Bi-layer Beam Research Articles

Topology optimization design of recoverable bistable structures for energy absorption with embedded shape memory alloys

In this work, multistable mechanical metamaterials with recoverable capabilities are designed for high energy absorption and resistance to repetitive impacts. Based on the known curved beam with energy dissipation characteristics, the shape memory alloys (SMAs) curved beam is added and optimized to achieve recoverability of the bi-layer beam structure. To simultaneously achieve bistable characteristics and recoverability in the designed metamaterial, the optimization model is formulated to maximize the energy absorption capacity of the structure while constraining the peak and valley forces. To solve this complex and highly nonlinear topological optimization problem with stringent constraints, the topological design of the SMAs layer is represented using a limited number of design variables along with the material-field series expansion strategy, and the optimization problem is subsequently solved using a non-gradient-based optimization algorithm. Finite element simulation results demonstrated that the optimized design possesses a substantial capacity for energy absorption. Additionally, the design structure can recover to its initial state from buckling induced by the initial load by regulating the external temperature. Different multistable metamaterials, including those designed to prevent repetitive impacts, have been further developed based on the designed recoverable high-energy-absorbing bistable unit cells, utilizing combinations of varying energy absorption capacities.

Characteristics of truncation resonances in periodic bilayer rods and beams with symmetric and asymmetric unit cellsa).

Truncation resonances are resonant frequencies that occur within bandgaps and are a prominent feature of finite phononic crystals. While recent studies have shed light on the existence conditions and modal characteristics of truncation resonances in discrete systems, much remains to be understood about their behavior in continuous structures. To address this knowledge gap, this paper investigates the existence and modal characteristics of truncation resonances in periodic bilayer beams, both numerically and experimentally. Specifically, the effect of symmetry of the unit cells, boundary conditions, material/geometric properties, and the number of unit cells are studied. To this end, we introduce impedance and phase velocity ratios based on the material and geometric properties and show how they affect the existence of truncation resonances, relative location of the truncation resonances within the bandgap, and spatial attenuation or degree of localization of the truncation resonance mode shapes. Finally, the existence and mode shapes of truncation resonances are experimentally validated for both longitudinal and flexural cases using three-dimensional (3D) printed periodic beams. This paper highlights the potential impact of these results on the design of finite phononic crystals for various applications, including energy harvesting and passive flow control.

Design, modeling and experimental investigation of a novel solar sail with high area-to-mass ratios for efficient solar sailing

Solar sailing is a promising propellant-free approach to propelling spacecraft in space. However, the propelling efficiency of conventional solar sail spacecraft is limited by their area-to-mass ratios. This paper proposes a novel design of micro solar sails with area-to-mass ratios above 100 m2/kg for next-generation chip-scale spacecraft. Bilayer thin films developed by Microelectromechanical Systems (MEMS) technologies were patterned into grid microstructures, and theoretical analysis of a sail prototype was conducted. The electro-thermal and thermo-mechanical models of the solar sail in geospace were established by taking effects of Joule heating, solar radiation, and thermal re-emission into consideration, enabling rapid prediction of its three-dimensional (3-D) reconfiguration from the as-released two-dimensional (2-D) microstructure. Adjustment of the ChipSail’s acceleration arising from the sail’s morphing was also analytically modeled. Fabrication and characterization of the sail prototype made of multiple Al/Ni50Ti50 bilayer beams were accomplished. In-situ SEM imaging of the sail prototype in vacuum chamber witnessed an active and continuous 3-D reconfiguration under Joule heating, and over 90° deformation was detected by applying a DC voltage of 0.078 V. Theoretical and experimental work on the solar sail with at least 10 times higher area-to-mass ratios than conventional ones will lay a solid foundation for efficient solar sailing.

Modelling the dynamic magnetic actuation of isotropic soft magnetorheological elastomers

Soft magnetorheological elastomers (s-MRE) are a kind of smart material with soft magnetic particles embedded in an elastomer matrix. Under a magnetic field, there is pronounced magnetostriction and magnetically controllable mechanical properties for s-MRE, offering broad application prospects in soft robotics, surface pattern control and vibration control. While most existing literature on s-MRE focuses on the quasi-static behaviour, neglecting inertia effect, the dynamic behaviour and potential nonlinear oscillation phenomenon in certain scenarios of s-MRE-based actuators remain underexplored. In order to addressing this gap, a novel dynamic model which incorporates the magnetization, nonlinear viscoelasticity and inertia effects of isotropic s-MRE is proposed to explore the interplay among magnetic field, inertia and viscoelasticity on its dynamic behaviour. After developing the corresponding two-dimensional finite element implementation platform, this study examines the magnetic-induced dynamic behaviour of an isotropic s-MRE-based bilayer beam through numerical simulation. The influence of inertia and viscoelasticity on the magnetic-induced deformation as well as the unique nonlinear vibration characteristics of isotropic s-MRE-based system, such as superharmonic and resonance jump, are explored. Furthermore, to further enhance practical applications, novel magnetic field control algorithms aimed at mitigating harmonic distortion and tuning the vibration frequency of isotropic s-MRE-based magnetic actuation systems are introduced. These findings significantly advance the understanding the dynamic behaviour of s-MRE, paving the way for practical applications of s-MRE in magnetic field-driven loudspeakers and active noise control devices.

Vibration Attenuation in a Beam Structure with a Periodic Free-Layer Damping Treatment

In order to improve the vibration reduction performance of damping treatments, a new damping structure consisting of a uniform base layer and two periodically alternating free layers was examined in this study. Closed-form solutions for both the band structure and the forced response of the periodic bi-layer beam were theoretically derived and verified via numerical solutions using the finite-element method. The results showed that the structure with periodic free-layer damping (PFLD) treatment reduced broadband vibrations, and the levels of reduction were dominated by Bragg scattering in the band gaps and damping in the passbands. The vibration experiment verified the derived theory’s accuracy and showed that the PFLD treatment could increase vibration reduction levels in low-frequency band gaps compared with traditional free-layer damping treatments. The effects of the parameters—cell lengths, sub-cell-length ratios, and thickness ratios—were also discussed, providing further understanding of the vibration reduction performance of the bi-layer beam with the PFLD treatment, and this can be used to help designers optimize the periodic bi-layer beam to achieve better performance.

Design principles for 3D-printed thermally activated shape-morphing structures

Morphing structures can change their shape in response to thermal excitation and are commonly used to enhance the performance of actuators, soft robotics, and biomedical devices. One of the main challenges is the inverse design problem, in which a deformed target shape is prescribed and the initial material properties, distribution, and geometry are to be determined. To tackle this challenge, a model for the thermo-mechanical response of free standing multi-layered struts that experience moderate to large deflections is developed. The model is validated through thermally activated 3D-printed bi-layer beams. Next, the model is exploited to develop an efficient inverse design algorithm that accepts a target function as an input and computes the referential configuration that can achieve the required thermally-activated deformations. It is shown that the solution to the inverse problem is not unique, thus providing flexibility in design. The merit of the algorithm is illustrated through the inverse design of three thermally-activated strut-based target shapes. The simplicity and robustness of the algorithm reveals fundamental principle guidelines for inverse design of thermally activated shape morphing structures and enables its extension to other stimuli.

Variational-based modeling of a piezoelectric/elastic bilayer beam with flexoelectricity

Flexoelectricity incorporating electric polarization and strain gradients exists in all dielectrics. In the present work, the function of Hamilton’s principle of the elastic dielectric materials considering the flexoelectric effect is established and its stationary conditions are also obtained. A bilayer beam composed of elastic and piezoelectric parts is modeled to investigate flexoelectricity under both mechanical and electrical loads. Based on Hamilton’s principle, the governing equation and boundary conditions of a piezoelectric/elastic bilayer beam with generalized supporting ends are deduced. Accordingly, the analytical solutions to the horizontal displacements are derived. It is found that the flexoelectric effects depend on the size heavily, which is dominant for the structures at nanoscale but had hardly influence on the larger ones. Moreover, the piezoelectric/elastic bilayer beam behaves much better on controlling of the bending flexibility by adjusting the thickness ratio of the two parts. It’s hopeful to provide guidance for designing and optimizing nanoscale electronic devices.

A numerical framework for the simulation of coupled electromechanical growth

Electro-mechanical response exists in growing materials such as biological tissues and hydrogels, influencing the growth process, pattern formation and geometry remodelling. To gain a better understanding of the mechanism of the coupled effects of growth and electric fields on the deformation behaviour, a finite element framework for coupled electro-elastic growth is established. Based on the extended volume growth theory, the governing equations of the growing electro-elastic solid are obtained. A coupled three-field mixed displacement-pressure-potential finite element formulation using inf–sup stable combinations is adapted. The finite element formulation is implemented in ABAQUS via a user element subroutine. The implementation is validated first by comparing the deformation and stress components of a growing tubular structure under axial strain and radial voltage. Using the example of a bi-layer beam actuator, it is illustrated that growth parameters and the external voltage can precisely control the bending angle. The framework is then applied to simulate pattern formation and transition behaviour, such as doubling and tripling of wrinkles, by specifying growth parameters and external voltage in a 3D stiff film/soft substrate structure. Furthermore, the suppression of wrinkles by applying external voltage is demonstrated. It is observed that the electric field plays a significant role in stress redistribution and guiding growth, resulting in the promotion or suppression of wrinkles, which is demonstrated by the numerical simulation of a long tubular structure. The proposed finite element scheme provides an accurate, efficient and stable tool for numerical simulation of electro-elastic solids incorporating growth effect, which can be used for understanding coupled growth phenomenon in biological soft matter and developing smart devices for medical treatment.

Electrothermally Driven Reconfiguration of Microrobotic Beam Structures for the ChipSail System

Solar sailing enables efficient propellant-free attitude adjustment and orbital maneuvers of solar sail spacecraft with high area-to-mass ratios. However, the heavy supporting mass for large solar sails inevitably leads to low area-to-mass ratios. Inspired by chip-scale satellites, a chip-scale solar sail system named ChipSail, consisting of microrobotic solar sails and a chip-scale satellite, was proposed in this work. The structural design and reconfigurable mechanisms of an electrothermally driven microrobotic solar sail made of Al\Ni50Ti50 bilayer beams were introduced, and the theoretical model of its electro-thermo-mechanical behaviors was established. The analytical solutions to the out-of-plane deformation of the solar sail structure appeared to be in good agreement with the finite element analysis (FEA) results. A representative prototype of such solar sail structures was fabricated on silicon wafers using surface and bulk microfabrication, followed by an in-situ experiment of its reconfigurable property under controlled electrothermal actuation. The experimental results demonstrated significant electro-thermo-mechanical deformation of such microrobotic bilayer solar sails, showing great potential in the development of the ChipSail system. Analytical solutions to the electro-thermo-mechanical model, as well as the fabrication process and characterization techniques, provided a rapid performance evaluation and optimization of such microrobotic bilayer solar sails for the ChipSail.

Soft Actuators Based on Spin‐Crossover Particles Embedded in Thermoplastic Polyurethane

Molecular spin‐crossover (SCO) complexes are phase‐change materials that develop large spontaneous strains across the thermally induced phase transition, which can be advantageously used in designing soft actuators. Herein, a bilayer bending cantilever, made of thermoplastic polyurethane (TPU) with embedded [Fe(NH2trz)3](SO4) SCO particles (25 wt%), is presented. The proposed actuator is fabricated by blade casting an SCO@TPU layer on a conducting Ag@TPU film to convert electrothermal input into mechanical response. Experiments are conducted to characterize the curvature of bilayer beams, which is then further analyzed using the Euler–Bernoulli beam theory. The beam curvature change, free transformation strain, and effective work density associated with the SCO are 0.11 mm−1, 1.6%, and 1.25 mJ cm−3, respectively. Further, the open‐ and closed‐loop response of the actuator is investigated using a custom‐built setup. The open‐loop identification suggests that the actuator gain increases monotonously when the control current increases. This natural adaptive character can explain the drastically diminished response time in closed‐loop proportional–integral–derivative control experiments (2–3 s). Finally, tracking experiments are carried out to evaluate the robustness of the actuator with and without payloads. The results for 30 240 endurance cycles reveal a mean positioning error of 0.8%.

Cohesive-zone based fracture mechanics model of an edge delamination in bimaterial beam under mixed-mode bending test

The problem of an edge-split bilayer beam consisted of bonded dissimilar materials under mixed-mode bending (MMB) is investigated by using a structural mechanics procedure. In this analytical procedure, the bilayer beam is modeled as two Timoshenko beams joined by using interface tensile and shear springs, and the fracture mechanics parameters including the strain energy release rate and phase angle are estimated from the spring responses. Numerical examples of bilayer beams consisted of isotropic or orthotropic bimaterials and with symmetric or asymmetric dimensions are presented and compared to continuum based finite-element solutions with either cohesive-zone or perfectly-bonded interface models. It is shown that the strain energy release rates obtained from these models are in good agreement. The phase angles obtained from the analytical model and the cohesive-zone-interface based continuum model are also consistent with each other, and agree to the crack-tip deformation. On the other hand, the phase angles obtained from the oscillating crack-tip fields related to the perfectly-bonded interface do not match to the crack-tip deformation as well as the cohesive-zone interface models. Consequently, it is recommended to characterize the mode-mixity dependent interfacial adhesion and fatigue responses by using the fracture mechanics parameters obtained by using the analytical solution for the MMB fracture problem.

An Improved Experiment for Measuring Lithium Concentration-Dependent Material Properties of Graphite Composite Electrodes.

The in situ curvature measurement of bilayer beam electrodes is widely used to measure the lithium concentration-dependent material properties of lithium-ion battery electrodes, and further understand the mechano-electrochemical coupling behaviors during electrochemical cycling. The application of this method relies on the basic assumption that lithium is uniformly distributed along the length and thickness of the curved active composite layer. However, when the electrode undergoes large bending deformation, the distribution of lithium concentration in the electrolyte and active composite layer challenges the reliability of the experimental measurements. In this paper, an improved experiment for simultaneously measuring the partial molar volume and the elastic modulus of the graphite composite electrode is proposed. The distance between the two electrodes in the optical electrochemical cell is designed and graphite composite electrodes with four different thickness ratios are measured. The quantitative experimental data indicate that the improved experiment can better satisfy the basic assumptions. The partial molar volume and the elastic modulus of the graphite composite electrode evolve nonlinearly with the increase of lithium concentration, which are related to the phase transition of graphite and also affected by the other components in the composite active layer. This improved experiment is valuable for the reliable characterization of the Li concentration-dependent material properties in commercial electrodes, and developing next-generation lithium batteries with more stable structures and longer lifetimes.

On the use of negative thermal expansion engineered structures in flexural-mode solid-state thermoacoustics

Recent numerical studies have shown evidence of self-sustained oscillations in solids due to externally-applied spatial thermal gradients. In analogy with its acoustic counterpart in gases, this phenomenon was dubbed solid-state thermoacoustics (SSTA). Such heat-driven oscillation can give rise to either longitudinal or flexural motion, depending on the specific design of the system. Although an experimental proof of self-sustained motion in flexural-mode SSTA (F-SSTA) devices has yet to be produced, previous experimental studies pointed to the reduction of the effective damping as a clear indicator of the thermo-mechanical energy conversion process at the core of the F-SSTA mechanism. The F-SSTA theory suggested that negative thermal expansion (NTE), which is not a common property in natural materials, offers a remarkable opportunity to enhance the F-SSTA instability. The present study explores a design approach that leverages the unique features afforded by the solid state design in order to improve the overall performance of F-SSTA’s devices and reduce the technological gap to achieve, in a near future, a successful experimental validation. The proposed design approach leverages a hybrid bilayer beam concept where one of the two layers is designed to exhibit NTE properties. More specifically, the NTE layer is composed of a bi-material octet truss that contracts in the axial direction upon heating. This axial contraction is particularly beneficial to induce a strong thermal bending moment that ultimately enhances the F-SSTA instability. In addition, this work also furthers the conceptual understanding of the F-SSTA process by presenting an analytical perturbation energy budget developed on the basis of a simplified discrete model. These theoretical considerations provide new important insights in the energy conversion mechanism at the basis of the F-SSTA process, hence helping reducing the gap of knowledge towards a successful experimental realization of the F-SSTA effect. • Improved performance of F-SSTA systems via architectured NTE materials. • Identification of parameters controlling the flexural thermoacoustic instability. • A simplified analytical energy budget to understand the energy conversion mechanism.

Flexural behaviour and cost effectiveness of layered UHPC-NC composite beams

This paper presents a pilot numerical study to investigate the flexural performance of simply-supported layered ultra-high performance concrete (UHPC)-normal strength concrete (NC) beams consisting of two UHPC layers with an NC core layer sandwiched in between. A three-dimensional finite element model (FEM) is developed for the beam and is validated against the existing experimental results of UHPC-NC bi-layer composite beams. The effects of the bonding between UHPC and NC layers, the fraction of UHPC and NC in the beam, and the mechanical properties of UHPC material on the flexural performance of the beam are discussed in detail. Numerical results show that the flexural behavior of the layered UHPC-NC beam is significantly influenced by the interfacial bonding between UHPC and NC layers that is represented by the cohesive stiffness which should be higher than 3 to avoid possible delamination failure in the beam. The material cost effectiveness of the layered UHPC-NC beam is also evaluated. It is found that with properly designed UHPC layer thickness, the beam with a thick NC core layer can not only sustain the same loading as a pure UHPC beam with the same thickness but is also much less costly, indicating the excellent mechanical performance and great cost effectiveness of the proposed layered UHPC-NC beam.

Novel bi-layer beam elements for elastic fracture analysis of delaminated composite beams

A general finite element method is proposed for linear elastic fracture analysis of delaminated bilayer composite beams. An interface deformable bilayer beam model is adopted in modeling the virgin portions of bilayer beams, and it is capable of guaranteeing the continuity condition of internal forces at the tip of delamination because the bilayers are modeled as two separate shear deformable sub-beams and both the interface normal and shear compliances are introduced to account for interface deformation. The stiffness matrices of bilayer beams using the linear and quadratic interpolation polynomials are both derived using the principle of minimum potential energy. Then, a finite element program is developed by assembling the element stiffness matrices of virgin and delaminated portions of bilayer beams and applying the corresponding equivalent nodal forces. Two typical fracture specimens (i.e., single leg bending and end-notched flexure bilayer beams) are analyzed using the proposed bilayer beam elements. The computed displacement and energy release rate are compared well with those of analytical solutions, and the mode components of energy release rate for single leg bending specimen are also obtained using the virtual crack closure technique. It demonstrates that the proposed novel bilayer beam elements are capable of effectively and efficiently predicting the displacement and energy release rate (including its mode components) of delaminated bilayer beams. The developed bilayer beam element is general in nature and accurate and efficient in particular, because it can achieve the same accuracy as the high order beam theory and be easily implemented in the existing commercial finite element software.

Effect of steel fiber on flexural performance of bilayer concrete beams with steel and GFRP rebars: Experiments and predictions

Replacing steel rebars with glass fiber reinforced polymer (GFRP) rebars in concrete beams can lead to the production of lightweight and durable structural members. Meanwhile, layering concrete beams and using different volume fractions of steel fibers in the layers can be a proper method for improving structural performance and reducing construction costs of fiber reinforced-concrete beams. Therefore, this research aims to evaluate how bilayer steel fibrous concrete beam specimens with GFRP rebars behave under flexure. For this, 14 beam specimens reinforced with GFRP and steel fibers were manufactured in seven experimental groups without using any shear reinforcement. The effect of key variables such as reinforcement ratio, the volumetric content of steel fiber, and compressive strength of concrete on the performance of bilayer beams was examined. The main experiment of the current study involved three-point flexural tests, which were conducted on flexural specimens. The effective parameters on flexural behavior of beams such as flexural resistance, flexural stiffness, toughness, fracture energy, and load–displacement curve were extracted from the results. The results showed that the flexural properties of concrete beams increased by adding 0.75% steel fibers. Nevertheless, per the same fiber ratio, bilayer fibrous beam specimens had weaker flexural performance relative to one-layer fibrous concrete beam specimens. Additionally, when the GFRP bar was replaced with steel bar in the bilayer concrete flexural specimen, flexural resistance, toughness, fracture energy, and stiffness decreased while deflection in peak load increased significantly. Moreover, using high-strength concrete (HSC) in comparison to normal strength concrete (NSC) in bilayer GFRP reinforced beams improved flexural properties by almost 28%. After comparing the formulation to capture the flexural capacity of beam specimens in different specifications with results observed in this research, it is concluded that ACI 440.1R-06 and CAN/CSA S806-12 predict the deformation in service mode to great accuracy for beams reinforced with FRP as well as ACI 318, CAN/CSA A23.3, and ACI 440.1R-15 for steel-reinforced beams.

Simulation and investigation of MEMS bilayer solar energy harvester for smart wireless sensor applications

In this paper, design, optimization and simulation of piezoelectric based bilayer MEMS solar energy harvester to power smart wireless sensors is proposed. The electric potential is produced from the solar’s infrared power by using the thermal conduction principle and piezoelectric effect. Bilayer cantilever made of aluminium (Al) and silicon-di-oxide (SiO2) is designed such that it absorbs heat from the sun, causes bending. This induces stress at the fixed end from where the electric potential can be generated by placing the piezoelectric material. With the sinusoidal input heat flux of 1050 W/m2, finite element analysis is carried out in COMSOL software. The bilayer beam with different thickness, thickness aspect ratio and with different heat absorption materials are designed, simulated, compared with numerical calculations and simulation results. Then, different shapes of the beam are taken into account, compared with experimental results in our previous work and judged that triangular could perform with even more displacement comparing with other shapes. The optimized structure is analyzed with aluminium nitride (AlN) piezoelectric material for open circuit voltage generation. AlN is chosen due to its appealing properties such as larger Curie temperature, strong chemical and mechanical properties, low dielectric losses, low leakage current and stability of the piezoelectric coefficient for temperature changes. The designed harvester, on an average, can generate open circuit voltage of 0.81 V which could be further used to charge the rechargeable batteries in remote locations or for powering low power electronics.

Stress peaks, stiffening and back-flow in bilayer poro-elastic metamaterials

In the present work, we present a linear poroelastic model for a quasi-static oscillating bilayer beam made by two thick strata in perfect bond at their interface, characterized by different elastic moduli and permeability, both directly influenced by porosity. The solution is built up by considering the structure as a three-dimensional object and is obtained analytically for the full coupling of mass balance and mechanical equations, by imposing weak boundary conditions on the sole forces emerging at the lateral outermost surfaces, neglecting the inertial effects. After verifying the accuracy of the solution by comparing theoretical outcomes and numerical results from Finite Element simulations, ad hoc sensitivity analyses were then carried out in order to investigate the effects on the stress distribution and fluid flow due to prescribed inhomogeneities related to variations of material and geometrical parameters across the beam thickness, by keeping constant the total volume of the porous solid skeleton and applying self-equilibrated and oscillating in time axial forces and bending moments at two opposite sides of the structure. Some dynamic analyses were also performed to highlight proper periods and frequencies ranges where pulse loadings ensured the quasi-static response of the system, however discussing interferences due to transient regimes for selected cases on the basis of numerical analyses. Finally, we show that, by playing with ratios between elastic moduli, thickness and porosity of the two layers, a number of counterintuitive or even non-conventional behaviors can be observed, which give rise to unexpected back-flow phenomena and anomalous fluid content distributions, as well as to stress peaks kindled by moving the layer interface and overall stiffening that could be all exploited for the design of new multi-objective poroelastic metamaterials.

The Effect of Dentin Bonding and Material Thickness on the Flexural Properties of a Lithium-Disilicate Glass-Ceramic.

Thanks to adhesive techniques and strengthened glass ceramics, ultrathin bonded occlusal veneers have been recently introduced. However, since a universally accepted thickness limit for ultrathin ceramics has yet to be established, their resistance to fracture needs to be better investigated. The purpose of this in vitro study was to evaluate the effect of dentin bonding on the flexural properties (ie, fracture load and flexural strength) of a lithium-disilicate (LD) glass ceramic when used in thicknesses equal to or less than the manufacturer's recommendations for occlusal restorations. A total of 96 dentin slices (2.0 mm thick and 15 mm long) were obtained by sectioning bovine teeth along their long axes. LD slices of different thicknesses (1.5 mm/1.3 mm/1.0 mm/0.8 mm/0.6 mm) and 15 mm in length were cut from CAD/CAM LD blocks (IPS e.max CAD-C16). In each of 5 experimental groups, 16 dentin slices were adhesively luted to 16 LD slices (n = 16) of the same thickness, in order to create 16 bi-layered dentin-LD bonded assemblies. In the control group, the 16 remaining dentin slices were conventionally cemented to 1.5-mm-thick LD slices (n = 16) using a resin-modified glass-ionomer cement (FujiCEM 2). All dentin-LD assemblies were cut perpendicularly to their joint interface, in order to obtain 1-mm-wide, 15-mm-long bi-layered prismatic beams, having the following final thicknesses: for the 5 experimental groups, 2 mm (dentin layer) + 1.5 mm/ 1.3 mm/1.0 mm/0.8 mm/0.6 mm (LD layer); for the control group, 2 mm (dentin layer) + 1.5 mm (LD layer). All prismatic beams were subjected to a three-point bending test (14-mm span, load applied on the LD side). Fracture loads (N) and flexural strengths (MPa) were recorded. Data were analyzed using one-way ANOVA on ranks tests (α = 0.05). The correlations between the recorded flexural strengths and the dentin:LD thickness ratio and between the flexural strength and the luting strategy were also investigated. The failure modes were observed and classified. No statistically significant differences were recorded between the conventionally luted control group (LD thickness 1.5 mm; fracture load 35.26 N; flexural strength 60.44 MPa) and the thinnest adhesively luted experimental group (LD thickness 0.6 mm; fracture load 28.97 N; flexural strength 90.01 MPa) in terms of fracture load and flexural strength. A fracture involving both the dentin and the LD of the bi-layered prismatic beam, but without any debonding between the LD and the dentin substrates of the broken specimen, was the most common failure mode observed on the adhesively luted samples. Compared to conventional cementation, when LD is bonded to dentin, the flexural properties of the whole system are improved, and the two different substrates seem to behave like a single unit. Once adhesively luted, 0.6-mm-thick LD has the same fracture load and flexural strength as that of the conventionally luted 1.5-mm-thick LD.

Metamaterials with remarkable thermal–mechanical stability and high specific modulus: Mechanical designs, theoretical predictions and experimental demonstrations

In the fields of aerospace, flexible electronics, intelligent manufacturing, and MEMS, the mechanical metamaterials with remarkable zero thermal expansion of coefficient (CTE) are of increasing interest due to their advantages in maintaining their original shapes upon a temperature change. Though recently published researches have demonstrated several designs in achieving a desirable CTE, it is still very challenging to develop the mechanical metamaterial with high-level thermal–mechanical stability (i.e., CTE < 0.5 ppm/°C). Additionally, most of these studies only focused on obtaining a remarkable zero CTE through optimizing the geometrical parameters, and did not provide enough performances in consideration of their mechanical behaviors (e.g., lightweight, high specific modulus), imposing certain limitations on their operation in devices that require combined thermal–mechanical attributes. This paper demonstrates a mechanical metamaterial design concept with lightweight, high specific modulus properties and high-level thermal–mechanical stability. Each of the unit cell in our designs composed of two or four bilayer beams filled by hourglass lattices in Al and Ti materials offers a tunable CTE from negative to positive, revealing its capability to offer remarkable zero CTE. A theoretical model that preciously predicts the design’s thermal and mechanical performances provides a clear understanding of the effects of geometric parameters on their corresponding effective properties, facilitating the design of metamaterials with desired mechanical and thermal expansion performances. Excellent agreements between theoretical predictions, FEAs, and experiments demonstrate the advantages of our design in achieving the combined attributes of lightweight (i.e., relative density ρ¯Uniaxial ¡ 0.123 for the design with uniaxial thermal–mechanical stability and ρ¯Biaxial ¡ 0.069 for the one with biaxial thermal–mechanical stability), high specific modulus (i.e., 1104 kN⋅ mm/kg and 1203 kN⋅ mm/kg for the designs with uniaxial and biaxial thermal–mechanical stability), and a remarkable zero CTE (αeffective ¡ 0.32 ppm/°C). Ashby plot of the effective CTE with respect to density, serving as an especially useful tool in selecting materials according to the requirements of practical applications, provides quantitative evidences for our design’s outstanding thermal–mechanical performances as compared to the previously reported studies.