtain the optimal designs of smooth-shell lattice-filled structures, the PRS metamodels and NSGA-II are employed, while the peak crushing force (PCF) and specific energy absorption (SEA) are chosen as the optimization objectives. The force–displacement responses of three filled-tubes are fitted in the end. The investigation results show that the smooth-shell lattice-filled tube has more bending crashworthiness than the traditional foam-filled tube with the same weight. The smooth-shell lattice-filled tube can be used as excellent energy absorption structure in impact engineering.

The Effect of Wire Rope Material on Vibration Characteristics

Wire rope vibration isolators (WRI) are used to protect particularly sensitive and high technology products from severe dynamic loads such as shock and vibration. WRI is widely used in many industries, especially in the defense and space industry. In this study, the effect of rope material used in WRIs on vibration characteristics was experimentally investigated. WRIs were fabricated using nuflex, stainless steel and galvanized steel ropes as the main material component of the rope. Design and fabrication of 3 identical WRI models each with a rope diameter of 3 mm, namely Nufleks (NWRI), stainless (SWRI) and galvanized steel rope vibration isolator (GWRI), were performed. The produced WRI models were subjected to tensile-compression tests under different speed and pre-load conditions and then, force-displacement responses were obtained. In addition, dynamic vibration tests of WRI models were performed using the shaker system and accelerometers. As a result of the studies, it was observed that the rope material used in the WRIs significantly affected the vibration characteristics. When the quasi-static test results are examined, it is clearly understood that GWRI exhibits a more rigid characteristic compared to other models. At the same time, when the damping ratios obtained from hysteretic cycles are compared, it is clearly seen SWRI has the highest damping ratio. When the dynamic tests performed by shaker are examined, it is clearly seen that the isolator with the best vibration isolation characteristics is SWRI.

Lateral force–displacement response of buried pipes in slopes

A series of full-scale experiments was conducted to estimate lateral soil constraints on pipes buried in dense sandy slopes at different burial depths. The experimental data indicated that the soil force on the pipe increases with increase in the slope grade and burial depth ratio. The lateral soil force against relative pipe displacement response observed from the experiments is presented and compared to those arising from level ground conditions. The study was extended to larger burial depth ratios by simulating pipes under sloping ground conditions using a numerical (finite-element) model that was initially calibrated using the results from physical modelling. The findings from the study in terms of the variation of peak lateral soil restraint as a function of the slope grade and burial depth ratio are presented for consideration in pipeline design.

Constitutive behavior and fracture of intermetallic compound layer in bimetallic composite materials: Modeling and application to bimetal forming process

This paper presents a novel experimental and computational methodology to characterize the fracture behavior of the intermetallic bonding layer particularly for the bimetallic forming applications. The proposed methodology was applied to Al-Sn bearing alloy/mild steel bimetallic composite. Tensile-shear bimetal samples were fabricated to test the metallurgical bonding layer under shear conditions. Based on the macroscopic behavior, the coupled elasto-plasticity and damage constitutive equations for the bond material were formulated and implemented. The used damage model is written within the framework of the thermodynamic of irreversible processes with the concept of internal state variables and the framework of continuum damage mechanics (CDM). The characterization of the shear fracture behavior of the bond has included FE numerical simulation of tensile-shear tests of the bimetallic composite using ABAQUS/Explicit® FE code with the specially developed VUMAT subroutine. Accordingly, a calibration approach has been proposed to identify the fracture parameters of the bond based on the correspondence between the numerically predicted and experimental global shear force–displacement responses. These parameters have been applied to FE model of the U-bending testing of Al-Sn/mild steel bimetallic composite. A qualitative correspondence between numerically predicted results and U-bending experiment of the bimetal conducted under high-speed camera is deemed extremely satisfactory.

Lateral force-displacement response of rat-trap bonded masonry

Rat-trap bond (RTB) masonry is one of the most economical, fast, and energy efficient construction technique for brick masonry buildings. Many developing countries including India, Nepal, Sri Lanka and Pakistan have constructed large number of buildings using this technique. However, structural stability and performance validation are as important as the economy in any construction project. Therefore, this study presents the results of in-plane quasi-static cyclic load tests on three wall specimens constructed in RTB. The pre-compression load was adjusted to simulate the load condition of a typical two storey building. The key parameters evaluated include stiffness, ductility, damping, energy dissipation, force-displacement behaviour, lateral strength, etc. The experimentally obtained results were also compared with the existing research of similar nature on conventional masonry as well as with the results predicted by various empirical equations. The comparison indicates that the lateral strength and stiffness of rat-trap masonry is significantly less than those of conventional masonry because of the reduced effective thickness, while other properties like ductility, damping and energy dissipation do not show any significant variation.

Design of isotropic porous plates for use in hierarchical plate-lattices

This work deals with the elastic and plastic properties of two-dimensional periodic metamaterials. Design maps are developed to ensure their isotropic elastic response while attaining the theoretical stiffness limits. Numerical simulations of two different topologies - triangular and round hole staggered patterns - are performed to analyze their large deformation response for relative densities ranging from 0.1 to 0.9. The investigations show that the strength of triangular perforated plates is profoundly dependent on the unit cells’ direction concerning the axial loading; 0 and 30 degrees have the lowest and highest yield strength over the entire range of volume fractions. In contrast, the round hole staggered patterns exhibit an almost uniform yield strength in all directions. The yield strength of the circular patterns is significantly lower at low- and intermediate-density ranges; whereas they outperform the triangular ones at relative densities higher than 0.6. Additionally, validation experiments are performed on specimens of 0.3 relative density that have been extracted from DP980 steel sheets using micro waterjet cutting, showing good agreement in terms of force-displacement response and surface strain fields. A foam-like structure is built from periodic sheets and the scaling of the elastic properties of the resulting hierarchical 3D metamaterial are discussed.

Linearized modeling and optimization of shared mooring systems

Shared mooring systems, where adjacent platforms are tethered directly to each other, can reduce anchor quantities and mooring line lengths in a floating array but also introduce new modeling and design challenges. This paper presents and demonstrates a first-order approach to modeling and designing shared mooring systems that simplifies these challenges. We formulate a general, linearized model for the force–displacement response of shared mooring systems, including inter-platform couplings. Using this linearization, we realize significant simplifications to the shared mooring system design problem and propose a corresponding design optimization approach. Finally, we demonstrate the complete approach on a variety of shared-mooring floating wind farm layouts with generic design assumptions and constraints. Some fundamental observations about shared mooring systems can be made from the results. Polygonal array layouts with perpendicular anchor positions appear to maximize shared mooring system efficiency. Also, arrays with greater levels of sharing tend to exhibit larger deviations in offsets between platforms. Overall, the results show how the linearized approach can be applied to efficiently evaluate and systematically optimize preliminary shared mooring system designs.

Two-Intervals Hardening Function in a Phase-Field Damage Model for the Simulation of Aluminum Alloy Ductile Behavior

The aluminum alloys (AA) are among the most utilized materials in engineering structures, which induces the need for careful investigation, testing, and possibilities for accurate simulation of the structure’s response. AA 5083-H111 specimens were used to investigate the possibility of employing a Phase-Field Damage Model (PFDM) for the simulation of AA structures’ behavior. The specimens were mechanically tested by uniaxial tensile loading tests. Based on the obtained results, the PFDM was employed with a von Mises plasticity model, implemented in the Finite Element Method software. The plasticity model was extended by modification of the hardening function defined in two-intervals: a linear hardening and a Simo-type hardening. An excellent superposition of the simulation and experimental force-displacement response was recorded. These findings suggest that the AA structures’ response can be successfully simulated in the elastic-plastic domain, as well as its failure by damage being controlled.

Thermomechanical performance analysis and experiment of electrothermal shape memory alloy helical spring actuator

In this paper, an electrothermal shape memory alloy helical spring actuator constructed from shape memory alloy with copper-cored enameled wire is presented and fabricated. Based on the shear constitutive model of a shape memory alloy, the Thermo equilibrium equation and the geometrical equation of helical spring establish the thermomechanical theoretical model of helical spring actuator with electrothermal shape memory alloys under different scenarios. The thermomechanical behaviors of the actuator were verified by numerical simulation with experimental tests, and the actuator thermomechanical properties were derived from the analysis with current, temperature, response time, restoring force, and axial displacement as parameters. The experimental results show that the actuator produces a maximum recovery force of 70.2 N and a maximum output displacement of 7.7 mm at 100°C. The actuator response time is 26 s at a current of 3A. It is also demonstrated that the theoretical model can effectively characterize the complex thermo-mechanical properties of the actuator due to the strong nonlinearity of the shape memory alloy. The experimental temperature-force response and temperature-displacement response, as well as the force-displacement response at different temperatures, provide references for the design and fabrication of electrothermal shape-memory alloy coil spring actuators.

Prepeak energy evolution properties of sandstone subject to diametrical splitting with different loading rates

To understand the energy evolution properties during rock splitting under different loading rates, four groups of Brazilian test with a loading-unloading cycle corresponding to four orders of magnitude of controlled loading rate (10−1, 100, 101, 102 kN/min) were conducted on red sandstone using the MTS 322 testing system. The energy characteristics were interpreted by mathematically integrating the force-displacement responses of the tested rock specimens. It was found that at each loading rate, the input energy was a linear function as the elastic energy and dissipated energy, while these three types of energy nonlinearly grew with the unloading level. Importantly, the loading rate was found to exert an insignificant influence on the evolution of the linear energy properties (referring to the linear functions between the three types of energy); the energy storage coefficient (ESC) and/or energy dissipation coefficient (EDC) remained constant under various loading rates, exhibiting an approximate independency on loading rate. Based on this, a unified formula for describing the rate-independence of linear energy properties was presented in the tested loading rate range. It is also noted that rock mechanical parameters such as the peak force and peak displacement and the ESC and EDC are closely comparable versus the increasing loading rate, and hence the energy parameters are likely to be used to characterize the rock mechanical ones. Finally, the relevancy between energy allocation and rock failure patterns was discussed.

Energy-absorbing characteristics of hollow-cylindrical hierarchical honeycomb composite tubes inspired a beetle forewing

This paper investigates the superior energy-absorbing characteristics of hollow-cylindrical-joint hierarchical honeycomb composite tubes under axial quasi-static crushing. Biomimetic multi-cell tubes (BMCTs), inspired by the forewing of a beetle, were manufactured using the vacuum bag moulding method. Quasi-static compression tests were conducted to characterize the force–displacement response, the progression of failure, the crashworthiness characteristics, and the corresponding energy absorbing mechanisms. The experimental results show that the fiber orientation (α) has a significant effect on the energy-absorbing characteristics of these structures. The crush load efficiency (CLE) and specific energy absorption (SEA) tend to initially decrease and then increase with increasing α. It has also shown that the SEA of the BMCTs can be significantly affected by employing different fiber orientations. The highest SEA value measured on these structures, 77.3 J/g, is more than double of 34.9 J/g measured on the single circular tube counterpart. The energy-absorbing capacity of the composite structures is devisable and can be enhanced by integrated biomimetic design.

Experimental and numerical assessment of confined infill walls with openings and textile-reinforced mortar

This work's primary objective is to present an experimental campaign, comprised of three full-scale in-plane tests. It was assessed the effect of the openings (central window) and of using textile-reinforced mortar strengthening. The slenderness is also studied by comparing the results herein obtained with other test existing in the literature. The masonry infill walls were built with horizontal hollow clay bricks. All the tests consisted of applying cyclic (loading-unloading-reloading) history of imposed displacements in the in-plane direction employing a top horizontal load. The mechanical properties of the adopted materials are characterized and presented. The results will be presented in terms of in-plane force-displacement responses, damage evolution and energy dissipation capacity. A literature review of numerical modelling approaches to simulate the masonry infill walls seismic behaviour was provided after that. In the end, the experimental tests were simulated in the software OpenSees through a simplified modelling approach. The openings reduced the in-plane maximum strength and energy dissipation capacity by about 40% and 18%, respectively. On the other hand, the textile-reinforced mortar increased the initial stiffness, maximum peak strength and energy dissipation capacity by about 31%, 15% and 38%, respectively.