Quasi-static Compression Experiments Research Articles

Characterization of mechanical equivalent properties for node enhanced graded lattice structure

Abstract Considering the stress concentration at the rod connection of traditional body-centered cubic (BCC) lattice structure, a node enhanced BCC (NBCC) lattice structure was proposed. In recent years, graded lattice structure has gradually attracted attention due to their unique mechanical properties. In this paper, two different graded NBCC lattice structures were designed and their static mechanical properties were evaluated through quasi-static compression experiments and simulations. Moreover, homogenization theory was applied to calculate the equivalent modulus of lattice structure. This method was extended from uniform lattice structure to graded lattice structure by improving the application of periodic boundary conditions. The obtained results were in good agreement with the experimental and simulation data. The quasi-static compression tests demonstrated that NBCC can effectively reduce the stress concentration and improve the load-bearing capacity about 25% compared to BCC. The graded lattice structures exhibit varying mechanical properties depending on their design and present better mechanical performance in the anisotropic direction. Finally, the relative relationship between the equivalent elastic modulus and the equivalent shear modulus in the lattice structure was studied. The prediction formula for equivalent shear modulus was extended based on the Gibson-Ashby formula.

Mechanical Properties Directionality and Permeability of Fused Triply Periodic Minimal Surface Porous Scaffolds Fabricated by Selective Laser Melting.

Titanium alloy porous scaffolds possess excellent mechanical properties and biocompatibility, making them promising for applications in bone tissue engineering. The integration of triply periodic minimal surface (TPMS) with porous scaffolds provides a structural resemblance to the trabecular and cortical bone structures of natural bone tissue, effectively reducing stress-shielding effects, enabling the scaffold to withstand complex stress environments, and facilitating nutrient transport. In this study, we designed fused porous scaffolds based on the Gyroid and Diamond units within TPMS and fabricated samples using selective laser melting technology. The effects of the rotation direction and angle of the inner-layer G unit on the elastic modulus of the fused TPMS porous scaffold were investigated through quasi-static compression experiments. Furthermore, the influence of the rotation direction and angle of the inner-layer G unit on the permeability, pressure, and flow velocity of the fused TPMS porous scaffold structure was studied using computational fluid dynamics (CFD) based on the Navier-Stokes model. The quasi-static compression experiment results demonstrated that the yield strength of the fused TPMS porous scaffold ranged from 367.741 to 419.354 MPa, and the elastic modulus ranged from 10.617 to 11.252 GPa, exhibiting stable mechanical performance in different loading directions. The CFD simulation results indicated that the permeability of the fused TPMS porous scaffold model ranged from 5.70015 × 10-8 to 6.33725 × 10-8 m2. It can be observed that the fused porous scaffold meets the requirements of the complex stress-bearing demands of skeletal structures and complies with the permeability requirements of human bone tissue.

A study of multi-stage energy absorption characteristics of hybrid sheet TPMS lattices

Triply periodic minimal surface (TPMS) has many excellent properties, such as stable energy absorption, a high specific strength, a large surface area, etc. The functional multi-stage design and research of TPMS lattices were carried out to improve the mechanical performance. The deformation modes and curves of three uniform TPMS lattices (Primitive, Gyroid, and Diamond) and their hybrid lattices were analyzed by quasi-static compression experiments and numerical simulations. Based on the uniform TPMS lattice, hybrid sheet TPMS lattices were designed to realize the multi-stage energy absorption (multi-stage platform) and multi-stage protection integrated porous structure. The two-stage energy absorption characteristics of hybrid sheet TPMS lattices were systematically studied, and the effects of hybrid TPMS composition, width of the transition layer, relative weight, and hybridization method on the multi-stage energy absorption were obtained. The results indicated that the Gyroid–Diamond hybrid lattice performed the best, with the specific energy absorption (SEA) increasing by 30.48% and 0.51%, and the yield stress decreasing by 14.01% and 30.07%, respectively, as compared to the single TPMS lattice. Width of the transition layer has little effect on the two-stage energy absorption. The relative weight will shorten or widen the length of the two-stage platform stress. The hybridization method shows that the sequence hybridization along the loading direction based on the TPMS lattice yield strength is the best arrangement to achieve the effect of multi-stage energy absorption. Finally, the three-stage energy absorption characteristics of hybrid Primitive–Gyroid–Diamond lattices are further studied. The results show that with the increase of layers of TPMS lattices, the fluctuation of the multi-stage curve and the yield stress will increase.

A novel hybrid lattice structure for improving compression mechanical properties

Lattice structures are widely used in load-bearing and energy-absorption applications for their lightweight, high specific stiffness, high specific strength and excellent energy-absorption. A novel hybrid lattice cell that combining octet cell and body-centered cube cell was proposed, and quasi-static compression experiments and finite element simulations were performed to investigate their energy-absorption characteristic and deformation mechanisms. The effects of the relative density, configuration of cell and component ratio sub-cell on the compression responses were also explored. The results showed that hybrid lattice improves compression modulus and yield strength by 10% and 16% maximally, respectively, and the energy-absorption of enhancement is 20% higher than the conventional lattices. In addition, the hybrid lattice can significantly alleviate the stress softening. By increasing the volume ratio of body centered cubic in the hybrid lattice structures, the energy-absorption can be improved. Under dynamic loading, the proposed hybrid lattice structures displayed outstanding normalized yield strength, which is superior to majority of porous structures. Inspired by the precipitation hardening mechanisms used in metallurgy to design high-performance alloys, two dual-phase lattices are developed. The quasi-static compression of dual-phase lattices shows three stages plateau stress and has a higher third stage than that of traditional dual-phase lattices. These findings provided design strategy for lightweight structure.

Quasi-static and dynamic mechanical characterization of clay and ballistic soap

Ballistic gelatin, soap, and clay are three human simulated target materials commonly used in the field of wound ballistics research. Currently, there are more studies on ballistic gelatin’s mechanical properties, but rarely on clay and soap. In this paper, the mechanical properties of clay and soap materials were tested by using universal material testing machine and Hopkinson bar, respectively, and their stress-strain curves were obtained under different temperatures (4°C, 15°C, and 25°C) from quasi-static to dynamic loading. The test results showed that the clay material was sensitive to temperature and strain rate in quasi-static conditions, its stress-strain curves showed nonlinear strengthening characteristics, and the stress always increased without strength decrease during the loading process; the dynamic compression mechanical properties of clay were significantly higher than the quasi-static mechanical properties, showing obvious strain rate strengthening effect. In quasi-static compression experiments, the stress-strain curves of soap material showed bilinear elastic-plastic material characteristics; when the strain was less than 0.1, it was insensitive to temperature and strain rate, and only when the strain was more significant than 0.1 did it show a certain temperature and strain rate correlation. The dynamic compressive mechanical properties of soap are significantly higher than the quasi-static mechanical properties, showing a significant strain-rate strengthening effect. The stress of soap at the same strain rate is slightly less than that of clay. These results not only help provide more accurate material parameters for relevant numerical calculations but also help to provide references for the development of new bionic materials.

A comparative study of different constitutive models to predict the dynamic flow behaviour of a homogenised AT61 magnesium alloy

In the present work, phenomenological and physical models were established to predict the plastic flow behaviour of homogenised AT61 magnesium alloy. The models were developed using experimental data obtained from compression experiments under quasi-static and dynamic loading conditions over a wide range of strain rates (10−4–4000 s−1) and temperatures (25–250 °C). The quasi-static and high strain rate compression experiments were performed on a universal testing machine and a split Hopkinson pressure bar, respectively. Several types of basic and modified (m-) constitutive models, including Johnson-Cook (JC), Khan-Huang-Liang (KHL), and Zerrilli-Armstrong (ZA), were calibrated to predict the plastic flow behaviour of an AT61 alloy. The prediction capabilities of these constitutive models were compared statistically in terms of average relative error and correlation coefficient. It was noticed that the predictions of the models JC, m-JC, and m-KHL were quite similar to the experimental findings; however, ZA model deviates more from the experimental data.

A novel hybrid auxetic honeycomb with enhanced load-bearing and energy absorption properties

Auxetic structures with negative Poisson's ratio exhibit excellent performance in cushioning, shear resistance and energy absorption, but their load-bearing capacity is usually poor. To address this drawback of the conventional Auxetic structure, a star-rhombic honeycomb (SRH) design is proposed in this paper to improve its load-bearing capacity. Analytical models of the elastic modulus and Poisson's ratio of this structure for different loading directions are developed. Quasi-static compression experiments were conducted on SRH specimens fabricated by selective laser melting (SLM) technique. Good agreement was achieved between the simulated and experimental stress response curves and deformation patterns. It was found that the SRH structure possessed better elastic modulus and energy absorption capacity than the SH structure without sacrificing the auxetic properties. The elastic modulus and Poisson's ratio of SRH under the x loading direction are more sensitive to the changes of structural parameters. An optimum energy absorption performance is achieved for an appropriate ratio of the inner rhombic strut thickness to outer reentrant strut thickness (k = 0.5). The specific energy absorption of SRH is improved by 136% and 75% compared to that of the conventional reentrant honeycomb (RH) and star honeycomb (SH), respectively. It has advantages for application scenarios with requirements for both auxetic and load bearing properties.

Simulating progressive damage behaviors of carbon fiber reinforced composite tubes triggered by various initiators under axial crushing

We develop finite element models to describe the progressive damage behaviors of two types of carbon fiber reinforced epoxy (CF/EP) composite tubes triggered by three types of initiators, i.e. a flat surface plate, an outward-triggering plug and an inward-triggering cap, using a continuum damage mechanics-based approach. First, the quasi-static compression experiments were conducted to capture the load–displacement relation, failure mode, and microscopic damage of CF/EP composite tubes. These experimental results were utilized to validate the proposed finite element models. The numerical crushing response agreed well with the experimental data. Then, a comparative study on the progressive damage behaviors of two types of CF/EP composite tubes subjected to three typical initiators was performed. The failure mechanisms were systematically articulated, showing that the fiber breakages were significant due to the concentration of compressive stress caused by external loads, while the matrix and interlaminar damage behaviors were predominant under any of these initiators.

Analytical design of stretching-dominated truss lattices with tailored elasticity from transversely isotropic base materials

Incorporating the process-induced material anisotropy into design framework of additively manufactured lattice structures is crucial to ensure the accuracy of design and analysis models. This work proposes an analytical approach to design stretching-dominated truss lattices with tailored elastic properties, including isotropic elasticity, tailored zero/negative Poisson’s ratios, tailored Young’s moduli ratios along specified directions. The transversely isotropic elasticity is adopted to represent the micro lase powder bed fusion (LPBF) process-induced anisotropy of base materials. The lattices are designed through combination of elementary bars with appropriate volume fractions. An analytical homogenization theory is established to determine elastic constants of combined lattices. An analytical design approach is proposed to obtain elastically isotropic truss lattices. A traversal searching is performed to determine ranges of Young’s moduli, Poisson’s ratios of combined lattices, and find most manufacturable ones with tailored Young’s moduli ratios and Poisson’s ratios. Finite element analysis reveals all designed lattices from anisotropic materials achieve better agreements to design targets than those designed from isotropic materials, thus validating the superiority of the proposed method. The lattices with isotropic elasticity, tailored zero/negative Poisson’s ratios are fabricated in stainless steel 316L via micro-LPBF, and quasi-static compression experiments are performed to further validate the proposed design approach.

Koch Hierarchical Honeycomb: A Fractal-Based Design for Enhanced Mechanical Performance and Energy Absorption.

A novel energy-absorbing structure, the Koch hierarchical honeycomb, which combines the Koch geometry with a conventional honeycomb structure, is proposed in this work. Adopting a hierarchical design concept using Koch has improved the novel structure more than the honeycomb. The mechanical properties of this novel structure under impact loading are studied by finite element simulation and compared with the conventional honeycomb structure. To effectively verify the reliability of the simulation analysis, quasi-static compression experiments were conducted on 3D-printed specimens. The results of the study showed that the first-order Koch hierarchical honeycomb structure increased the specific energy absorption by 27.52% compared to the conventional honeycomb structure. Furthermore, the highest specific energy absorption can be obtained by increasing the hierarchical order to 2. Moreover, the energy absorption of triangular and square hierarchies can be significantly increased. All achievements in this study provide significant guidelines in the reinforcement design of lightweight structures.

Study and optimization of energy absorption characteristics of a new concave polygon tube

To improve the energy absorption characteristics of the traditional convex polygonal tube and the existing concave polygonal tube, a new evolutionary scheme for the concave polygonal tube was proposed. The energy absorption characteristics of different concave tubes evolved from the common scheme (Scheme-I) and the new evolution scheme (Scheme-II) were studied through quasi-static compression experiments and numerical simulations. The results show that under the same mass, the concave polygonal tube evolved by Scheme-II has better energy absorption characteristics. The folded half-wavelength is smaller at the same compression distance, and compared with the traditional pentagon tube, the energy absorption (EA) of the pentagon concave of Scheme-II (N5E-CT) is improved by 218%, and the crushing force efficiency (CFE) is improved by 69%. Secondly, the mean crushing force of convex and concave tubes is derived and verified by the folded element theory. The mode of deformation of concave tubes under different structural sizes was investigated, and the size range within which the concave tube can remain stable was obtained. In addition, the evolution of the specific energy absorption (SEA) of the concave tubes was explored, and the SEA and the number of structural sides (N) show a trend of first increasing and then decreasing. Finally, the multi-objective optimization of the pentagon concave tube with excellent energy absorption characteristics was conducted, and the initial peak crushing force of the optimized structure was reduced by 19.92%.

Design and Microscale Fabrication of Negative Poisson’s Ratio Lattice Structure Based on Multi-Scale Topology Optimization

The current design of negative Poisson’s ratio lattice structures is mainly forward-looking and predominantly dependent on several known deformation patterns. To automate the generation of structures with programmable Poisson’s ratio, the study utilized the energy homogenization method and the Solid Isotropic Material with Penalization (SIMP) method to establish an optimization model for negative Poisson’s ratio. By proposing a relaxed objective function and eliminating damping in the Optimality Criteria (OC) method, the study achieves the automatic evolution of negative Poisson’s ratio programmable lattice unit cells, with the lowest Poisson’s ratio achieving −0.5367, and an equivalent elastic matrix is derived. The iterative process’s efficiency is comparable to that of commercial software, with a maximum iteration time of 300 s, enabling the prompt identification of fundamental configurations. To validate the method’s effectiveness, finite element analysis was performed on four tubular structures, revealing evident tension–compression deformation patterns. Moreover, the microscale selective laser melting was used to successfully prepare multiple sets of tubular samples made from 316L stainless steel, each with a height of 5 mm. Quasi-static compression experiments showed negative Poisson’s ratio effects and buckling forms that align with finite element analysis results, providing valuable insights for industry applications.

Experimental and numerical investigation on saturated concrete subjected to underwater contact explosion

The hydraulic concrete structures were partially or fully in direct contact with water during the service life. The mechanical properties of saturated concrete are different from dry concrete because of the presence of water. To investigate the underwater blast resistance mechanism of saturated concrete, saturated concrete slabs were first tested in underwater explosion experiments with different TNT masses of 2.5 g, 5 g, and 10 g. The experimental results showed that the crater on the front of the concrete slab was smaller than those on the back and the size of the crater increased with increasing mass of TNT. Numerical simulations were conducted and material parameters were determined based on additional tests: The damage model under different stress states was proposed by repeated loading and unloading tests in tension and compression under different confining pressures. The damage model was then embedded into the Holmquist-Johnson-Cook (HJC) model. Quasi-static and dynamic compression experiments were conducted to determine the material parameters of the saturated concrete. A three-dimensional fluid-solid coupling numerical model in ABAQUS was proposed for simulating the underwater explosion and its interaction with the saturated concrete slab. Finally, the mechanisms that produce differences in the damage pattern of concrete slabs at different explosive masses are revealed.

In-plane elastic property prediction of straight-arc coupled auxetic structures

Auxetic metamaterials with two components exhibit a wide variety of potential engineering applications due to their exotic mechanical properties. In this work, a novel straight-arc coupled structure (SACS) is designed by introducing a circular arc structure to a classical re-entrant structure. This work aims to explore the linear and geometrical nonlinear mechanical of SACS at large strains. According to Castigliano’s second theorem, the in-plane linear theoretical model is established to obtain equivalent Poisson’s ratio and elastic modulus. A geometrical nonlinear model is further established based on large deflection theory and chain algorithm. The finite element method is used to verify the prediction of the theoretical solution, and linear and nonlinear mechanical properties of the SACS are studied by numerical simulation. The influence of geometric parameter re-entrant angle and arc radius on the mechanical properties of the SACS is investigated to compare the linear and nonlinear mechanical properties. The linear numerical simulation of SACS with two transverse ribs (SACS-TR) and classical re-entrant honeycomb structure with two transverse ribs (CRS-TR) is carried out to analyze the in-plane elastic properties. These results demonstrate that considering the geometric nonlinear model can predict the actual structural deformation more accurately, which is verified by the quasi-static compression experiment results at large strains. The SACS design can enhance the auxetic effect and structure Young’s moduli under the same dimension.

Influence of density gradient and hybrid effect on quasi-static axial crushing behavior of lattice cylindrical structures

Uniform/gradient lattice cylindrical structures (ULCS/GLCS) and hybrid uniform/gradient lattice cylindrical structures (HULCS/HGLCS) are innovatively designed and fabricated. The axial crushing behaviors of these four-type cylindrical structures are investigated by the quasi-static axial compression experiments and numerical simulations. The influence of the density gradient and the hybrid effect (metal skin+ABS core) on the deformation mode, loading capacity, and energy absorption of the lattice cylindrical structures are elaborated systematically. The results show that the gradient design realizes the function of regulation and controllability of the structural deformation. The softer layers (with smaller relative density) in GLCS begin to deform first and then gradually extend to the harder layers (with larger relative density). And it effectively reduces the initial peak compression force (PCF), and makes the load more stable on the premise of energy absorption. However, unstably catastrophic failures are observed before the final densification in both ULCS and GLCS during the compression due to the brittleness of the ABS material and the compression–expansion​ deformation of structure. For HULCS/HGLCS, it presents progressive crushing mode and overcome the unstably catastrophic failure due to the ductility and constraint of the metal skins. The effect of “1 ＋ 1 > 2” on energy absorption from hybrid effect is achieved in HULCS/HGLCS, in which the EA of HULCS and HGLCS increases by 74.62% and 100.78% comparing the sum of all components individually compressed. Moreover, the progressive peak with increasing trend of HGLCS demonstrated that the hybrid design enhances the advantages of gradient design in sandwich structures.

Study on axial compression property of thin walled tube filled with negative Poisson’s ratio lattice

In this paper, a new type of thin-walled energy absorbing structure filled with auxetic lattice structure has been proposed. The deformation mode and mechanical responses of the new filled tube under compression load have been studied through quasi-static compression experiment and numerical simulation. A theoretical model for predicting the average compression force has been established and verified with simulation analysis. The influences of the geometrical parameters in the compression performance of the filled tube have been studied. The results show that the failure mode of the filled tube under compression load is local buckling failure. Compared with the single thin-walled tube and the lattice structure, the filled tube has better compression resistance. Through parameter analysis, it is clear that the anti-compression property of the filled tube can be significantly improved by increasing the wall thickness of the cell rod and the angle of the lower support rod, which will provide an important reference for the anti-impact optimization design of the negative Poisson’s ratio lattice filled structure.

Buckling of lipidic ultrasound contrast agents under quasi-static load.

Collapse of lipidic ultrasound contrast agents under high-frequency compressive load has been historically interpreted by the vanishing of surface tension. By contrast, buckling of elastic shells is known to occur when costly compressible stress is released through bending. Through quasi-static compression experiments on lipidic shells, we analyse the buckling events in the framework of classical elastic buckling theory and deduce the mechanical characteristics of these shells. They are then compared with that obtained through acoustic characterization. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Variation Pattern of the Compressive Strength of Concrete under Combined Heat and Moisture Conditions

The compressive strength of concrete is not the same in high temperature humid environments and normal temperature dry environments. In this study, quasi-static uniaxial compression experiments of concrete with different temperatures and water contents were carried out to investigate the variation pattern of the compressive strength of concrete under combined heat and moisture conditions. The results showed that the temperature softening effect and water softening effect of the compressive strength of concrete were coupled with each other. The compressive strength exhibited a variation trend from increase to decrease with the increase in both temperature and water content, and the relations among the heat-moisture coupling factor, temperature, and relative saturation ratio were obtained. The water absorption of concrete after immersion had a more significant effect on the compressive strength than the free water content stored inside the specimen before immersion. The "pseudo-temperature strengthening effect" distinguished the thermodynamic response of immersed concrete from that of dry concrete, and the functional relationships among the heat-moisture coupling factor, temperature, and relative water absorption ratio were established. The evolutionary mechanism of the competition between the microcrack expansion and healing of concrete under combined heat and moisture conditions was revealed.

Compressive Properties and Energy Absorption Behavior of 316L Steel Foam Prepared by Space Holder Technique

The effect of porosity and pore size on the quasi-static compression properties and energy absorption characteristics of the steel foam was investigated in this paper. The 316L steel foams were prepared through powder metallurgy using urea as the space holder. The macrostructure of steel foam and microstructure of the pore walls were characterized, and the quasi-static compression experiments were conducted on the specimens in the axial direction at a strain rate of 10-3 s-1. The results show that the increase in porosity decreases the yield strength and plastic modulus of the steel foam but increases the densification strain of the steel foam. The yield strength of the steel foam decreases significantly when the pore size is 2.37 mm. However, the pore size has little effect on the plastic modulus. Moreover, the energy absorption per volume of the steel foam decreases with increasing porosity at the same strain. The effect of porosity on energy absorption efficiency is greater than that of pore size.

A 3D re-entrant structural metamaterial with negative Poisson’s ratio reinforced by adding arrow structures

Structural metamaterial with negative Poisson’s ratio often has low stiffness due to its porous structure. For engineering applications, the various strategies have been developed to enhance its stiffness but also weaken the negative Poisson effect. In this work, we propose a 3D reinforced re-entrant structure (RRS) by adding arrow structures to the classical re-entrant structure (RS), which is fabricated by photocuring 3D printing of photosensitive resin. The structure-properties correlative mechanism of RRS is systematically analyzed by combining experiment (quasi-static compression experiment) and finite element simulation (ABAQUS). It is found that the equivalent elastic modulus and negative Poisson’s ratio of RRS can be tuned by various structural parameters (i.e. the thickness ratio η, the length ratio of the slant rod α, the length ratio of the vertical rod β, and the angle θ of the re-entrant cells). By optimizing the structure parameters, the equivalent elastic modulus of RRS with the negative Poisson’s ratio of −0.28 can be significantly increase to 13.67 MPa, which is 12.32 times larger than that of RS with the same negative Poisson’s ratio. Due to the flexible design of stiffness and negative Poisson ratio, our proposed 3D reinforced re-entrant structural metamaterial provides a potential way for designing engineering materials with desirable performance.