3D Strain Distribution Research Articles

Multimodal deep learning framework to predict strain localization of Mg/LPSO two-phase alloys

This study proposes a method for predicting three-dimensional (3D) local strain distribution under compressive deformation of as-cast Mg/LPSO two-phase alloys from 3D microstructure images. The 3D local strain distribution was obtained by applying the digital volume correlation method to X-ray CT images before and after compression tests. Three microstructure descriptors were extracted from the 3D microstructure images around each strain measurement point: volume fractions of the phases, persistent diagrams that can express the connectivity of the phases, and two-phase spatial correlation that can express the spatial distribution of the phases. A deep learning model was then constructed to predict local strain from the three microstructure descriptors. Since two types of descriptors were used in this study, numerical data and image data, multimodal deep learning was employed to make predictions. Thus, the use of multiple microstructure descriptors enabled predictions to be made with higher accuracy than when predictions were made from a single descriptor. Feature importance of the descriptors was assessed through correlation analysis and occlusion sensitivity analysis. The results revealed that high strain tended to occur in the region where the hard phase, LPSO phase, had a large elongated phase oriented at a 45° direction to the loading direction. This result is consistent with other previous studies and indicates that the proposed method is effective in elucidating the relationship between the microstructure and the deformation behavior of the material.

Coaxial panoramic 3D-DIC system for full inner surface deformation measurement

A coaxial panoramic three-dimensional digital image correlation (3D-DIC) system was developed for full 360o inner surface deformation measurement. The panoramic observation was realized by using a convex mirror. Two cameras were arranged coaxially to ensure the largest overlapping observation area. After the coordinate transformation and correlation calculation, the 3D displacement and strain distributions were reconstructed. The principles of the system were presented in detail, and the internal morphology and deformation of pipes subjected to compression loading were described to verify the effectiveness, practicality, and accuracy of the proposed system.

Tensile damage evolution and mechanical behaviour of SiCf/SiC mini-composites through 4D in-situ micro-CT and data-driven modelling

Damage evolution of SiCf/SiC ceramic matrix mini-composites (CMMCs) was characterised by using a 4D in-situ micro-computed tomography (CT) tensile test and digital volume correlation (DVC) technique. Additionally, a CT damage data-driven shear lag model was developed to predict its tensile stress-strain response. A 4D in-situ X-ray CT tensile test of a unidirectional SiCf/SiC mini-composite was first carried out. Then two ad-hoc deep-learning image segmentation models were developed to automatically identify its microstructure and damages induced by tension, respectively. Damage evolution was quantitively characterised by visualising the initiation and propagation of matrix cracks in three-dimensions (3D). A two-step approach was employed to evaluate its 3D internal strain distributions at various loading levels, which further revealed strain concentrations and helped establishing the tensile stress-strain response of the CMMCs. It was observed that transverse cracking is the predominant damage mode, and the average crack opening displacement increases with loading. A high-fidelity X-ray CT data-driven shear lag model was developed, incorporating inputs of transverse matrix crack spacing calculated by the 4D in-situ CT test data. The predicted stress-strain response showed a good correlation with the experimental results.

Full-Field Strain Measurements of the Muscle-Tendon Junction Using X-ray Computed Tomography and Digital Volume Correlation.

We report, for the first time, the full-field 3D strain distribution of the muscle-tendon junction (MTJ). Understanding the strain distribution at the junction is crucial for the treatment of injuries and to predict tear formation at this location. Three-dimensional full-field strain distribution of mouse MTJ was measured using X-ray computer tomography (XCT) combined with digital volume correlation (DVC) with the aim of understanding the mechanical behavior of the junction under tensile loading. The interface between the Achilles tendon and the gastrocnemius muscle was harvested from adult mice and stained using 1% phosphotungstic acid in 70% ethanol. In situ XCT combined with DVC was used to image and compute strain distribution at the MTJ under a tensile load (2.4 N). High strain measuring 120,000 µε, 160,000 µε, and 120,000 µε for the first principal stain (εp1), shear strain (γ), and von Mises strain (εVM), respectively, was measured at the MTJ and these values reduced into the body of the muscle or into the tendon. Strain is concentrated at the MTJ, which is at risk of being damaged in activities associated with excessive physical activity.

Strain and crystallographic identification of the helically concaved gap surfaces of chiral nanoparticles

Identifying the three-dimensional (3D) crystal plane and strain-field distributions of nanocrystals is essential for optical, catalytic, and electronic applications. However, it remains a challenge to image concave surfaces of nanoparticles. Here, we develop a methodology for visualizing the 3D information of chiral gold nanoparticles ≈ 200 nm in size with concave gap structures by Bragg coherent X-ray diffraction imaging. The distribution of the high-Miller-index planes constituting the concave chiral gap is precisely determined. The highly strained region adjacent to the chiral gaps is resolved, which was correlated to the 432-symmetric morphology of the nanoparticles and its corresponding plasmonic properties are numerically predicted from the atomically defined structures. This approach can serve as a comprehensive characterization platform for visualizing the 3D crystallographic and strain distributions of nanoparticles with a few hundred nanometers, especially for applications where structural complexity and local heterogeneity are major determinants, as exemplified in plasmonics.

Omnidirectional 3D-DIC method for determining inner deformation in pipelines

An omnidirectional three-dimensional digital image correlation (DIC) system was developed for full 360-degree inner surface deformation measurements using a pyramid reflector to realize panoramic observation. After the coordinate transformation, the 3D displacement and strain distributions were reconstructed. The basic principles, optical arrangements, and experimental procedures were described in detail. Morphology and rigid-body displacement experiments were conducted to evaluate the efficiency and accuracy of the 3D shape and displacement determination. The experimental results agree well with the actual values and the data obtained by multiple measurements using the traditional 3D-DIC method. Moreover, the proposed method was successfully applied to evaluate the inner deformation distributions of pipes subjected to compression loading. The experimental results further validated the applicability of the proposed method.

Strain distribution in the bursal rotator cuff based on whole-muscle and muscle subregion-specific loading: A cadaveric study.

Rotator cuff (RC) tears are common injuries leading to significant dysfunction of the shoulder. Rotator cuff tears alter tension and strain in muscles and tendons. Anatomical studies demonstrated that rotator cuff muscles are comprised of anatomical subregions. However, the strain distribution within the rotator cuff tendons generated from the tension from each anatomical subregion is unknown. We hypothesized that subregions would present distinct 3-dimensional (3D) strain distributions within the rotator cuff tendons, and that the anatomical insertion configuration of the supraspinatus (SSP) and infraspinatus (ISP) tendons might dictate strain, thus tension, transmission. 3D-strains in the bursal side of the SSP and ISP tendons of eight fresh-frozen cadaveric intact shoulders were obtained by applying tension on the whole SSP and ISP muscles, and on their subregions using an MTS system. Strains in the anterior region of the SSP tendon were higher than in the posterior region with whole-SSPanterior-region (p < 0.05) and whole-SSP muscle loading. Higher strains were observed in the inferior half of the ISP tendon with whole-ISP muscle (p < 0.05), middle-subregion (p < 0.01), and superior-subregion (p < 0.05) loading. Tension generating from the posterior-region of the SSP was primarily transmitted to the middle facet via an overlap between the SSP and ISP tendons insertions, while the anterior-region mainly distributed its tension into the superior facet. Tension generating from the middle and superior-regions of the ISP was distributed into the inferior portion of the ISP tendon. These results emphasize the importance of the distinct anatomical subregions of the SSP and ISP muscles in distributing the tension to the tendons.

In situ high-temperature 3D imaging of the damage evolution in a SiC nuclear fuel cladding material

Silicon carbide (SiC)-based nuclear fission fuel rod cladding has been considered as one of the possible designs for accident tolerant fuels. It is in the form of a SiC fibre reinforced SiC matrix composite tube (SiCf-SiCm) with monolithic SiC outer and/or inner coating layers. This study focuses on the deformation and fracture processes in this material using in situ X-ray micro-computed tomography (XCT) at room temperature (RT) and 1200 °C in an inert gas environment in a C-ring compression loading configuration. Prior to testing, local properties and residual stresses were characterised using nanoindentation and Raman spectroscopy since they can impact the mechanical behaviour of the material. The 3D strain distribution, crack formation and propagation processes including the toughening mechanisms (e.g., crack deflection, micro-cracking, crack bridging and bifurcation) are investigated in the coating and underlying composites at RT and 1200 °C. There is no particular sequence which toughening mechanism occurs first – this is very different from the conventional toughening theory in ceramic-matrix composites under uniaxial tension loading. Indeed, no evidence of fibre pull-out or fibre fracture was observed in this SiCf-SiCm nuclear cladding material in the current C-ring compression configuration. The correlation between local measurements and bulk mechanical behaviour are discussed.

Damage evolution and full-field 3D strain distribution in passively confined concrete

The damage evolution of concrete under multiple stress states is complicated because the triaxial stress on the heterogeneous concrete affects mesoscale interactions between aggregates and mortar, which further alters the internal cracking of concrete and its load bearing mechanism. Hence, probing the internal cracking evolution of concrete under a complex stress state is the key to better understanding the characteristics and failure mechanism of concrete material. This study conducted a series of X-ray computed tomography (X-CT) tests on fiber-reinforced polymer (FRP) confined concrete with varied in situ axial load levels. Different cross-sections of concrete specimens—circular, square with round corners, and square with sharp corners—were designed to achieve uniform or nonuniform passive confinement conditions. The obtained volumetric images from X-CT clearly exhibited the internal damage evolution of concrete, where crack growth, shear banding, and failure localization were displayed for the concrete under varying triaxial stress states. The development of damage to concrete due to cracking with increasing load was also quantified by image segmentation. In addition, the digital volumetric correlation technique (DVC) was employed to produce the volumetric displacement field and strain distribution in the confined concrete according to the image variation of natural speckles. A three-dimensional internal strain analysis revealed that strain localization was mainly caused by mesoscale concrete heterogeneity and nonuniform confinement. More importantly, this study provides the first database of full-field strain tensors for FRP-confined concrete under different axial load levels. These data are valuable for the development of concrete mechanics, failure criteria of materials, and computational modeling of concrete materials and their structures, especially for concrete under complex stress states.

Rotation of the Stress Tensor in a Westerly Granite Sample During the Triaxial Compression Test

We simulated the spatiotemporal modelling of 3D stress and strain distributions during the triaxial compression laboratory test on a westerly granite sample using finite-difference numerical modelling implemented with FLAC3D software. The modelling was performed using a ubiquitous joint constitutive law with strain softening. The applied procedure is capable of reproducing the macroscopic stress and strain evolution in the sample during triaxial deformation until a failure process occurs. In addition, we calculated focal mechanisms of acoustic emission (AE) events and resolved local stress field orientations. This detailed stress information was compared with that from numerical modelling. The comparison was made based on the 3D rotation angle between the cardinal axes of the two stress tensors. To infer the differences in rotation, we applied ANOVA. We identified the two time levels as the plastic deformation phase and the after-failure phase. Additionally, we introduced the bin factor, which describes the location of the rotation scores in the rock sample. The p values of the test statistics F for the bin and phase effects are statistically significant. However, the interaction between them is insignificant. We can, therefore, conclude that there was a significant difference in the time between the rotation means in the particular bins, and we ran post hoc tests to obtain more information where the differences between the groups lie. The largest rotation of the stress field provided by the focal mechanisms of AE events from the numerically calculated stress field is observed in the edge bins, which do not frame the damage zone of the sample.

Numerical analysis of the strain distribution in skin domes formed upon the application of hypobaric pressure.

Suction cups are widely used in applications such as in measurement of mechanical properties of skin in vivo, in drug delivery devices or in acupuncture treatment. Understanding mechanical response of skin under hypobaric pressure is of great importance for users of suction cups. The aim of this work is to predict the hypobaric pressure induced 3D stretching of the skin. Experimental skin tensile tests were carried out for mechanical property characterization. Both linear elasticity and hyperelasticity parameters were determined and implemented in Finite Element modelling. Skin suction tests were performed in both experiments and FEM simulations for model validation. 3D skin stretching is then visualized in detail in FEM simulations. The simulations showed that the skin was compressed consistently along the thickness direction, leading to reduced thickness. At the center of the dome, the radial and angular strain decreases from the top surface to the bottom surface, although always in tension. Hyperelasticity modelling showed superiority over linear elasticity modelling while predicting the strain distribution because the stretch ratio reaches values exceeding the initial linear elastic stage of the stress-strain curve for skin. Hyperelasticity modelling is an effective approach to predict the 3D strain distribution, which paves a way to accurately design safe commercial products that interface with the skin.

Full-field strain of regenerated bone tissue in a femoral fracture model.

The mechanical behaviour of regenerated bone tissue during fracture healing is key in determining its ability to withstand physiological loads. However, the strain distribution in the newly formed tissue and how this influences the way a fracture heals it is still unclear. X-ray Computed Tomography (XCT) has been extensively used to assess the progress of mineralised tissues in regeneration and when combined with in situ mechanics and digital volume correlation (DVC) has been proven a powerful tool to understand the mechanical behaviour and full-field three-dimensional (3D) strain distribution in bone. The purpose of this study is therefore to use in situ XCT mechanics and DVC to investigate the strain distribution and load-bearing capacity in a regenerating fracture in the diaphyseal bone, using a rodent femoral fracture model stabilised by external fixation. Rat femurs with 1 mm and 2 mm osteotomy gaps were tested under in situ XCT step-wise compression in the apparent elastic region. High strain was present in the newly formed bone (εp1 and εp3 reaching 29000 µε and -43000 µε, respectively), with a wide variation and inhomogeneity of the 3D strain distribution in the regenerating tissues of the fracture gap, which is directly related to the presence of unmineralised tissue observed in histological images. The outcomes of this study will contribute in understanding natural regenerative ability of bone and its mechanical behaviour under loading.

Compositionally Graded AlGaN Nanostructures: Strain Distribution and X-ray Diffraction Reciprocal Space Mapping

The strain distribution in compositionally graded AlGaN planar structures, pillars, and nanowires (NWs) has been studied by 3D strain calculations based on numerical finite element method (FEM) and X-ray diffraction reciprocal space mapping. First, new fitting analyses of the reciprocal space maps (RSMs) are demonstrated to evaluate the depth profiles of strain and Al concentration, the film thickness, and the density of threading dislocation in compositionally graded AlGaN planar heterostructures. A good correlation between calculated and experimental RSMs for graded AlGaN thin film grown epitaxially on a GaN(0001) substrate was obtained. Second, by performing a FEM simulation of 3D strain distribution, we determined the influence of surface-to-volume ratio of compositionally graded AlGaN nanostructures of different diameters and on different substrates on the effectiveness of strain relaxation. The results show a faster strain decay with increasing surface-to-volume ratio from NWs to pillars. The AlGaN ...

In-situ 3D fracture propagation of short carbon fiber reinforced polymer composites

This paper explored the 3D progressive fracture process of a short carbon fiber reinforced polymer composite under uniaxial tensile loading via high-resolution in-situ micro X-ray computed tomography (μXCT). Microstructural features extracted from the μXCT images were analyzed with the Halpin-Tsai model, laminate analogy approach, and shear-lag model to calculate the mechanical properties and interpret the different fracture morphologies and progressions observed in the “skin-core-skin” structure. The in-situ μXCT scanning revealed a clear fracture progression in the skin layer, which was defined by four stages, i.e., nucleation of small pores at fiber ends, coalescence of pores, initiation of cracks, and propagation of cracks until fracture, whereas no significant fracture feature was found in the core layer. To analyze the difference in the fracture mechanisms in the skin and core layers, the maximum fiber normal stress and average interfacial shear stress were calculated from the microstructural features. The results were also confirmed by the 3D strain distribution quantified via a volumetric digital image correlation method. It was determined that the dominant fracture mechanism in the skin layer was fiber pull-out, rather than fiber breakage, as a consequence of pore formation at the fiber ends; its extent mainly depended on the fiber length and orientation angle. Fiber/matrix debonding was the main fracture mechanism in the core layer, which resulted from the propagation of cracks initiated from the skin layer.

Coherent-x-Ray Imaging of Nanoparticle Alloy Electrodes and Catalysts

Bragg coherent diffraction imaging (BCDI) studies of silver nanoparticles revealed a new dissolution mechanism that has not previously been observed.1 We find that a long incubation time, ~30 sec, before start dissolution reaction when the particle starts from the pristine state. During the incubation period, however, electrochemical potential-induced pressure nucleates a dislocation loop within the nanoparticle that eventually exposes to the surface. Only then, rapid dissolution is activated at the surface sites. This result points to an important connection between structure and stability of silver in an electrochemical environment and demonstrates the potential of BCDI to elucidate this relationship. Understanding silver dissolution process is important in studying dealloying process of binary alloys. Dealloying is a selective dissolution of one element in an alloy resulting in a porous, strained structure often with new properties, such as highly active electrocatalysts.2 In the past, the pore formation during dealloying has been visualized using electron microscopy and the dealloying-induced strain has been studied at the ensemble level using x-ray diffraction.3 However, the information on lattice strain, which has been unavailable, could play an integral role in understanding and controlling properties and activities for a variety of applications. In our BCDI studies, 3D strain distributions of individual nanoparticles and thin film grains of silver-gold alloys were investigated during dealloying in nitric acid.4 Isolated particles exhibit dramatic changes in their shapes as expected (See the graphical abstract). Our results (not shown) also demonstrate that significant local strains occur as a result of dealloying. The same dealloying process was used for nanoscale grains of a thin film instead of the isolated nanoparticles. The results show that isolated nanoparticles are significantly more strained than the grain embedded in the film texture,4 primarily because strain can be relieved via grain boundaries in the case of the single grain. These observations demonstrate that the unique capabilities of BCDI techniques. We also have begun working on alloys under catalytic environment where the compositions and shapes of alloy nanoparticles are highly sensitive to gas and temperature environment. We will present some preliminary results as time permits in my presentation. Liu, Y., et al., Nano Letters (2017) 17 (3), 1595Erlebacher, J., et al., Nature (2001) 410 (6827), 450Yang, R. Z., et al., Journal of Physical Chemistry C (2011) 115 (18), 9074Cha, W., et al., Advanced Functional Materials (2017) 27 (25) Figure 1

MACHINE LEARNING OF THREE-DIMENSIONAL LEFT VENTRICULAR DEFORMATION FOR AUTOMATED DIAGNOSTIC SUPPORT IN AMYLOID, FABRY, AND HYPERTROPHIC CARDIOMYOPATHY: A CARDIOVASCULAR MRI IMAGING STUDY

Cardiac Magnetic Resonance (CMR) is considered a reference standard diagnostic tool for the evaluation of cardiomyopathy, and is frequently used to differentiate cause of left ventricular hypertrophy (LVH). The capacity to differentiate etiology based upon myocardial deformation alone is particularly attractive when contrast is contraindicated. 3-dimensional (3D) feature tracking allows for spatial mapping of both conventional (radial, circumferential and longitudinal) and principal strain markers from routine, non-contrast 2D cine images. In this study, we investigated the potential of this analysis approach to differentiate the cause of LVH in patients with confirmed cardiomyopathies associated with Left Ventricular Hypertrophy (LVH): Hypertrophic cardiomyopathy (HCM), Fabry cardiomyopathy, and cardiac amyloidosis (CA). Forty-five subjects were recruited with confirmed LVH and a known cardiomyopathy state (HCM, N=15; Fabry, N=15; Cardiac Amyloid, N=15). All cardiomyopathy states were confirmed by published CMR criteria (HCM and CA) and/or genetic testing (Fabry and HCM). CMR imaging was performed at 3T using a standardized protocol inclusive of multi-planar cine imaging. LV ejection fraction (LVEF) was quantified using commercially available software (cvi42, Circle Cardiovascular Imaging Inc.). 3D strain analysis was performed using custom in-house software (GIUSEPPE) with generation of endocardial, epicardial and transmural spatial strain maps using a dynamic 3D mesh model. Principal component analysis was performed (Matlab, MathWorks) on the amplitude of peak-systolic strain obtained in all AHA segments in both conventional (longitudinal, circumferential, radial) and principal directions. The mean age was 57.9±15.2 years with 17 (37%) female. The respective LVEFs were 57.9±13.6%, 69.1±6.1%, and 69.5±9.8% among CA, Fabry’s, and HCM, respectively. 3D strain distributions were successfully computed for all patients. Segmental strain amplitude measures were subjected to principal component analysis. The first and second principal components of the regional strain data were used as a diagnostic marker by means of a Naive Bayes classifier. Both the posterior predictive distribution and the classification probability were visualized (Figure 1), showing capacity for disease state discrimination. The confusion matrix revealed an overall accuracy of 0.80, with true positive rates of 0.73 for CA, 0.8 for Fabry’s, and 0.67 for HCM. The concomitant evaluation of regional values of systolic strain amplitude in multiple directions was able to correctly classify patients by disease, based on the exclusive knowledge of regional strain amplitude patterns. These results offer strong promise for the use of 3D strain analysis to assist in the diagnosis of cardiomyopathy state among patients with LVH.

A three-dimensional strain measurement method in elastic transparent materials using tomographic particle image velocimetry.

BackgroundThe mechanical interaction between blood vessels and medical devices can induce strains in these vessels. Measuring and understanding these strains is necessary to identify the causes of vascular complications. This study develops a method to measure the three-dimensional (3D) distribution of strain using tomographic particle image velocimetry (Tomo-PIV) and compares the measurement accuracy with the gauge strain in tensile tests.Methods and findingsThe test system for measuring 3D strain distribution consists of two cameras, a laser, a universal testing machine, an acrylic chamber with a glycerol water solution for adjusting the refractive index with the silicone, and dumbbell-shaped specimens mixed with fluorescent tracer particles. 3D images of the particles were reconstructed from 2D images using a multiplicative algebraic reconstruction technique (MART) and motion tracking enhancement. Distributions of the 3D displacements were calculated using a digital volume correlation. To evaluate the accuracy of the measurement method in terms of particle density and interrogation voxel size, the gauge strain and one of the two cameras for Tomo-PIV were used as a video-extensometer in the tensile test. The results show that the optimal particle density and interrogation voxel size are 0.014 particles per pixel and 40 × 40 × 40 voxels with a 75% overlap. The maximum measurement error was maintained at less than 2.5% in the 4-mm-wide region of the specimen.ConclusionsWe successfully developed a method to experimentally measure 3D strain distribution in an elastic silicone material using Tomo-PIV and fluorescent particles. To the best of our knowledge, this is the first report that applies Tomo-PIV to investigate 3D strain measurements in elastic materials with large deformation and validates the measurement accuracy.

3D FEM simulations and experimental validation of plastic deformation of pure aluminum deformed by ECAP and combination of ECAP and direct extrusion

Rigid-viscoplastic 3D finite element simulations (3D FEM) of the equal channel angular pressing (ECAP), the combination of ECAP + extrusion with different extrusion ratios, and direct extrusion of pure aluminum were performed and analyzed. The 3D FEM simulations were carried out to investigate the load–displacement behavior, the plastic deformation characteristics and the effective plastic strain homogeneity of Al-1080 deformed by different forming processes. The simulation results were validated by microstructure observations, microhardness distribution maps and the correlation between the effective plastic strain and the microhardness values. The 3D FEM simulations were performed successfully with a good agreement with the experimental results. The load–displacement curves and the peak load values of the 3D FEM simulations and the experimental results were close from each other. The microhardness distribution maps were in a good conformity with the effective plastic strain contours and verifying the 3D FEM simulations results. The ECAP workpiece has a higher degree of deformation homogeneity than the other deformation processes. The microhardness values were calculated based on the average effective plastic strain. The predicted microhardness values fitted the experimental results well. The microstructure observations in the longitudinal and transverse directions support the 3D FEM effective plastic strain and microhardness distributions result in different forming processes.

Dealloying in Individual Nanoparticles and Thin Film Grains: A Bragg Coherent Diffractive Imaging Study

Dealloying is a process whereby selective dissolution results in a porous, strained structure often with new properties. The process is of both intrinsic and applied interest, and recently has been used to make highly active catalysts. The porosity has been studied using electron microscopy while the dealloying‐induced strain has been studied at the ensemble level using X‐ray diffraction. Despite the importance of local, for example, at the individual particle or grain level, strain in controlling the properties of the dealloyed material, it remains unresolved due to the difficulty of imaging 3D strain distributions with nanometer resolution in reactive environments. This information could play an integral role in understanding and controlling lattice strain for a variety of applications. Here, 3D strain distributions in individual nanoparticles and thin film grains in silver–gold alloys undergoing nitric acid‐induced dealloying are imaged by Bragg coherent diffractive imaging. Particles exhibit dramatic changes in their local strains due to dealloying but grains do not. The average lattice in both grains and particles contracts during dealloying. In general, the results reveal significant dealloying‐induced strain heterogeneity at the nanoscale in both isolated and extended samples, which may be utilized to develop advanced nanostructures for a variety of important applications.

Strain recovery analysis and stiffness verification of non-uniform composite beam with arbitrary cross section and material distribution using VABS

This paper presents a theory related to a two-dimensional linear cross-sectional analysis, recovery relationship, and a one-dimensional nonlinear beam analysis for composite wing slender structure with initial twist. Using VABS including a related theory, the design process of the composite rotor blade has been described. Cross-sectional analysis was performed at cutting point including all the details of geometry and material. Stiffness matrix and mass matrix were linked to each section to make 1D beam model. The 3D strain distributions within the structure were recovered based on the global behavior and load of the 1D beam analysis and visualize numerical results. Comparison between the analytical and experimental results shows that the proposed analytical procedure can provide an accurate and efficient prediction of the both deflection, flexural stiffness, strain of multilayer composite slender structure. Verified comparison results can be used to efficiently design accurate complex slender structure properties for detail design and manufacture. These sentences will appear after the conclusion when an article is finally published.