Initial Peak Load Research Articles

A Cylindrical Crash Absorber with Discontinuous Protrusions and Its Manufacture Using a Successive Partial Rubber-Bulging Method

In an effort to improve impact energy-absorption characteristics, this study introduces a cylindrical crash absorber (CAP) with discontinuous protrusions and a continuous local-expansion plastic-forming method for its manufacture. The mechanical properties of the cylindrical energy-absorption structure were modified by installing multiple particle protrusions on the cylinder sidewall to reduce the initial pickup load and improve the impact energy-absorption performance. To facilitate manufacture of the proposed CAP, a cylindrical rubber piece was placed into a cylindrical tube and pressure was applied to the rubber from both ends of the tube. The CAP was formed by the bulging force of the rubber. The formability was verified by developing a successive local bulge-forming experimental device and comparing the manufactured CAP with the results of numerical simulations. Testing of quasi-static collapse conducted on a CAP manufactured using this device verified the effectiveness of the proposed CAP design and its plastic-forming method. It was determined that this design reduced the initial peak load, and the crash absorber could maintain stability over a long, continuous distance during crushing deformation.

Reversed-Torsion-Type Crush Energy Absorption Structure and Its Inexpensive Partial-Heating Torsion Manufacturing Method Based on Origami Engineering

Abstract Current vehicle energy absorbers face two problems during a collision in that there is only a 70% collapse in length and there is a high initial peak load. These problems arise because the presently used energy-absorbing column has no deployment shrinkage function. It has been shown that a column called the Reversed Spiral Origami Structure (RSO) developed by Nojima solves the above two problems. However, in the case of the existing technology of the RSO, the forming cost of hydroforming is too expensive for application to a real vehicle structure. Therefore, a new structure imitating RSO, named the Reversed Torsion Origami Structure (RTO), has been developed, which has excellent energy absorption in simulation. Here, a manufacturing system is developed for the RTO cheaply. Excellent results are obtained also in a physical experiment. The RTO can replace conventional energy absorbers and is expected to be widely used in not only automobile structures but also building structures.

Meso-fracture mechanism of Longmaxi shale with different crack-depth ratios: Experimental and numerical investigations

The mechanical properties and fracture mechanism of shale are vital to the design of hydraulic fracturing schemes. To better understand the formation and evolution of hierarchical crack networks in shales, a scanning electron microscope (SEM) with a loading device was applied to carry out three-point bending experiment on Longmaxi shale with different crack-depth ratios (CDR). The micro-damage and fracture processes of shale were observed in situ. Based on the double-K fracture criterion, the subcritical crack length, and the initial and unstable fracture toughness were calculated theoretically. The results demonstrated that the crack initial load, peak load, and subcritical crack length decreased significantly with the increase of the CDR. Both the initial and unstable fracture toughness were relatively stable when the CDR was between 0.3 and 0.5, and they can be regarded as constants. The meso-failure mechanism of shale was tensile and shear failure, and fracture patterns were inter-granular, trans-granular and coupled fracture. Generally, tensile failure typically results in irregular rough sections, whereas shear failure results in smooth sections with parallel slip lines. The micropores inside and between the crystals can induce the connection and penetration of cracks. The initiation of microcracks is the result of the continuous accumulation and nucleation of multiple micro/nanoscale damage, and the tortuous crack path is caused by the variation in the local stress field at the crack tip. In addition, clump and smooth joint model (SJM) were introduced to simulate the effect of the sedimentary particle and bedding plane on crack propagation based on particle flow code in two dimensions (PFC2D). The simulation results were in good agreement with the experimental observations.

Bending response and energy absorption of sandwich beams with novel auxetic honeycomb core

In recent years, the enhanced auxetic honeycomb structure has attracted attention owing to its high strength and negative Poisson’s effect. The purpose of this study is to explore the bending response and energy absorption of the star-triangular honeycomb core (STH-C) and sandwich beam with an STH-C (STH-SW). Three-point bending tests and a series of numerical simulations are conducted to investigate the bending performance of the sandwich beams. The results indicate that STH-C exhibits only local bending deformation in the loading region, whereas the cells of the STH-SW undergo shrinkage deformation in the loading region, and the neighboring cells undergo tensile deformation. In addition, the deformation mode of the STH-SW is influenced by the compression position and structural parameters. Increasing the face sheet thickness and changing the thickness arrangements is beneficial to improving the load-bearing capacity of the sandwich beams, especially when tf/tb>1. Furthermore, the load-bearing capacity of the sandwich beams increase with the increase of the cell-wall angle and t/l, and increasing the t/l can change the cells from a global deformation to a local deformation mode. Subsequently, the complex proportional assessment method (COPRAS) is implemented to determine the influence weights of the structural parameters on the load-bearing capacity of the sandwich beams. The results demonstrate that the cell structure parameters have a more significant influence on the bending performance, especially the t/l. Finally, the bending performance of the STH-SW is compared with that of sandwich beams with different cores (star-shaped, re-entrant hexagonal and triangular corrugated structures). The results show that the energy absorption capacity of the STH-SW is 24.34% and 37.97% higher than that of sandwich beams with star-shaped and re-entrant hexagonal cores, respectively. Although the energy absorption capacity of the STH-SW is 10.25% less than that of multi-layer triangular corrugated core sandwich beam, there is no initial peak load for the STH-SW. This study is expected to provide some insights for further investigations on the bending performance optimization of sandwich beams with auxetic cores.

Crashworthiness analysis and optimization of bionic corrugated sandwich structures

To improve the crashworthiness of thin-walled sandwich structures, a series of bionic corrugated sandwich structures with triangular elements (the height-to-width ratios of the elements are defined as γ) were designed inspired by the structures of shrimp chelas, including single-layer, double-layer and three-layer corrugated sandwich structures (γ1, γ2 and γ3 denotes the height-to-width ratios of single-layer, double-layer and three-layer elements, respectively). To analyze the deformation and mechanical response of the bionic thin-walled structures, the finite element method was adopted based on LS-DYNA and HyperMesh. By taking the initial peak load Fp and specific energy absorption Es as crashworthiness indexes, the influences of γ on the crashworthiness of the corrugated sandwich structures were discussed. The crashworthiness of the single-layer sandwich structures becomes worse gradually when the parameters γ exceed a certain value. For the double-layer sandwich structures, the influences of the parameters γ2 in the lower layers on the crashworthiness is greater than that of the parameters γ1 in the upper layers.. The Fp decreases by 37.8% with the increase of γ2, which means the greater γ2 of the lower layer is beneficial to improve the crashworthiness of the structure. For the three-layer sandwich structures, the influence of γ on crashworthiness indexes was investigated by range and variance analysis methods. The results show that the γ3 has the most significant influence on Es, and the significance level reaches 0.1. Finally, the optimal parameters of the bionic corrugated sandwich structures were obtained by using the multi-objective particle swarm optimization method based on a polynomial regression (PR) meta model. The optimal results show that the crashworthiness of the single-layer corrugated sandwich structures improves with the increase of γ. For the double-layer corrugated sandwich structures, The γ of the lower layer affects the crashworthiness more significantly than the γ of the upper layer. The three-layer corrugated sandwich structure with lower γ has higher Es. The optimal dimensions of the single-layer, double-layer and three-layer structures are γ = 0.8; γ1 = 0.5 and γ2 = 1.2; γ1 = 0.6, γ2 = 0.6 and γ3 = 0.9, respectively. The above results are helpful for the design of the thin-walled sandwich structures.

Codeposition of Polyethyleneimine/Catechol on Fully Drawn Polyester Fiber‐Bundles for Investigating Interfacial Properties with Epoxy Resin

AbstractMussel‐inspiration is extensively utilized for multifunctional modification on the surface of universal materials. Polyphenols are more and more exploited for mussel‐inspired chemistry to replace polydopamine owing to their ubiquitousness and inexpensiveness. Herein, to explore the interfacial properties between fully drawn yarn (FDY) polyester fiber‐bundle and epoxy matrix, codeposition of polyethyleneimine/catechol (PEI/CCh) is used to modify FDY polyester fiber‐bundles by mussel‐inspired method. The orthogonal experiments are performed to obtain the optimum formula which is 2 g L−1 PEI, 1 g L−1 CCh, and 24 h codeposition time. The results of surface structure characterization measured via Fourier transform infrared spectroscopy, X‐ray photoelectron spectroscopy, scanning electron microscope, and energy dispersive X‐ray indicate that PEI/CCh aggregates are uniformly coated on fiber surface to fabricate continuously lamellar structures. The surface hydrophilicity and water infiltration rate constant are acquired by water contact angle. These results elucidated that FDY fiber surface is successfully endowed with polyethyleneimine/catechol aggregates and surface hydrophilicity greatly improved. Single fiber‐bundle pull‐out tests are conducted to evaluate the interfacial strength. Compared to pure fiber‐bundle specimens, there are 67.57%, 57.63%, and 45.07% increase of initial debonding load, peak load, and interfacial shear strength, respectively.

Experimental Study on Quasi-Static Energy Absorption Characteristics of Foam Concrete with Different Design Density by Hydroxypropyl Methyl Cellulose

The foam concrete test blocks with different design densities were prepared. Different dosages of hydroxypropyl methylcellulose on the quasi-static energy absorption characteristics of foam concrete were studied through comparative experiments. The results show that the foam nominal load-displacement curve can be divided into three stages: elastic compression stage, plateau stage, and a densification stage. The higher the density of the foam concrete, the higher the initial peak load, the more outstanding the load fluctuation, and the worse the protective performance. The smaller the density, the longer the compression platform stage. 0.06% of HPMC improves the energy absorption characteristics of foam concrete with different densities the most, and the smaller the density, the greater the improvement ratio.

Study of mixed mode I/II cohesive zone models of different rank coals

The present work studies the Park–Paulino–Roesler (PPR) model, a unified potential-based cohesive zone model (CZM), for mixed mode I/II fractures in different rank coals, including weakly caking coals, fat coals and anthracite, by using disk-shaped compact tension (DC(T)) tests and punch-through shear (PTS) tests. The PTS experiments show that with the increase in coal rank, the initial shear stiffness and shear peak loads grow and the maximum tangential crack opening displacement (δt) decreases gradually. Additionally, the post-peak softening curve tends to have a linear shape, and the shear crack surface is rougher and more tortuous for the lower rank coals. The mode II fracture energy (Φt) was evaluated by calculating the area under the shear load–displacement curves. Φt is remarkably higher than mode I fracture energy (Φn) for the same coal rank, and the average value of Φt decreases from 145.54 J/m2 to 70.11 J/m2 as the coal rank of the specimens increases from weakly caking coals to anthracite. In order to verify the obtained PPR CZMs, mixed mode I/II single-edge notched beam (SENB) tests were performed and the experimental results are in good agreement with the numerical simulation. Moreover, we conducted SENB tests with different-size specimens, and the established PPR CZM model demonstrated its ability of describing the size effect of the mixed mode I/II fracture in coals.

Tensile behavior and load transfer mechanism of concrete-filled square steel tube exterior-diaphragm connections stiffened with PBL

An innovative concrete-filled square steel tube (CFSST) exterior-diaphragm connection stiffened with perfobond ribs (PBL) is proposed to overcome the limits of CFSST exterior-diaphragm connections. Different CFSST connections, including one ordinary CFSST connection, one CFSST exterior-diaphragm connection, two CFSST exterior-diaphragm connections stiffened with PBL, and two CFSST connections stiffened with PBL, were tested under tensile loads. The tensile behavior, including failure modes, initial stiffness, yield load, peak load, and deformation of different connections, was analyzed and compared based on the test results. By analyzing the stress distribution in critical sections of branch plates or exterior diaphragms and the contribution of different parts to the total tensile load in critical sections of joint regions at different loading stages using the finite element method, the load transfer mechanism of different connections was analyzed and compared quantitatively. The results showed that the PBL transferred a considerable percentage of the tensile load from the branch plates or exterior diaphragms to the core concrete, which resulted in a more uniform stress distribution in the branch plates and exterior diaphragms and caused the core concrete to have a direct function in the load transfer in joint regions; thus, the load transfer and deformation condition of connections were improved. The innovative CFSST exterior-diaphragm connections stiffened with PBL had excellent tensile behavior with the largest initial stiffness, yield load, and peak load, the smallest joint region deformation, and the most uniform stress distribution, thus failed due to the yielding of branch plates.

An experimental and numerical study on the crush responses and energy absorption characteristics of single- and bi-layer cups under low-velocity impact

Observations on the crush responses and the energy absorption characteristics of single- and bi-layer deep-drawn cups subjected to experimental axial impact loading are presented in this manuscript. Bi-layer plates composed of aluminum and stainless steel alloys were fabricated by joining with adhesive and formed by a deep drawing process to produce the final cup shape. Impact testing was performed using a custom-built drop-tower system with a mass of 45.45 kg and impact velocities ranging from 2.8 m/s to 4.5 m/s. Various material and geometric parameters for the bi- and single-layer cups were considered in the study. Numerical simulations were conducted to investigate the deformation mechanisms and crushing behavior of the combined shells. Furthermore, based on the polynomial response surface method and using non-domain sorting genetic algorithm II, some multi-objective optimizations were performed on specific energy absorption, stroke efficiency, specific total efficiency, and initial peak load. Experimental and numerical results illustrated that the deformation of the bi-layer cups was different from the single-layer cups, especially in the head zone. Moreover, the specific total efficiency for specimens having a diameter of 55 mm and 65 mm were approximately 35% and 55% less than cups with a diameter of 45mm, respectively. It was found that the layer order of the bi-layer cup influences the energy absorption capacities of the specimen. Specifically, cups with steel as the outer layer experienced crush force efficiency and total efficiency of 6% and 5% higher than those with an aluminum outer layer, respectively.

Deformation and energy absorption properties of cenosphere/aluminum syntactic foam-filled circular tubes under lateral quasi-static compression

Cenosphere/aluminum syntactic foam filled thin-walled tubes were prepared by inserting aluminum matrix syntactic foams reinforced with three kinds of industrial fly ash cenospheres with different average particle sizes (150μm, 200μm and 300μm) into empty steel tubes. In order to investigate the response of syntactic foam-filled tubes under lateral compression, quasi-static compression experiments were performed on thin-walled empty tubes, cenosphere/aluminum syntactic foam cylinders and cenosphere/aluminum syntactic foam-filled tubes by electronic universal material testing machine. LS-DYNA finite element software was used to verify and numerically predict the mechanical properties and energy absorption performance of foam-filled tubes. The results showed that the foam-filled tube exhibits a deformation mode of six plastic hinges under lateral compression. The initial peak load and specific energy absorption of the foam-filled tube increase with the decrease of the average particle size of cenospheres. The tube wall has obvious restraint effect on the filler, but the increase of the tube wall thickness will reduce the energy absorption capacity of the whole foam-filled tube.

Flexural Behavior of Reinforced Concrete Slabs Reinforced with Innovative Hybrid Reinforcement of Geogrids and Steel Bars

This paper aims to innovate a hybrid reinforcement system for concrete slabs, consisting of geogrids and steel bars, by conducting an experimental comparative study between using different types, tensile strengths, and layers of geogrids as additional reinforcement to steel bars in comparison to conventional steel-reinforced concrete control slab. These concrete slabs were tested under a four-point loading system until they failed due to bending. As an addition, strain gauges were attached to the concrete slabs bottom reinforcement (geogrids and steel bars) to provide a close examination of geogrids and steel bars as a hybrid reinforcement system. Results show that the innovated hybrid reinforcement system of uniaxial geogrids and steel bars more preferred as concrete slabs reinforcement as it provided more benefits values (including, but not limited to, initial-peak load, steel-yield load, post-peak load, displacement ductility index, and energy absorption capacity) and more efficient utilization (including, but not limited to, higher benefits to cost values and better flexural performance) than the case of using conventional reinforcement of steel bars and the cases of using triaxial geogrids as additional reinforcement to the steel bars; however, triaxial geogrids provide lower deflection values and higher first-crack load values.

Modification of the design of circular thin-walled tubes to enhance dynamic energy absorption characteristics: Experimental and finite element analysis

A thin-walled tube is an energy absorber device that functions to dissipate kinetic energy into another form of energy during impact. The design of thin-walled tubes is a significant factor which affects to the energy absorption characteristics. This paper provides a comparative study between the original thin-walled tube designs and several modified tube designs that have been proposed. The main objective is to improve the energy absorption characteristics, such as energy absorption capacity, initial peak load, specific energy absorption (SEA) and crush force efficiency (CFE). Throughout this research, aluminium alloy AA6061-T6 has been used as the material for all tubes. For comparison, all of the tubes are developed with a circular shape with the same diameter, thickness and length. In addition, they are also impacted at the same kinetic energy under dynamic axial loading. Validated LS-DYNA finite element (FE) models have been used to simulate the impact of the thin-walled tubes. Compared to the original tube design, the modified tubes have improved energy absorption characteristics. A conical tube with a flat end cap was identified as the best performing tube among the modified tubes because it had the lowest initial peak load, a moderate energy absorption capacity and an excellent CFE and SEA. The findings from this study can be used as a guidance in designing thin-walled structure.

Research into the mechanical properties of wet-sprayed polypropylene fibre-reinforced concrete

As the depth of mines increases, the in situ stress increases gradually, resulting in increasingly demanding requirements for the support strength of coal-mine roadways and making it more difficult to provide this support. For this reason, more effective forms of support are needed. Concrete is a typical support form, but ordinary concrete has low support strength, cracks easily and is prone to brittle failure, whereas polypropylene fibre-reinforced concrete has a good inhibition effect on crack propagation and can remarkably improve the post-cracking performance and toughness of concrete. This paper studies the mechanical properties and application effects of wet-sprayed polypropylene fibre concrete in the mining context. A final mix proportion is obtained, a flexural toughness test on the round slabs of the concrete is conducted, and the corresponding initial cracking strength, peak strength, fracture energy and toughness are studied. This wet-sprayed polypropylene fibre concrete was applied and its application effect investigated. The results show that wet-sprayed polypropylene fibre concrete has advantages such as enhanced integrity and more uniform stress distribution. The initial cracking strength, peak load and energy absorbed of wet-sprayed polypropylene fibre concrete specimens are higher than those of dry-sprayed reinforcing mesh concrete specimens. An engineering practice application indicates that the resilience rate and dust concentration were significantly reduced during wet-sprayed polypropylene fibre concrete construction, and construction efficiency and economic benefits clearly increased. The research achievements are of great theoretical and practical significance in developing a further understanding of the fracture instability mechanism and mechanical properties of wet-sprayed polypropylene fibre concrete. This method may be applied widely in sinking and driving engineering to improve the support effect and ensure mine safety.

Damage assessment of braided composite tube subjected to repeated transverse impact

In this study, damage behavior and failure mode of braided composite tube subjected to repeated transverse low-velocity impact were investigated by combining experimental and numerical methods. The effects of impact energy (2.0 J, 5.6 J and 10.5 J) and impact position (identical, adjacent and opposite positions) on impact responses were evaluated. A finite element (FE) model with high computational efficiency was also established to predict the effect of single impact on the repeated impact response by varying boundary conditions. When subjected to single impact, the braided tube presented delamination-dominated damage behaviors caused by obvious structural deformation. The top part sunken and both lateral sides bulged, were found to have correlation with the mechanical response of tube with respect to initial scope and peak load, respectively. The delamination area increased at higher impact energies due to increasing shear stress caused by adjacent braided layers. Delamination induced by the first impact had different role on repeated impact responses. At identical position, it caused larger sinking deformation at top part of the tube and thus a lower initial scope. At adjacent position with impact energy of 5.6/10.5 J, the delamination damage caused a reduced resistance to bulging deformation at one lateral side of the tube, leading to a lower peak load. At opposite position, it had no obvious influence on repeated impact response.

Effects of creep recovery on the fracture properties of concrete

To study the influence of creep recovery on the fracture properties of concrete, the pre-notched specimens were firstly subjected to three-point bending (TPB) loading at 60% peak load (Pmax) over 30 days. Afterwards, the load was removed and the creep recovery tests were performed for 1, 2, 3 and 15 days, respectively. Thereafter, the quasi-static TPB tests were conducted on the creep recovery specimens. The deformation versus time curves, initial cracking load (Pini), peak load and fracture energy in the quasi-static TPB tests after creep recovery were obtained. Also, the numerical analyses were conducted by combining with the Norton-Bailey model to investigate the stress variations at the crack tip and the time-dependent behaviour of concrete. By comparing the fracture parameters for the specimens with and without undergoing creep recovery, the effects of creep recovery on the fracture characteristics of concrete were assessed. The results showed that during the creep stage, the stress relaxation generated at the crack tip due to viscoelastic characteristics of concrete enlarged the deformation. In contrast, the reversed stress would occur at the crack tip during the recovery stage, and its relaxation over the time contributed to the time-dependent deformation during the creep recovery stage. By comparing with the specimens under the quasi-static TPB loading, Pini and Pmax for the creep recovery specimens would increase, and the increments slowed down over the recovery time. However, the increases in Pini and Pmax for the creep recovery specimens could not enhance the initial and critical fracture toughnesses and these toughnesses were approximately equal to those under the quasi-static tests.

On low-velocity impact response of foam-core sandwich panels

This study aimed to investigate low-velocity impact responses and crashworthiness of different aluminum foam-core sandwich structures. Several drop-weight dynamic impact tests were first conducted on both sandwich structures and their individual components to explore the mechanism of energy absorption and interactive effect between the foam core and facesheets. Different shapes and sizes of impactors were used in the experiments. The full-field deflection distribution was acquired by a 3D optical scanner to assess the failure patterns. A full-scale finite element model was then created to simulate the low-velocity impacting response of the foam-core sandwich panels. After the finite element model was validated against the experimental results, it was used to further explore the crash behavior of multi-layered sandwiches. It was found that multi-layer sandwich structure had much better performance in the crush force efficiency than those with single-layer foam core. Based upon the energy principle, an energy-based analytical model was also derived to estimate the initial peak load. It was demonstrated that the analytical predictions were in good agreement with the experimental and numerical results. The presented experimental, numerical and analytical studies are anticipated to provide systematic understanding and new knowledge for design of multilayer sandwich configurations aiming at more desirable impact resistance and better lightweight characteristics.

Experimental investigation of the crashworthiness performance of fiber and fiber steel-reinforced composites tubes

Crashworthiness plays a key role in energy absorption and hence in vehicle accidents. The energy absorption capacity of laminated composite materials is heavily investigated in the industry due to their low cost, corrosion resistance, and high strength to weight ratio. Thus, this paper experimentally investigates the effect of the addition of woven fiber laminates and fiber steel sandwich laminates on the strength and energy absorption capacity of PVC polymer tubes. The sandwich-structured composite is formed from two glass-fiber composite layers with a steel layer in between. Four normal and hybrid reinforcement configurations are proposed, evaluated, and compared to the benchmark unreinforced tube. The crashworthiness characteristics of the reinforced composite tubes were identified using quasi-static axial compression tests. The crushing parameters, in terms of load–displacement response, load-carrying capacity, Specific Energy (SE) absorption capability, and Crush Force Efficiency (CFE) were determined for each sample. Moreover, Scanning Electron Microscope (SEM) analysis was carried out to investigate the microstructures, which clearly indicate the fractured surfaces. The results show that the tube reinforced with a 1 mm steel layer sandwiched between 2 layers and 4 layers of woven glass-fiber has the highest SE and CFE of 14 J/g and 0.91, respectively, while the tube reinforced with 7 layers of glass fiber layers only has the highest Initial Peak Load (IPF) of 139.36 kN.

Anisotropic Material Damage Model of Randomly Oriented Thermoplastic Composites for Crash Simulation

<div class="section abstract"><div class="htmlview paragraph">In this research, a material model was developed that has orthotropic properties with respect to in-plane damage to support finite element strength analysis of components manufactured from a randomly oriented long-fiber thermoplastic composite. This is a composite material with randomly oriented bundles of carbon fibers that are approximately one inch in length. A macroscopic characteristic of the material is isotropic in in-plane terms, but there are differences in the tension and compression damage properties. In consideration of these characteristics, a material model was developed in which the damage evolution rate is correlated with thermodynamic force and stress triaxiality. In-plane damage was assumed to be isotropic with respect to the elements. In order to validate this material model, the results from simulation and three-point bending tests of closed-hat-section beams were compared and found to present a close correlation. However, in the case of axial compression of double-hat-section beams, it was found that although the initial peak load corresponded closely, the peak loads after the second peak did not match. As a cause for this, it is conceivable that the damage applied in the transverse direction differs from that of axial compression direction. A test that would identify the relationship between these different instances of damage was devised, and the damage characteristics were measured. It was found from the results of this test that the in-plane damage evolution would need to be given orthotropic properties. The orthotropic damage characteristics were additionally implemented in the material model and the load-stroke curves from axial compression testing of closed-hat-section beams and from simulation were compared. It was confirmed that the loads increased from the second load peak and on, suggesting that the conceptual approach of the material model was correct.</div></div>

Energy Absorption Analysis and Multi-objective Optimization of Tri-layer Cups Subjected to Quasi-static Axial Compressive Loading

In this paper, the energy absorption features of tri-layer explosive-welded deep-drawn cups subjected to quasi-static axial compressive loading are investigated numerically and experimentally. To produce the cups, tri-layer blanks composed of aluminum and stainless steel alloys were fabricated by an explosive-welding process and formed by a deep drawing setup. The quasi-static tests were carried out at a rate of 2 mm/min. Based on the structure of the tri-layer cups and to calculate the energy absorption features of these structures, a numerical model was established and validated by experimental findings. Moreover, based on a surrogate model and using non-domain sorting genetic algorithm II, multi-objective optimizations were performed on specific energy absorption and initial peak load. The results indicated that the total absorbed energy and mean crush force of the pure stainless steel tri-layer cup were about 5.8 and 5.7 times the values of those for the pure aluminum specimen, respectively.