Minimum Strain Research Articles

Freestanding Serpentine Silicon Strips with Ultrahigh Stretchability over 300% for Wearable Electronics.

Well-functionalized electronic materials, such as silicon, in a stretchable format are desirable for high-performance wearable electronics. However, obtaining Si materials that meet the required stretchability of over 100% for wearable applications remains a significant challenge. Herein, a rational design strategy is proposed to achieve freestanding serpentine Si strips (FS-Si strips) with ultrahigh stretchability, fulfilling wearable requirements. The self-supporting feature makes the strips get rid of excessive constraints from substrates and enables them to deform with the minimum strain energy. Micrometer-scale thicknesses enhance robustness, and large diameter-to-width ratios effectively reduce strain concentration. Consequently, the FS-Si strips with the optimum design could withstand 300% stretch, bending, and torsion without fracturing, even under rough manual operation. They also exhibit excellent stability and durability over 50,000 cycles of 100% stretching cycles. For wearable applications, the FS-Si strips can maintain conformal contact with the skin and have a maximum stretchability of 120%. Moreover, they are electrically insensitive to large deformations, which ensure signal stability during their daily use. Combined with mature processing techniques and the excellent semiconductor properties of Si, FS-Si strips are promising core stretchable electronic materials for wearable electronics.

Dominant slip systems of quartz under lower amphibolite-facies conditions identified from microstructures and CPOs in quartz phenocrysts

Identifying the dominant slip systems in naturally deformed quartz is crucial for understanding continental crust rheology. Although the basal <a> slip system is considered dominant in quartz under upper to middle crustal conditions, its activity is controversial because an oriented nucleation and growth model has been proposed for the c-axis distribution near the minimum strain axis. This study examined the crystallographic orientation and shape of quartz phenocrysts in a deformed granitic porphyry in the Ryoke belt, SW Japan, to clarify the dominant slip systems in naturally deformed quartz at temperature conditions of ∼400–500 °C utilizing optical and electron backscatter diffraction (EBSD) observations. Identified active slip systems include prism <a>, basal <a>, prism [c], and rhomb <a> through misorientation analyses. The aspect ratios of phenocrysts with dominant prism <a> and basal <a> slip systems are higher than prism [c] and rhomb <a> slip systems, indicating similar strengths between prism <a> and basal <a> slip systems, which are weaker than prism [c] and rhomb <a> slip systems under lower amphibolite-facies conditions. The c-axis of phenocrysts with dominant basal <a> distribute at pole figures peripheries, indicating basal <a> activation over the proposed oriented nucleation and growth model.

Stress Changes in the Canine Radius after Locking Plate Fixation Using Finite Element Analysis.

The aim of this study was to evaluate the stress changes in the radii beneath the locking plates (LP) of dogs implanted with LP using finite element analysis (FEA). The study included radii harvested from eight dogs. After computed tomography (CT) scans of the forelimb, the articular surface of the radius was fixed using resin. Material tests were conducted to identify the yield and fracture points and for verification with FEA. The CT data of the radius were imported into FEA software. The radii were classified into three groups based on the placement of the LP (nonplate placement, intact group; 1 mm above the radial surface, LP + 1 mm group; 3 mm above the radial surface, LP + 3 mm group). Equivalent, maximum, and minimum principal stresses and minimum principal strain were measured after FEA at the radial diaphysis beneath the plate. In shell elements, the LP + 1 mm and LP + 3 mm groups showed a significantly lower maximum principal stress compared with the intact group. In solid elements, the LP + 1 mm and LP + 3 mm groups showed a significantly higher equivalent stress and a significantly lower maximum principal stress compared with the intact group. When an axial load is applied to the radius, LP placement reduces the tension stress on the cortical bone of the radius beneath the plate, possibly related to implant-induced osteoporosis and bone formation in the cortical bone beneath the plate.

A minimum strain energy release-based thermal–mechanical damage model for fracture process simulation of quasi-brittle materials under high temperatures

A minimum strain energy release-based thermal–mechanical damage model for fracture process simulation of quasi-brittle materials under high temperatures

Creep deformation and cavitation in an additively manufactured Al-8.6Cu-0.4Mn-0.9Zr (wt%) alloy

Creep deformation and cavitation were investigated at 300 ºC in both tension and compression for an additively manufactured Al-8.6Cu-0.5Mn-0.9Zr (wt%) alloy in the as-fabricated state and after various aging treatments (aging at 300 °C/200 h or 350 °C/24 h and overaging at 400 °C/200 h). Creep mechanisms at 300 °C were determined by relating the measured creep response to corresponding microstructural and X-ray computed tomography observations. In compression, alloys in the as-fabricated and two aging conditions exhibited similarly high creep resistance. Overaging (400 °C/200 h) led to substantial coarsening of intragranular θ-Al2Cu precipitates and an expected drop in their Orowan strengthening contribution. In tension, minimum strain rates comparable to those in compression were obtained at any given stress; however, upon accumulation of some plastic strain in the matrix, creep cavities started to form, leading to accelerated tertiary stage creep deformation and rupture. Cavitation occurred exclusively along melt pool boundaries due to locally enhanced diffusion enabled by (ⅰ) large grain-boundary area in adjacent fine-grained zones and (ⅱ) localization of creep strain in nearby heat-affected zones. Although cavity growth was initially diffusion-controlled, its rate was determined by matrix creep rate, consistent with constrained cavity growth mechanisms. This study reveals how microstructural complexities induced by the additive manufacturing process affect the creep and cavitation behavior of Al-Cu-Mn-Zr alloys. The underlying creep and cavitation mechanisms uncovered in this study point to pathways that improve the high-temperature properties of additively manufactured alloys.

Crystallographic texture and multiscale boundaries mediated creep anisotropy in additively manufactured Ni-based Hastelloy C276 superalloy

The microstructure and high-temperature creep mechanisms of Ni-based Hastelloy C276 superalloy fabricated using wire and arc-based directed energy deposition were investigated systematically and innovatively. The microstructural investigation revealed that the as-fabricated samples comprise γ-Ni matrix and topologically close-packed (TCP) P phase precipitates. The γ matrix subgrains and grains are spread over multiple highly textured columnar dendrites, with a majority of γ <001> crystallographic orientations closely aligned along the deposition direction. Moreover, the interdendritic regions exhibit severe Mo segregation, P phase particles, and dislocation bands. Creep tests were conducted on miniature samples under various temperature and stress conditions, loaded either in the deposition direction (DD) or travel direction (TD). DD samples exhibit lower minimum strain rates, greater strains-to-failure, and longer creep rupture lifetimes than TD samples, indicating significant creep anisotropy. Dislocation creep was identified as the primary creep mechanism for both DD and TD conditions. During creep, dynamic precipitation of TCP phases occurred in the interdendritic regions, resulting in varying creep resistance between interdendritic and dendritic core regions. Isostress and isostrain models, considering both crystallographic texture and precipitation strengthening, reasonably predicted the observed creep anisotropy during the secondary creep stage. Additionally, variations in the Schmid factor led to significant deformation incompatibility among dendrites in TD samples. Dislocation accumulation in TD sample interdendritic regions promoted new grain nucleation, triggering dynamic recrystallisation, facilitating grain boundary sliding, and accelerating tertiary creep. Furthermore, TCP phase particles in the interdendritic regions contributed to microcrack development, further accelerating creep fracture, especially in the TD condition.

In-Plane Mixed-Mode Brittle Fracture Assessment of Harsin Marble Using HCSP Specimen

The primary objective of this manuscript is studying the effect of T-stress term (T) on the crack propagation angle (CPA) and fracture toughness of in-plane mixed mode loading by utilizing a generalized form of minimum strain energy density (SED) criterion. The generalized criterion considers the influence of the first non-singular term of the Williams stress field as well as the conventional stress intensity factors (SIFs). A specimen known as a holed-cracked square plate (HCSP) composed of white Harsin marble is used for a wide range of in-plane mixed-mode fracture studies. HCSP is a square plate containing two cracks that are placed along each other in the circumference of a hole at the center of the specimen. The experimental results from mixed-mode fracture test by using proposed geometry are then compared with the results obtained theoretically from the conventional and generalized form of SED. It is demonstrated that the generalized criterion which includes the T, is substantially in agreement with the experimentally observed in-plane mixed-mode fracture results when compared to the SED criterion.

The loading direction dramatically affects the mechanical properties of the mouse tibia.

Introduction: The in vivo tibial loading mouse model has been extensively used to evaluate bone adaptation in the tibia after mechanical loading treatment. However, there is a prevailing assumption that the load is applied axially to the tibia. The aim of this in silico study was to evaluate how much the apparent mechanical properties of the mouse tibia are affected by the loading direction, by using a validated micro-finite element (micro-FE) model of mice which have been ovariectomized and exposed to external mechanical loading over a two-week period. Methods: Longitudinal micro-computed tomography (micro-CT) images were taken of the tibiae of eleven ovariectomized mice at ages 18 and 20weeks. Six of the mice underwent a mechanical loading treatment at age 19weeks. Micro-FE models were generated, based on the segmented micro-CT images. Three models using unitary loads were linearly combined to simulate a range of loading directions, generated as a function of the angle from the inferior-superior axis (θ, 0°-30° range, 5° steps) and the angle from the anterior-posterior axis (ϕ, 0°: anterior axis, positive anticlockwise, 0°-355° range, 5° steps). The minimum principal strain was calculated and used to estimate the failure load, by linearly scaling the strain until 10% of the nodes reached the critical strain level of -14,420με. The apparent bone stiffness was calculated as the ratio between the axial applied force and the average displacement along the longitudinal direction, for the loaded nodes. Results: The results demonstrated a high sensitivity of the mouse tibia to the loading direction across all groups and time points. Higher failure loads were found for several loading directions (θ = 10°, ϕ 205°-210°) than for the nominal axial case (θ = 0°, ϕ = 0°), highlighting adaptation of the bone for loading directions far from the nominal axial one. Conclusion: These results suggest that in studies which use mouse tibia, the loading direction can significantly impact the failure load. Thus, the magnitude and direction of the applied load should be well controlled during the experiments.

Creep life assessment of modified 9Cr-1Mo steel based on Monkman–Grant relationship considering temperature and stress dependences of strain required for rupture

ABSTRACT Regarding the application of the Monkman-Grant relationship to creep strength enhanced ferritic steels such as modified 9Cr-1Mo and 12Cr steels, there have been many reports showing that results tend to be an overestimation of the creep life in the long-term region. To address this issue, an author conducted a study to improve the estimation accuracy in the long-term region by the Monkman Grant relationship. Analysing the published creep test data for modified 9Cr-1Mo steel, the author found that the product of the minimum creep strain rate and rupture time (Ɛ MG ) is not constant but depends on the loading conditions, which are test temperature and stress. Then, the author proposed an extended Monkman-Grant relationship considering the dependence of Ɛ MG on the loading conditions. When this model was applied to the data for modified 9Cr-1Mo and 12Cr steels, the creep life was predicted with good accuracy from the short-term to long-term regions.

Printability of Nixtamalized Corn Dough during Screw-Based Three-Dimensional Food Printing.

This study aimed to analyze the printability of corn-based dough during screw-based three-dimensional (3D) food printing (3DFP) by relating its rheological and mechanical properties to its screw-based 3DFP performance, with the objective of providing insights into the utilization of corn-based dough to produce 3D-printed foods. Screw-based 3DFP was performed using seven corn-based doughs with different nixtamalized corn flour (NCF) and water contents. Afterward, their rheological and mechanical properties were analyzed and associated with their screw-based 3DFP performance. The results showed that stable printability was obtained within a specific range of NCF content in the dough (30-32.5 wt%). Below this range, the 3D-printed foods flattened, while above it, the extrudability of the dough was affected. The printability of the dough was influenced by different rheological and mechanical properties, depending on the stage of the screw-based 3DFP process. During the extrusion stage, the loss tangent at nozzle strain, yield stress, apparent viscosity, and adhesiveness mainly affected the extrudability of the dough. In contrast, the loss tangent at minimum strain, elastic modulus, Young's modulus, and hardness influenced the self-supporting stage. Therefore, it is important to find a balance between all of these properties, where stable extrudability and self-supporting of the 3D structure are achieved.

A Strategy for Enhancing Perpendicular Magnetic Anisotropy in Yttrium Iron Garnet Films.

In future information storage and processing, magnonics is one of the most promising candidates to replace traditional microelectronics. Yttrium iron garnet (YIG) films with perpendicular magnetic anisotropy (PMA) have aroused widespread interest in magnonics. Obtaining strong PMA in a thick YIG film with a small lattice mismatch (η) has been fascinating but challenging. Here, a novel strategy is proposed to reduce the required minimum strain value for producing PMA and increase the maximum thickness for maintaining PMA in YIG films by slight oxygen deficiency. Strong PMA is achieved in the YIG film with an η of only 0.4% and a film thickness up to 60nm, representing the strongest PMA for such a small η reported so far. Combining transmission electron microscopy analyses, magnetic measurements, and a theoretical model, it is demonstrated that the enhancement of PMA physically originates from the reduction of saturation magnetization and the increase of magnetostriction coefficient induced by oxygen deficiency. The Gilbert damping values of the 60-nm-thick YIG films with PMA are on the order of 10-4. This strategy improves the flexibility for the practical applications of YIG-based magnonic devices and provides promising insights for the theoretical understanding and the experimental enhancement of PMA in garnet films.

Impact of Stoma Baseplate Convexity on Tension and Compression Around the Stoma Site: A Finite Element Analysis.

For patients living with intestinal or urinary stomas, skin barriers play an essential role in protecting the peristomal skin and preventing peristomal complications. Convex baseplates press into the peristomal skin and are suitable for retracted stomas that do not protrude, peristomal skin with creases, folds, or dips, and stomas where frequent leaking can occur with flat pouching systems. However, there is a lack of data on the magnitude and location of tension applied to the abdomen by convex baseplates. We evaluated the impact of a range of convex baseplates applied to a simulated stoma site. A comparative finite element analysis investigation was conducted to evaluate the impact of eight different convex stoma system baseplates applied to an idealised flat abdomen, representing skin, subcutaneous tissue, and musculature layers. The baseplates considered had varying convexity with depths of 3.5 mm and 7 mm and internal structural diameters between ~30 mm and ~60 mm. The convex product range provided tension in the skin (maximum principal strain) and compression through the fat layer (minimum principal strain). Large differences in the locations and magnitudes of skin tension and fat layer compression were seen between the baseplates under analysis, with both the depth and diameter of convexity influencing the strain experienced across the abdominal topography. The results generated highlight the importance of having an appropriate range of convexity products available and selecting an appropriate option for use based on the stoma type and condition of the peristomal skin.

Quantification and assessment of the error associated with engineering stress-strain analysis in stress accelerated creep tests in 316H stainless steel

ABSTRACT Historically, reduction of area has been neglected during uniaxial creep tests, and engineering rather than true stress-strain and strain rate have been considered. In high load accelerated tests, there is an increasing error associated with the engineering stress and strain, hence this assumption is no longer valid. In this work, uniaxial creep tests on Type 316H austenitic stainless steel at 480–550 °C have been analysed for both engineering and true stress–strain and strain rate. Significantly higher stresses and lower minimum strain rates were determined from true stress-strain rate relationships for as-received 316H. These differences diminish as the material is strain hardened, limiting plastic loading strains and reducing creep ductility. The true stress-strain rate analysis method is shown to be more accurate, however, the engineering stress-strain analysis predicts higher creep strain rates for a given stress and is the more conservative measure for component lifetime assessments.

Metal chalcogenide nanorings for temperature-strain dual-mode sensing.

Most metal chalcogenides exhibit layered structures and anisotropic morphologies such as nanosheets, nanoplates, and nanotubes, as well as nanosheet-assembled nanoflowers. Unconventional morphologies such as nanorings may bring appealing properties to functional materials, but they have not been realized with metal chalcogenides. Herein, we report that Sn0.2Mo0.8S2 nanorings with a mixed 1T/2H phase were synthesized by etching SnS2 cores from Sn1-xMoxS2/SnS2 lateral heterostructures. Flexible electronic sensors based on these Sn0.2Mo0.8S2 nanorings exhibited excellent temperature and strain sensing performance, with a negative temperature coefficient of resistance of -0.013 °C-1 and a minimum detectable strain of 0.09%. In addition, the dual-functional flexible electronic sensors with easy fabrication and good wearability showed great promise for tracking human activities and monitoring inapparent health-related signals.

A Methodology for Designing a Fish-Friendly Turbine Rotor Applied to High-Power Generation

Most large hydropower facilities employing conventional hydraulic turbines, e.g., Francis, Kaplan, or Bulb turbines, etc., cause significant harm to fish, resulting in high mortality rates, during turbine operation. This results from strong injury-inducing mechanisms at the rotor, including shear stresses, pressure variations, and pressure drop through the rotor. The study outlines a methodology for designing a fish-friendly turbine that is suitable for high-power generation applications. This methodology for a hydraulic channel design within the turbine rotor was derived based on classical fundamental applications of a rotor design, supplemented by subsequent assessments that incorporate fish-friendly design parameters that have been documented in the existing literature. A spiral curve characterized by a linear angle variation between the rotor's inlet and outlet was employed to project the blade geometry. Here, the Göttingen hydrofoil series was used, while a second-order polynomial function guided the hub design. Both of these parametrizations sought to enhance the turbine's hydraulic efficiency. Minimum Absolute Pressure, Strain Rate, and Pressure Variation Rate intervals were established as assessment criteria for fish survival for certain species, as has also been previously explored in the literature. The findings were outlined in terms of hydrodynamic performance and flow behavior within the rotor. An improvement in hydraulic efficiency was observed, transitioning from a Preliminary Turbine geometry design to an Optimized Turbine Geometry design. The turbine rotor was optimized using Computational Fluid Dynamics (CFD) simulations, generated from a Design of Experiments (DOE). Modifications to the hydrofoil type, the sweep angle, and the trailing edge angle of the blades were all made, coupled with integrations of assessments considering fish-friendly parameters.

The stress state of a plate with several holes under the action of axial tensile load

The purpose of the research is to develop a numerical method for determining the stress state of plates with several holes. The research approach is based on the development of the superposition method for singular solutions. The study objective is to solve a practical problem of determining the stress concentration coefficients in a plate with two holes of the same diameter. The study uses the numerical method of elasticity theory in the form of a superposition of four special solutions, each of which lies entirely within the corresponding hole contour. The resulting contour integrals in the displacement formula are replaced by their approximate values using the M-point trapezoidal formula or the Gaussian quadrature formula. Equating to zero the expression in variations of unknown constants (the principle of minimum potential strain energy), we have obtained a system of linear algebraic equations 4MN of unknown distribution densities. After determining the constants using known formulas, the stress-strain state of the plate with holes can be calculated. The error of the developed method is no more than 0.6% compared to the known solution.

Distributed phase-matching measurement for dynamic strain and temperature sensing based on stimulated Brillouin scattering enhanced four-wave mixing

A Brillouin dynamic grating (BDG) can be used for distributed birefringence measurement in optical fibers, offering high sensitivity and spatial resolution for sensing applications. However, it is quite a challenge to simultaneously achieve dynamic measurements with both high accuracy and high spatial resolution. In this work, we propose a sensing mechanism to achieve distributed phase-matching measurement using a chirped pulse as a probe signal. In BDG reflection, the peak reflection corresponds to the highest four-wave mixing (FWM) conversion efficiency, and it requires the Brillouin frequency in the fast and slow axes to be equal, which is called the phase-matching condition. This condition changes at different fiber positions, which requires a range of frequency injection for the probe wave. The proposed method uses a chirped pulse as a probe wave to cover this frequency range associated with distributed birefringence inhomogeneity. This allows us to detect distributed phase matching for birefringence changes that are introduced by temperature and strain variations. Thanks to the single shot and direct time delay measurement capability, the acquisition rate in our system is only limited by the fiber length. Notably, unlike conventional BDG spectrum recovery-based systems, the spatial resolution here is determined by both the frequency chirping rate of the probe pulse and the birefringence profile of the fiber. In the experiments, an acquisition rate of 1 kHz (up to fiber length limits) and a spatial resolution of 10 cm using a 20 ns probe pulse width are achieved. The minimum detectable temperature and strain variation are 5.6 mK and 0.37 με along a 2 km long polarization-maintaining fiber (PMF).

Grain-level effects on in-situ deformation-induced phase transformations in a complex-phase steel using 3DXRD and EBSD

A novel complex-phase steel alloy is conceived with a deliberately unstable austenite, γ, phase that enables the deformation-induced martensitic transformations (DIMT) to be explored at low levels of plastic strain. The DIMT was thus explored, in-situ and non-destructively, using both far-field Three-Dimensional X-ray Diffraction (3DXRD) and Electron Back-Scatter Diffraction (EBSD). Substantial α′ martensite formation was observed under 10% applied strain with EBSD, and many ɛ grain formation events were captured with 3DXRD, indicative of the indirect transformation of martensite via the reaction γ→ɛ→α′. Using ɛ grain formation as a direct measurement of γ grain stability, the influence of several microstructural properties, such as grain size, orientation and neighbourhood configuration, on γ stability have been identified. Larger γ grains were found to be less stable than smaller grains. Any γ grains oriented with {100} parallel to the loading direction preferentially transformed with lower stresses. Parent ɛ-forming γ grains possessed a neighbourhood with increased ferritic/martensitic volume fraction. This finding shows, unambiguously, that the nearby presence of α and α′ promotes ɛ formation in neighbouring grains. The minimum strain work criterion model for ɛ variant prediction was also evaluated, which worked well for most grains. However, ɛ-forming grains with a lower stress were less well predicted by the model, indicating crystal-level behaviour must be considered for accurate ɛ formation. The findings from this work are considered key for the future design of alloys where the deformation response can be controlled by tailoring microstructure and local or macroscopic crystal orientations.

Microstructural effects on the ambient temperature indentation creep behavior of metastable β Ti-5Al-5V-5Mo-3Cr alloy

Ti-5553 alloy is considered as a potential candidate for heavy structural components such as landing gears in aerospace industries, that operate particularly at room temperature. For achieving the targeted performance, microstructural modification and corresponding improvement in mechanical properties, particularly room temperature creep behavior of Ti-5553 alloy is of significant concern. In this regard, an optimized thermomechanical processing (TMP) schedule is employed to tailor the microstructure of as-cast Ti-5553 alloy. Typical bimodal microstructure containing both α and β phases is noted to evolve upon TMPing, as compared to its as-cast counterpart, having sole β phase. The size and volume fraction of αp are noted to be 0.85 ± 0.39 µm and 11.7 ± 0.5%, respectively. Such pronounced variation in the microstructural features is expected to alter the localized mechanical properties significantly. To assess that, room temperature small-scale creep behavior of as-cast and TMPed Ti-5553 alloys is investigated using nanoindentation technique. The effect of maximum load on different creep parameters are analyzed and correlated with the corresponding microstructures. It is noted that at any particular applied load level, creep deformation of TMPed Ti-5553 alloy is ∼ 20–64% lower than that for the as-cast one. This is reflected in significant reduction in the minimum creep strain rate from 10−4 s−1 for as-cast to 10−5 s−1 for TMPed Ti-5553 alloy. Dislocation creep mechanism is found to be active for both the alloys since creep exponent for both the as-cast and TMPed Ti-5553 alloys exceed the value of 2. Discontinuous semi-circular micro-shear bands are noted to form around the indents for the as-cast Ti5553 alloy. The kernel average misorientation map for this alloy reveals a lower degree of misorientation and a more homogeneous distribution of plastic strain. In contrary, the TMPed Ti-5553 alloy exhibits higher misorientation around the indent impression, thereby indicating towards the restriction of dislocation movement against α/β laths and hence positively influencing the creep behavior. Overall, the study highlights the important role of TMP in enhancing the creep resistance of Ti-5553 alloy for industrial applications.

Memeplex-based memetic algorithm for the multi-objective optimal design of composite structures

Hybrid construction is proposed to decrease costs in lightweight structures using fiber-reinforced plastics (FRP) composite materials. Minimum weight, minimum strain energy (stiffness), and minimum energy variability of the structural system response are the objectives of the robust design optimization approach applied to composite shell structures with stiffeners. The trade-off depends on given stress, displacement, and buckling constraints imposed on composite structures considering non-linear geometric behavior. The design variables are ply angles and ply thicknesses of shell laminates, the cross-section dimensions of stiffeners, and the variables related to the selection of materials and their distribution at the laminate level and subsequently of the laminates along the structure. A Multi-Objective Memetic Algorithm (MOMA) applies multiple learning procedures exploring the synergy of different cultural transmission rules. An enlarged virtual population with a dual age-dominance nature captures and updates the Pareto curve. The concept of memeplex controls the meme selection and their propagation along the hybrid genetic and cultural evolution path. The success of memetic learning procedures is analyzed by measuring each meme's relative and absolute success events according to different approaches, depending on the reference time used in evolutionary history. Results show that MOMA is promising in multi-objective optimization of composite hybrid structures.