International Journal of Applied Mechanics

The applications of composite materials and adhesive-bonded joints in the aviation industry have significantly increased in recent years and their damage assessment attracts a lot of research interest. This study investigates the slow growth damages of bonded metal-composite joints and develops a finite element-based numerical procedure to capture mechanical behaviors of those damages in the joints. The residual static strength and strain energy release rates (SERRs) (which determine the damage growth rates) of the joints are the two quantities that can be determined to predict the fatigue life of adhesive bonded joints. The absence of extensive experimental and numerical assessments for predicting the slow growth damage of bonded metal-composite joints necessitates the development of a numerical procedure to determine these quantities. Toward this end, a three-dimensional (3D) finite element (FE) model was created. From the FE analyses, the residual static strength and SERRs of bonded metal-composite joints were calculated as a function of varying disbond crack lengths following the adhesive element failure criterion and fracture mechanics approach, respectively. Additionally, the residual strength and SERR for joints with delamination of the composite adherend were also calculated by implementing a linear fracture mechanics-based failure index. The results suggested that the stable crack length of the joint with 180mm long overlap length was about 140mm and 100mm when the crack was initiated from taper and gap end, respectively. These lengths were consistent for both disbond and delamination scenarios. Residual strength values were 89kN and 65kN for joints with 10mm disbonds initiated from the taper end and gap region, respectively. With the material properties considered, the delamination propagation strengths for delaminated joints were notably lower than their disbonded counterparts. Based on the findings of this study’s analysis, a systematic strategy was developed for applying the slow growth technique for bonded joints, which would aid in the creation of an actual sample for experimental validation. The experiment in turn will provide calibration for the parameters in the model for practical applications.

In this study, a cubic NURBS-based isogeometric finite element method is developed to study the aeroelastic tailoring of variable stiffness composite laminated (VSCL) plates, including skew, skew-tapered, tapered, and circular shapes based on third-order shear deformation theory. Also, the first-order piston theory is employed to approximate aerodynamic loads with arbitrary yaw flow angles over the plate area to establish aeroelastic equations. The NURBS basis functions are then utilized to simulate exact geometries and estimate variable fields for discretizing governing equations by well-known isogeometric analysis. Finally, the free vibration and flutter analysis of a VSCL quadrilateral and circular plate will be presented via the obtained eigenvalue problem. The achieved results are compared with the available results in the literature to prove the accuracy and validity of the present method. The effect of different parameters such as the flow yaw angle, end and middle-length fiber orientation, longitudinal to transverse Young’s modulus ratio, geometric shape, boundary conditions, and turning symmetric layup to asymmetric layup is carried out on the critical flutter aerodynamic pressure and natural frequencies.

Lightweight materials such as aluminum alloys are, nowadays, well recognized as one of the most popular choices in the aerospace industry owing to their fantastic strength-to-weight ratio. Their fabricability is, nevertheless, doubtful down to their low elongation, especially in the present day where geometrical complexity is hugely demanded. Truly understanding fracture behaviors of such sheet metal would benefit all involved parties. To achieve that challenging goal, proper fracture-analysis models and implementation methods are definitely crucial. This work proposes the recent Lou–Huh fracture criterion to describe the rupture behavior of sheet aluminum alloy AA2024-T3. To build such a damage mechanics model, a string of Nakajima stretching and notched tensile tests must be performed to acquire critical strain data, precisely measured using the 2D-DIC principle. The data are used to calibrate the model. A fracture locus (FL), defining an extensive AA2024-T3 fracture threshold, is then established out of the fine-tuned model. The FL is directly coupled into an ABAQUS/Explicit FE process simulation model via the Fortran-based subroutine VUMAT. This leading-edge implementation can supposedly emulate realistic damage evolution by monitoring and actively removing the elements whose degree of injury has reached a certain limit. At the end, the complete integrative FE model is empirically validated through an industrial X-shaped specimen, deformed under nonlinear strain paths. Fracture locations, shapes and development on the FE-simulated specimen are observed and contrasted with those on the experimental one. It is obviously shown that the results from both approaches agree remarkably well in all aspects. When compared with the famous fracture forming limit curve (FFLC), the Lou–Huh FL combined with the element-removal VUMAT implementation clearly outperforms. In summary, the proposed model and the implementation procedure are practically outstanding fracture evaluators of AA2024-T3, wonderfully predicting and vividly laying bare crack appearance and growth.

The behavior of waves in granular materials is very complex and closely related to the macro-micro properties such as particle shape, packing, and particle size distribution. In this study, the influence of the aspect ratio (AR) and confining stress on wave propagation in 2D granular crystals consisting of ellipse-shaped particles is investigated based on discrete element method. The energy attenuation, wave velocity, wavefront shape, and frequency dispersion are mainly focused. The results show that the energy attenuation exhibits an increasing trend with bigger confining stress and smaller AR in the direction of wave propagation. The wave velocities increase with increasing AR, and the relation between compressive wave velocities and the confining stress and AR is obtained. Wavefront has the elliptical shape which has the same AR as elliptical particles of specimen, and its analytical expression is also obtained. The dispersion is affected by AR, which is mainly reflected in the modified particle spacing in sine fitted frequency dispersion curve. Larger confining stress allows a larger maximum frequency, and produces stronger dispersion. The above conclusion can provide a reference for wave-guided granular crystals design.

Computational modeling methods were used to explore how well the behavior of a surface with a micropatterned array of uniformly shaped and spaced semi-cylindrical ribs, as predicted through a deterministic model, may be represented using a traditional Coulomb-based bulk-effects friction model. The effects of the numerical solution method, contact enforcement method, material damage model, and the number of asperities considered were first examined when the micropatterned ribs were directly included in the computational domain. The tribological behavior, defined as the static and kinetic friction forces and the associated energy dissipated, was then recreated for a comparable smooth-surface system using a Coulomb-based bulk-effects friction model, exploring the influence of user-input parameters such as the friction coefficients. With properly selected bulk-effects model parameters, the tribological behavior could be matched between the two types of models. However, the bulk-effects model could not capture the local and time-dependent effects of the asperity interactions on the force and energy measures, which are important in designing micropatterned surfaces. Through the understanding of the influences on model function that is gained through this work, a means to determine the appropriateness of each of these interface model types in studying particular phenomena of interest is provided.

This research is devoted to semi-analytical stress and large deformation analyses of finite-length thick-walled incompressible Mooney–Rivlin hyperelastic cylindrical pressure vessels/pipes with fixed ends, employing the three-dimensional theory of hyperelasticity. The formulation accounts for the thickness reduction in both radial and axial directions. The governing system of equations and the boundary conditions are assembled using a large-weights penalty method, after utilizing central, forward, and backward second-order point collocation expressions for the discretization of the thick hollow cylinder in both longitudinal and radial directions. The resulting coupled highly nonlinear two-dimensional equations are solved by the Newton–Raphson iterative updating technique. The results include the radial, axial, and three-dimensional distributions of the deformations and all the stress components. Comprehensive parametric studies are accomplished to evaluate the effects of the hyperelasticity parameters, boundary conditions, and thickness and length-to-radius ratios of the pressure vessel/pipe. Results reveal that the sections located in the vicinity of the fixed edges and the mid-section of the cylinder undergo the highest stresses, at low and high pressures, respectively. Moreover, while the pipe undergoes an overall expansion due to the internal pressure, it experiences a bending moment that induces compressive stresses at the outer boundary, due to the fixed edge. The magnitudes of the radial deformation and the circumferential stress significantly grow by increasing the cylinder length and the nonlinearities in the cylinder responses and behaviors increase by increasing the cylinder length.

This paper investigates the elastic wave propagation through soft materials that are being subjected to finite deformations. The nonlinear elastic and linearized incremental theories have been exploited to formulate governing wave equations and elastic moduli in Lagrangian space. Semi-analytical finite element (SAFE) method, a numerical approach has been formulated for computing dispersive relations of guided waves in compressible hyper-elastic plates. This framework requires finite element discretization of the cross section of the waveguide and harmonic exponential function assumes the motion along the wave propagation direction. Here, explicit phase velocity results have been shown for soft materials with a prominent stiffening effect by employing the Gent model, and these results are analyzed for elastic wave propagation through compressible materials. It has been noticed that Lamb waves have a strong dependence on the frequency-thickness product, prestretch, and direction of wave propagation. Moreover, with the strain stiffening effect, the dependence becomes stronger, especially for fundamental symmetric and anti-symmetric modes. The numerical results display that at certain prestretch the Gent material encounter snap-through instability resulting from geometrical and material nonlinearities. The influence of material properties like Gent constant and direction of wave propagation on snap-through instability has been discussed. The proposed SAFE framework reveals that finite deformations can affect elastic wave propagation through stiffness and compressibility.

Types of running vary from jogging in parks to fast running in competitions. Humans strive for faster, stronger, and more sustainable running performances spanning short to long distances. In the near future, wearable devices will enable humans to run at high speeds and overcome human limits. Therefore, aerodynamic prediction is essential for the system design of a wearable device. This study focused on the aerodynamic drag and flow field according to the assumed human posture at takeoff and touchdown for various running speeds. Numerical simulations were conducted with the Reynolds-averaged Navier–Stokes equation, and a mathematical model, in conjunction with the use of simple geometric models, was developed to predict the aerodynamic drag. In addition, the power and energy were analyzed based on the generated aerodynamic drag. This study demonstrated the theoretical prediction of aerodynamic drag, and estimated the power and energy required to overcome it. The results from this study can be useful in the fields of sports, soft robotics, and biomechanics. Furthermore, the effects of wearable devices attached to the body on the aerodynamic drag can be analyzed by applying the presented methods, and this analysis is beneficial for the optimal design of wearable suits.

Finite element analysis (FEA) is widely used to investigate the crushing performance of thin-walled tubes, and carry out parametric studies. However, simulation results are not always in good agreements with experimental results especially in terms of deformation modes in published literature. In this paper, a systematic FEA study will be conducted to evaluate two main simulation techniques using indentation triggers and buckling modes to introduce imperfections in FEA. Axial compressive tests were first carried out on three types of thin-walled circular tubes with different geometrical parameters. The finite element models were subsequently developed and used to explore the effects of indentation triggers and buckling modes on the deformation modes and force–displacement curves of thin-walled tubes. The influences of indentation depths and indentation positions on the crushing performance were investigated. Similarly, the effects of the order of buckling modes and scale factors on the crushing characteristics were examined as well. It has been found that for thin-walled circular tubes, a suitable simulation technique with indentation triggers or buckling modes can be employed to precisely mimic the deformation mode and corresponding force–displacement curve. This study is expected to provide some practical techniques and insights into the numerical simulation of circular tubes.

An acoustic black hole (ABH) resonator is regarded as an efficient approach for controlling vibration caused by flexural wave energy. In this paper, the beam models with periodic ABH beam resonators are designed. Both the vibration absorption and isolation performances are investigated. Theoretical models based on the Transfer Matrix Method are presented to evaluate the reflection coefficient, which is validated both by the semi-analytic method combined with the Finite Element Method (FEM) and the Impedance Matrix Method. Meanwhile, FEM models of periodic ABH beam resonators acting as the beam terminator and isolator are established and analyzed. The results show that the periodic ABH beam resonators are of a better vibration reduction performance in lower frequency and have wider bandgaps for lower reflection coefficient and higher transmission loss than the single wedge. Moreover, with the increasing number of periods, the advantages of the periodic ABH beam resonators in reducing vibration become more obvious. Through the complex plane and dynamic analyses, it shows that multimode coupling and meta-damping effect lead to superior performance since the enriched modal content is introduced by the periodic ABH beam structure. This effect is also verified by the experimental result. Besides, the study also reveals the paradoxical relationship between vibration absorption and isolation performances. Additionally, parametric studies are conducted to disclose the effects of structural parameters. Based on the analyses, two approaches are proposed to enhance the vibration reduction performances, including the composite beam resonators and compound beam resonators. This paper illustrates a promising vision for applying the periodic ABH beam resonators to various vibration control fields.

In this paper, an approach to solve the normal contact forces of viscoelastic particles with the finite element method is presented. A viscoelastic constitutive model is deduced and established for the finite element solution, where the stress tensors of the Zener-type model expressed as partial differential equations are obtained by applying the generalized Hooke’s law, and the incremental equations are further deduced with the backward difference method. An iterative matrix of the viscoelastic constitutive model that depends on the current strain, current stress and strain increment is derived; a user material subroutine is programed based on the iterative matrix to implement the viscoelastic constitutive model in the displacement-based finite element modeling. The validity of the finite element solution to the normal contact forces of elastic particles is validated with the Hertz contact force model, and that of the solution to the normal contact forces of viscoelastic particles is verified by the experimental data. The results obtained by the proposed solution agree well with those predicted by the Prony series, and the computational efficiency of this solution is higher for different values of the shear viscosity.