In-plane Stiffness Research Articles

COD and CSD based model for in-plane stiffness of symmetric laminates with cracks in plies and local delaminations: Analysis of crack face sliding

COD and CSD based model for in-plane stiffness of symmetric laminates with cracks in plies and local delaminations: Analysis of crack face sliding

Evaluation of Secondary Buckling and Ultimate Strength Behaviour According to Boundary Conditions of Curved Plate Subjected to Compressive Load

This paper analyzed the buckling and ultimate strength characteristics of plate members with curvature, which are essentially used in ships and marine structures, through numerical analysis. Major structural members are affected by rotational velocity depending on the rigidity of structures placed around them, and it is very important to check how this affects buckling and ultimate strength. The aspect ratio of the curved plate was adopted as 2.5, 3.0, and 3.5 to reflect the plate thickness range and high-strength steel characteristics actually used. In the case of no curvature, and in the case of curvature, 5 degrees, 10 degrees, 15 degrees, 20 degrees, 30 degrees, and 45 degrees were considered. Under certain thickness and curvature conditions, secondary buckling occurs and the buckling state of the plate changes rapidly. Therefore, the final strength is evaluated lower than in the case where there is no curvature. Buckling and ultimate strength were high in a clamped condition around the curved plate, and there was no specificity in behavior depending on the aspect ratio change. In the four-side simply supported condition, the in-plane stiffness gradient changes depending on the aspect ratio due to the secondary buckling effect, and this characteristic is a phenomenon that is not considered at all in the existing classification method.

Efficient property-oriented design of composite layups via controllable latent features using generative VAE

Fiber-reinforced composites provide substantial tailoring potential, while the extensive parameters and complex coupling mechanisms pose formidable challenges to layup designs. This paper presents an efficient inverse design framework for composite layups utilizing a variational autoencoder (VAE), which is applicable to non-conventional laminates. By leveraging the VAE's exceptional feature extraction and generative capabilities, the decoder rapidly produces layups with desired properties through controllable feature vectors. Based on the stacking characteristics of layups, multi-scale one-dimensional convolutions precisely extract sequence features relevant to mechanical properties and specific manufacturing constraints. A customized loss function is formulated to constrain the latent features, while addressing the non-uniqueness problem for layups with certain mechanical properties. The developed property-oriented VAE can generate 100,000 layups in seconds, achieving an average success rate of 66.9% under comprehensive in-plane and bending stiffness design, and remains effective for 100-ply thick laminate. For comparison, the VAE model outperforms the genetic algorithm and the logic-based method in reinforced panel designs, reducing the retrieval error by 46.4% and 38.1%, respectively. The proposed approach demonstrates flexible and efficient design advantages using generative machine learning models, and is easily extendable to other inverse design scenarios.

A novel cellular structure with center-symmetric cell walls for morphing applications

Cellular structures are potential candidates for the supporting framework of flexible morphing skins. Unlike traditional zero Poisson’s ratio (ZPR) cellular structures with axisymmetric cell walls, this paper proposes a novel cellular structure with center-symmetric cell walls. The in-plane mechanical properties of this novel structure are explored through theoretical analysis and substantiated by both finite element simulations and experimental tests. Compared to the classic accordion honeycomb structure, the elastic modulus in the x-direction of the novel structure is reduced by an average of 58%, the strain amplification rate is increased by 122%, and the in-plane stiffness anisotropy is improved by 200%. These findings suggest that the proposed structure offers far superior stiffness anisotropy and large deformation potential, making it more suitable for morphing applications than the traditional ZPR cellular structures.

Low-velocity impact response of hybrid sheet moulding compound composite laminates

This work presents a comprehensive study on the impact damage tolerance of Sheet Moulding Compounds (SMCs). The performance of glass, carbon and hybrid glass/carbon SMCs are compared by means of tensile, compression, low-velocity impact and compression after impact experiments. Damage analysis of the impacted laminates was performed by ultrasonic and X-ray methodologies. The glass SMC exhibited the highest damage tolerance in low-velocity impact with the smallest damaged area, crack density and loss in compression after impact (CAI) strength. On the other hand, the carbon SMC demonstrated superior in-plane stiffness and strength, but exhibited a large damaged area and crack density under impact. The hybrid SMC displayed an optimal compromise, exhibiting intermediate tensile in-plane performance and excellent damage tolerance at lower impact energy levels, but suffered from extensive delamination at the highest impact energy. Overall, the findings highlight the suitability of hybrid SMCs for structural applications with potential impact risks.

Low-velocity impact (LVI) and compression after impact (CAI) of Double-Double composite laminates

Tailorability is a key advantage of fiber-reinforced composites over other material systems. While tailoring a single isolated laminate is relatively simple, challenges arise when designing larger integrated components while ensuring compatibility between laminates and avoiding sharp changes in local stiffness. The innovative Double-Double (DD) laminate design method simplifies the optimization and processing of laminates by incorporating 4-ply building blocks consisting of +ϕ, −ϕ, +ψ, and −ψ ply orientations. As a relatively new concept, DD laminate design requires careful assessment to ensure its performance is equivalent to that of conventional designs. The current study compares impact damage tolerance of quadriaxial (QUAD) laminates consisting of 0°, 90°, and ±45° ply orientations with equivalent DD laminates under Low-Velocity Impact (LVI) and Compression After Impact (CAI) loadings. To this end, a validated three-dimensional high-fidelity finite element model capable of capturing fiber breakage, splitting, kinking, as well as matrix cracking and delamination, was used. A computer tool was developed to identify equivalent DD laminates and to find the best stacking sequence for achieving layup homogenization. Three equivalent DD laminates were selected for the [0/45/90/−45]4s. The first laminate had an equal in-plane stiffness [A] matrix ([67.5/–22.5/22.5/−67.5]8T), the second laminate had an equal flexural stiffness [D] matrix ([64.5/−17/17/−64.5]8T), and the third laminate ([65.5/−18.5/18.5/−65.5]8T) had a similar [D] matrix while keeping the difference between each element of [A] matrices below 10 %. The results indicate that the QUAD laminates can be replaced by equivalent DD without compromising impact damage tolerance while benefiting from the improved design and manufacturing ease of the DD laminate configuration.

Chemochromism and Tunable Acoustic Phonons in Intercalated MoO3: Ag-, Bi-, In-, Mo-, Os-, Pd-, Pt-, Rh-, Ru-, Sb-, and W-MoO3.

Intercalation of several elements (Ag, Bi, In, Mo, Os, Pd, Pt, Rh, Ru, Sb, and W) is used to chemically alter a wide range of properties of two-dimensional layered α-MoO3. Intercalation modifies acoustic phonons and elastic constants, as measured with Brillouin scattering. Intercalation alters electronic bandgaps, color, structure, Raman shifts, and electron binding energies. Optical chemochromism is demonstrated with intercalants changing the color of MoO3 from transparent to brilliant blue (In, Mo, Os, and Ru) and orange (Ag). Correlations are investigated among material properties. There is evidence that in-plane longitudinal stiffness c11 correlates with changes in the bandgap, while various Raman modes appear to be connected to a variety of properties, including shear modulus c55, Mo binding energies, lattice constants, and the preferred crystal structure of the intercalant. The results indicate a surprising degree of complexity, suggesting competition among multiple distinct mechanisms and interactions involving specific intercalant species.

Ultimate strength of multi-ring-stiffened tube-gusset joints with dual-function stiffeners under combined bending and compressive loads

Tube-gusset (TG) joints play a crucial role in connecting crossarm chords to tower bodies in steel-pipe power transmission towers, bearing the highest loads in the entire tower structure. This study investigated TG joints with five-ring stiffeners under combined bending and compressive loads, using the middle stiffener plate as the connecting plate. Through experimental studies, numerical simulations, and theoretical analyses, insights were obtained into the failure mechanism and mechanical characteristics of TG joints. This study identifies the key factors influencing the ultimate strength of TG joints under combined bending and compressive loads and proposes a method for determining the joint bearing capacity. Notably, the mechanical performance of multi-ring-stiffened tube-gusset joints was minimally affected by the initial geometric defects under combined compression and bending moments. The load exerted on the gusset plate was primarily supported by the stiffeners, with the gusset plate demonstrating minimal bending deformation, owing to its substantial in-plane stiffness. Consequently, the gusset plate underwent an overall rotation or translation under the combined effects of compression and the bending moment. The proposed method accurately predicted the joint bearing capacity, ensuring the safety of TG joints. These findings provide valuable insights into the meticulous design of joints in steel-pipe transmission towers, thereby ensuring the safety and stability of transmission lines in the field of civil engineering.

Effects of adhesive and frictional contacts on the nanoindentation of two-dimensional material drumheads

Nanoindentation of suspended circular thin films, dubbed drumhead nanoindentation, is a widely adopted technique for characterizing the mechanical properties of micro- or nano-membranes, including atomically thin two-dimensional (2D) materials. This method involves suspending an ultrathin specimen over a circular microhole and applying a precise indenting force at the center using an atomic force microscope (AFM) probe. Classical solutions assuming a point load and a fixed edge, which are referred to as Schwerin-type solutions, are commonly used to estimate Young’s modulus of the membrane material out of load–deflection measurements. However, given the widespread experimental evidence for adhesive and frictional contacts between the probe tip and the membrane, as well as sliding between the membrane and its supporting substrate, quantitative investigations of the effects of these interactions are required. In this paper, we formulate a boundary value problem to rigorously model such effects, ensuring relevance to experimental operations. Our numerical analyses reveal that the adhesive effect at the tip-membrane interface diminishes as the indentation depth increases or the tip size decreases. Furthermore, frictional interactions at this interface shift the maximum membrane stress from the center to the tip-membrane contact line with increasing indentation depth and interfacial shear stress. At large indentation depths, the size of the indenter tip and the sliding of the membrane-substrate are found to have a large effect on the indentation load–deflection relationship. Thus, we propose a new approximate formula for this relationship assuming a non-adhesive and frictionless spherical tip of a finite radius and a slippery contact with the supporting substrate. This formula is more accurate than the widely used Schwerin-type solution. It can be used to simultaneously extract the in-plane stiffness of the membrane and the shear strength at the membrane-substrate interface.

Machine learning enables the discovery of 2D Invar and anti-Invar monolayers

Materials demonstrating positive thermal expansion (PTE) or negative thermal expansion (NTE) are quite common, whereas those exhibiting zero thermal expansion (ZTE) are notably scarce. In this work, we identify the mechanical descriptors, namely in-plane tensile stiffness and out-of-plane bending stiffness, that can effectively classify PTE and NTE 2D crystals. By utilizing high throughput calculations and the state-of-the-art symbolic regression method, these descriptors aid in the discovery of ZTE or 2D Invar monolayers with the linear thermal expansion coefficient (LTEC) within ±2 × 10−6 K−1 in the middle range of temperatures. Additionally, the descriptors assist the discovery of large PTE and NTE 2D monolayers with the LTEC larger than ±15 × 10−6 K−1, which are so-called 2D anti-Invar monolayers. Advancing our understanding of materials with exceptionally low or high thermal expansion is of substantial scientific and technological interest, particularly in the development of next-generation electronics at the nanometer or even Ångstrom scale.

Bending behaviors of carbon fiber composite honeycomb cores with various in-plane stiffness

Designing curved surfaces with a traditional straight-walled honeycomb is challenging due to its excessive in-plane stiffness, making it prone to fracturing during bending. The research motivation is overcoming the flexibility limitation of conventional straight-wall honeycombs with the new curved-wall design. Moreover, the three-dimensional failure mechanism map based on the theoretical models is expected to contribute to the design of a carbon fiber composite curved-wall honeycomb. This paper outlines the fabrication process using a modified co-curing method. It also includes theoretical models developed to examine the effect of the center angle of curved walls on the honeycomb’s in-plane stiffness and bending behavior. In-plane tensile and three-point bending tests were conducted to verify the theoretical modes. Finite element model was created to study the stress distribution and damage degree. The study is also aimed at examining the load-bearing capacity of sandwich beams with curved-wall honeycomb cores. A three-dimensional failure mechanism map shows how the failure modes of sandwich structures are affected by the center angle of the curved walls. The study offers a new approach to designing carbon fiber composite honeycombs with flexible bending deformation and high load-bearing capacity. These honeycombs could potentially be used in lightweight launch-vehicle shell structures.

A New Type of Wharf and a Study of Its Mechanical Properties by FE (Finite Element) and Experimental Methods

Due to the limitations of planar mode wharfs, this paper proposes a new type of wharf—the three-dimensional cantilevered wharf. The proposed wharf is defined as an improvement of the traditional wharf, extending the traditional wharf upward and cantilevering out to the sea. The three-dimensional cantilevered wharf is a composite truss structure that meets structural and functional requirements. The composite truss structure is formed by connecting the beams of frame structures as a whole. The material consumption of the three-dimensional cantilevered wharf is decreased by controlling stresses and optimizing components. A finite element model of the proposed wharf, with a length of 200 m, width of 105 m, and cantilever length of 80 m, was established to analyze the basic mechanical performance. In this paper, the force distribution of the pile foundation, the vertical force transfer efficiency of web members, the structural stiffness, and the natural frequencies of the proposed wharf are analyzed. Tests regarding the stress and stiffness of different plane cantilever trusses are carried out, and finite element analysis is used for comparison. The test results show that the high-rise cantilever truss has a great in-plane stiffness and a reasonable component stress distribution. Additionally, the three-dimensional cantilevered wharf significantly improves the utilization efficiency of the wharf.

Origami of multi-layered spaced sheets

Two-dimensional (2D) origami tessellations such as the Miura-ori are often generalized to build three-dimensional (3D) architected materials with sandwich or cellular structures. However, such 3D blocks are densely packed with continuity of the internal material, while for many engineering structures with multi-physical functionality, it is necessary to have thin sheets that are separately spaced and sparsely connected. This work presents a framework for the design and analysis of multi-layered spaced origami, which provides an origami solution for 3D structures where multiple flat sheets are intentionally spaced apart. We connect Miura-ori sheets with sparsely installed thin-sheet parallelogram-like linkages. To explore how this connectivity approach affects the behavior of the origami system, we model the rigid-folding kinematics using analytic trigonometry and rigid-body transformations, and we characterize the elastic-folding mechanics by generalizing a reduced order bar and hinge model for these 3D assemblies. The orientation of the linkages in the multi-layered spaced origami determines which of three folding paths the system will follow including a flat foldable type, a self-locking type, and a double-branch type. When the origami is flat foldable, a maximized packing ratio and a uniform in-plane shear stiffness can be achieved by strategically choosing the link orientation. We show possible applications by demonstrating how the multi-layered spaced origami can be used to build deployable acoustic cloaks and heat shields.

Investigation of microfriction properties of graphene/AlCoCrFeNi high entropy alloy

Applying graphene (Gr) coatings to high-entropy alloys (HEA) is anticipated to enhance their tribological characteristics. The current understanding of the mechanism by which the Gr/HEA is enhanced at the atomic level is still limited. Molecular dynamics simulations revealed the mechanical behavior and strengthening mechanism of the Gr/AlCoCrFeNi HEA during nanoindentation and nanoscratch. The results demonstrate a substantial increase in the indentation hardness of the Gr/AlCoCrFeNi HEA by about 2.4 times. When Gr changed from a single layer to three layers, it further improved (3.2 times for a double layer and 3.9 times for three layers). At the same time, the friction coefficient is effectively reduced. Furthermore, the elevated in-plane stiffness of the Gr coating leads to an expansion of the effective loading area, resulting in increased Shockley dislocation and stair-rod dislocation density within the Gr/AlCoCrFeNi HEA, thereby amplifying the strain hardening effect and reducing subsurface damage. Qualitative experiments confirmed the excellent wear resistance of the Gr/HEA, and coating Gr increased the width of scratches, effectively confirming our simulation results. These findings provide valuable insights for the development and design of Gr/HEA composite coatings with enhanced mechanical properties.

Prediction of a new 2D Janus monolayer MX2Si2Y2 (M = Mo, W and V; X/Y = N, P; X ≠ Y) from density functional theory

We devised the Janus monolayer MX2A2Y2 (M = Mo, W, V, Nb, Ta, Ti, Zr, Hf and Cr; X/Y = N, P and As; A = Si and Ge) and systematically investigated the structural parameters, phonon vibrations, thermal stability, the electronic and mechanical properties. Among the 26 systems, there are six stable Janus monolayers at room temperature: MoN2Si2P2, WN2Si2P2, VN2Si2P2, MoP2Si2N2, WP2Si2N2, CrN2Si2P2. Intriguingly, the MoP2Si2N2 and WP2Si2N2 show non-magnetic semiconductor properties. The MoN2Si2P2 and WN2Si2P2 demonstrate non-magnetic metallic ground states. The VN2Si2P2 and CrN2Si2P2 are magnetic metal with magnetic moments of 1.24 μB and 0.53 μB. Furthermore, the elastic constants of the MSi2N4 and five Janus monolayer MX2Si2Y2 (M = Mo, W and V; X/Y = N, P) meet the stability criteria, indicating they are mechanically stable. The in-plane stiffness of the MX2Si2Y2 increases with the increase of the number of metal atoms and are greatly reduced, compared with the corresponding MSi2N4. In addition, according to Poisson's ratio, the MN2Si2P2 with metallic characteristics are ductile, whereas the MP2Si2N2 with semiconductor characteristic are brittle. In short, the Janus monolayer MX2Si2Y2 enriches the family members of 2D materials. The rich electronic and mechanical properties make the MX2Si2Y2 have high application prospects for future novel mechanical electronic device applications.

Machine learning-based optimal design of an acoustic black hole metaplate for enhanced bandgap and load-bearing capacity

This paper introduces a novel machine learning-based optimization strategy for multi-functional acoustic black hole (ABH) metaplates. The primary objective is to achieve a multi-functional metaplate with excellent performance in elastic wave attenuation and load-bearing capacity simultaneously. The paper begins by describing the design of nanocomposite ABH metaplates, presenting a new pathway to realize multi-functional metaplates. Then, a semi-analytical method, based on plate theory and the Bloch–Floquet theorem, is introduced to consider the band structure of the nanocomposite metaplates. Through systematic analysis, the impacts of the ABH effect, nanocomposite reinforcements, and the viscoelastic damping layer on the bandgaps and strain energy compliance are highlighted. Meanwhile, two optimization objectives representing bandgap characteristics and in-plane stiffness are derived respectively. Subsequently, a deep learning surrogate model is employed to establish a relationship involving significant parameters with the optimization objectives. The performance evaluation confirms accuracy and computational speed of the surrogate model. Finally, an optimization strategy based on deep reinforcement learning is proposed to obtain multi-functional metaplates with superior bandgaps, enhanced in-plane stiffness, or both. The robustness and efficiency of the strategy are demonstrated under different tests. The results show that the proposed strategy can achieve identical results as the genetic algorithm and nondominated sorting genetic algorithm-II, while surpassing them in computational efficiency and balancing multiple objectives. The findings of this study serve as valuable references for the future development and application of multi-functional advanced metamaterials.

A set of calculation tools supporting the design, modelling and application of plywood-based seismic retrofitting interventions on timber floors in existing buildings

The application of timber-based strengthening solutions to existing wooden and masonry structures, combines several benefits, such as reversibility, compatibility, lightness, sustainability, affordability, and effectiveness. With reference to existing timber floors, an efficient method to enhance their seismic response is the fastening of an overlay of plywood panels to the existing sheathing, an intervention that greatly improves in-plane strength, stiffness, and energy dissipation. In order to promote the use of this retrofitting solution in practice, this work presents a set of calculation tools supporting the design and advanced numerical modelling of timber diaphragms strengthened with plywood panels. The suite of tools allows to first estimate the full nonlinear, cyclic in-plane response of the strengthened diaphragms starting from the geometrical and material properties of the existing sheathing and the plywood overlay, as well as the mechanical characteristics of the fasteners. As second step, such estimated in-plane response can be transformed into a constitutive law for performing nonlinear numerical simulations, by means of a user-supplied subroutine developed for finite element software DIANA FEA. The presented calculation examples and the performed validation against reference studies from literature, show that the developed tools can provide an accurate estimate of the in-plane response of the diaphragms, and enable an efficient numerical simulation of their seismic behaviour. The implemented tools can be used to both obtain preliminary indication for plywood-based seismic retrofitting design, and to calibrate the interventions on existing diaphragms based on the specific characteristics and needs of a building, relying on the adaptability and versatility of this strengthening method.

A novel Ductile Lightweight Fiber-Reinforced Concrete (DLFC) infill for seismic-prone zones: Experimental and numerical investigations

In urban construction, reinforced concrete (RC) with masonry infill predominates, though traditional masonry's brittle nature poses significant seismic vulnerabilities. This study introduces a novel approach using Ductile Lightweight Fiber-Reinforced Concrete (DLFC) as an infill to address these challenges. Composed of cement, water, expanded polystyrene (EPS), ultra-fine filler, and combined polyvinyl alcohol (PVA) and polypropylene (PPF) fibers, DLFC aims to enhance ductility, minimize damage, and amplify energy absorption in seismic events. Three RC frames, with height-to-span ratios of 0.77, 1.00, and 1.28, were designed and experimentally tested under simultaneous vertical and lateral cyclic loading to evaluate DLFC's seismic response. Results illustrated that DLFC-infilled RC frames boast impressive ductility, an 8% drift at complete failure, minimal out-of-plane behavior, and elevated damping ratios. Remarkably, DLFC's low in-plane stiffness led to reduced frame stiffness compared to traditional masonry. An empirical equation, closely aligning with experimental outcomes, was formulated to estimate the lateral strength of the infill wall, and a comparison with the bare frame was made, though it necessitates additional validation through further testing.

Evolutionary Search and Theoretical Study of Silicene Grain Boundaries' Mechanical Properties.

Defects such as grain boundaries (GBs) are almost inevitable during the synthesis process of 2D materials. To take advantage of the fascinating properties of 2D materials, understanding the nature and impact of various GB structures on pristine 2D sheets is crucial. In this work, using an evolutionary algorithm search, we predict a wide variety of silicene GB structures with very different atomic structures compared with those found in graphene or hexagonal boron-nitride. Twenty-one GBs with the lowest energy were validated by density functional theory (DFT), a majority of which were previously unreported to our best knowledge. Based on the diversity of the GB predictions, we found that the formation energy and mechanical properties can be dramatically altered by adatom positions within a GB and certain types of atomic structures, such as four-atom rings. To study the mechanical behavior of these GBs, we apply strain to the GB structures stepwise and use DFT calculations to investigate the mechanical properties of 9 representative structures. It is observed that GB structures based on pentagon-heptagon pairs are likely to have similar or higher in-plane stiffness and strength compared to the zigzag orientation of pristine silicene. However, an adatom located at the hollow site of a heptagon ring can significantly deteriorate the mechanical strength. For all of the structures, the in-plane stiffness and strength were found to decrease with increasing formation energy. For the failure behavior of GB structures, it was found that GB structures based on pentagon-heptagon pairs have failure behavior similar to that of graphene. We also found that the GB structures with atoms positioned outside of the 2D plane tend to experience phase transitions before failure. Utilizing the evolutionary algorithm, we locate diverse silicene GBs and obtain useful information about their mechanical properties.

Superpentagraphene C34: A two-dimensional network structure of C20 fullerene

The well-known smallest icosahedral fullerene C20 is comprising five-membered carbon-rings in all sp2 bonding states. Here we identify by ab initio calculations a new quasi two-dimensional (2D) carbon allotrope in sp2-sp3 bonding states, comprising the unusual five-membered C20 fullerene as the basic structural units, with a 34-atom hexagonal cell in P6/mmm(D6h1) symmetry, and term it as spg-C34 superpentagraphene. Total energy calculations show that it is energetically more stable than the previously reported 2D carbon forms such as pentagraphene and ph-graphene. Its structural stability has been verified by phonon mode analysis and ab initio molecular dynamics simulations. Electronic band calculations reveal that this 2D spg-C34 carbon is a semiconductor with a sizable indirect band gap of 3.31 eV. Moreover, we show that such 2D spg-C34 carbon structure has a larger layer modulus (281 N/m), a larger in-plane stiffness (524 N/m), and a smaller Poisson's ratio (0.069) than the values for graphene. These results establish a new exotic quasi-2D carbon phase and offer insights into its outstanding electronic and mechanical properties of two-dimensional carbon structure.