Appl. Mech., Volume 2, Issue 3 (September 2021) – 14 articles

Orthopaedic surgical cutting instruments are required to generate sufficient forces to penetrate bone tissue while minimising the risk of thermal and mechanical damage to the surrounding environment. This study presents a combined experimental–computational approach to determine relationships between key cutting parameters and overall cutting performance of a polyurethane-based synthetic trabecular bone analogue under orthogonal cutting conditions. An experimental model of orthogonal cutting was developed, whereby an adaptable cutting tool fixture driven by a servo-hydraulic uniaxial test machine was used to carry out cutting tests on Sawbone^® trabecular bone analogues. A computational model of the orthogonal cutting process was developed using Abaqus/Explicit, whereby an Isotropic Hardening Crushable Foam elastic-plastic model was used to capture the complex post-yield behaviour of the synthetic trabecular bone. It was found that lower tool rake angles resulted in the formation of larger discontinuous chips and higher cutting forces, while higher rake angles tended to lead to more continuous chip formation and lower cutting forces. The computational modelling framework provided captured features of both chip formation and axial cutting forces over a wide range of cutting parameters when compared with experimental observations. This experimentally based computational modelling framework for orthogonal cutting of trabecular bone analogues has the potential to be applied to more complex three-dimensional cutting processes in the future. Full article

In this work, an equivalent continuum of a barrel gridshell is introduced. Constitutive identification procedures based on periodic homogenization are provided in the literature for this purpose, based on a flat Representative Element Volume (REV), notwithstanding that the geometry of the structures concerned is curved. Therefore, the novelty of the present study is the selection of a curved REV to obtain the equivalent elastic constants. The numerical validation of the identification procedure is made comparing gridshell response to that of the equivalent shell under homogeneous load conditions. Finally, in order to highlight the effect of the curved geometry on the constitutive law of the continuum, the response of the proposed model is also compared to that of a continuum obtained from a flat REV. Full article

The following article extends a decomposition to the Navier–Stokes Equations (NSEs) demonstrated in earlier studies by corresponding author, in order to now demonstrate the existence of a vortex elliptical set inherent to the NSEs. These vortice elliptical sets are used to comment on the existence of solutions relative to the NSEs and to identify a potential manner of investigation into the classical Millennial Problem encompassed in Fefferman’s presentation. The article also presents the utilization of a recently developed versatile variational framework by both authors in order to study a related fluid-mechanics phenomena, namely the Raleigh–Plesset equations, which are ultimately obtained from the NSEs. The article develops, for the first time, a Lagrangian density functional for a closed surface which when minimized produced the Raleigh–Plesset equations. The article then proceeds with the demonstration that the Raleigh–Plesset equations may be obtained from this energy functional and identifies the energy dissipation predicted by the proposed Lagrangian density. The importance of the novel Raleigh–Plesset functional in the greater scheme of fluid mechanics is commented upon. Full article

The fluid–structure interaction of a pivoting rigid wing connected to a spring and subjected to freestream airflow in a wind tunnel is presented. Fluid–structure interactions can, on the one hand, lead to undesirable aerodynamic behaviour or, in extreme cases, to structural failure. On the other hand, improved aerodynamic performance can be achieved if a controlled application within certain limitations is provided. One application is the reduction of drag of road vehicles at higher speeds on a straight, while maintaining downforce at lower speeds during cornering. Conversely, another application concerns increased downforce at higher windspeeds, enhancing vehicle stability. In our wind tunnel experiments, the angle of incidence of the spring-mounted wing is either increased or decreased depending on the pivot point location and spring torque. Starting from a specified initial angle, the aerodynamic forces overcome a pre-set spring preload at incrementally increased freestream velocity. Reynolds numbers at a range of Re = 3 × 10⁴ up to Re = 1.37 × 10⁵ are considered. The application of a symmetrical NACA 0012 and a cambered NACA 6412 airfoil are tested in the wind tunnel and compared. For both airfoils mounted ahead of the aerodynamic centre, stable results were achieved for angles above 15 and below 12 degrees for the symmetrical airfoil, and above 25 and between 10 and −2 degrees for the cambered airfoil. Unsteady motions were observed around the stall region for both airfoils with all spring torque settings and also below −2 degrees for the cambered airfoil. Stable results were also found outside of the stall region when both airfoils were mounted behind the aerodynamic centre, although the velocity ranges were much smaller and highly dependent on the pivot point location. An analysis is reported concerning how changing the spring torque settings at each pivot point location effects performance. The differences in performance between the symmetrical and cambered profiles are then presented. Finally, an evaluation of the systems’ effects was conducted with conclusions, future improvements, and potential applications. Full article

The load-penetration curve in elastic nanoindentation of an elastic micropolar flat by a diamond spherical punch is analyzed. The presented results are obtained by a specifically developed numerical tool based on a judicious combination of the conventional boundary element method and strong form local point interpolation method. The results show that the usual linear relationship between the material depression and the square of the radius of the contact area is also valid in this case of micropolar elastic material. It is also shown that the relation between the indentation stress (applied load over the contact surface) and the indentation strain (ratio of contact radius by the punch radius) is linear. The proportionality coefficient which is none other than the indentation stiffness varies with the coupling factor of the micropolar elastic medium. A relation between the indentation stiffness of a micropolar solid and that of a conventional solid with the same Young modulus and Poisson ratio is derived. Full article

Understanding the effect of thermomechanical loads during finish cutting processes, in our case hard milling, on the surface integrity of the workpiece is crucial for the creation of defined quality characteristics of high-performance components. Compared to computationally generated modifications by simulation, the measurement-based determination of material modifications can only be carried out selectively and on a point-by-point basis. In practice, however, detailed knowledge of the changes in material properties at arbitrary points of the high-performance component is of great interest. In this paper, a modification of the well-known Johnson–Cook material model using the finite element software Abaqus is presented. Special attention was paid to the kinematic hardening behavior of the used steel material. Cyclic loads are relevant for the chip formation simulation because, during milling, after each cut, the material under the surface is loaded plastically several times and not necessarily in the same direction. Therefore, in analogy, multiple bending was investigated on samples made of 42CrMo4. A pronounced Bauschinger effect was observed in the bending tests. An adaptation of the material model to the results of the bending tests was only possible to a limited extent without kinematic hardening, which is why the Johnson–Cook model was supplemented by the Armstrong–Frederick hardening approach. The modified Johnson–Cook–Armstrong–Frederick material model was developed for practical use as a VUMAT and verified by bending tests for simulation use. Full article

Design of new materials is quite a difficult task owing to various time and length scales and affiliated uncertainties. The major challenge is to include all these in a conventional model. Hyperparameter models in machine learning can be used to overcome these issues. In this paper, an artificial neural network (ANN) model is developed to estimate the effective elastic parameters of unidirectional fiber reinforced composites using representative volume elements (RVE) considering uncertainty in the fiber diameter. The diameter probability distribution is constructed from the acquired gray images by employing image processing operations. The generalized Polynomial Chaos (gPC) expansion is then used to represent the distribution as a random input parameter for finite element analysis, from where the effective parameters are realized. Similarly, the outputs of the FE model, i.e., elastic parameters, are approximated by gPC expansions having unknown deterministic coefficients and random orthogonal Hermite polynomials. A set of collocation points are generated from roots of the random polynomials; from there, the unknown coefficients are estimated. The realization samples are utilized to train an ANN algorithm based on supervised deep learning. The developed ANN model is later tested and validated for a new sample set of data. It is shown that the ANN model with few hidden layers and neurons has a high accuracy for estimation of the elastic parameters directly from the information on the distribution of fiber diameters. Full article

The effect of the width to thickness ratio on the bendability of sheet metal is investigated using the finite element method (FEM) employing the Gurson–Tvergaard–Needleman (GTN) model. Strain path changes in the sheet with change in the width/thickness ratio. It is shown that bendability and fracture strain increase significantly by decrease in the width/thickness ratio. The stress state is almost uniaxial when the stress ratio (α) is close to zero for narrow sheets. Stress ratio is nothing but the major stress to minor stress ratio. This delays the growth and coalescence of micro-voids as the volumetric strain and stress triaxiality (pressure/effective stress) decrease. On the other hand, ductility decreases with increase in α for wider sheets. Fracture bending strain is calculated and, as expected, it increases with decrease in the width/thickness ratio. Furthermore, a brief study is performed to understand the effect of superimposed hydrostatic pressure on fracture strain for various sheet metals with different width/thickness ratios. It is found that the superimposed hydrostatic pressure increases the ductility, and that the effect of the width/thickness ratio in metals on ductility is as significant as the effect of superimposed hydrostatic pressure. Numerical results are found to be in good agreement with experimental observations. Full article

This work reviews different analytical formulations for the time-dependent aerodynamic load of a thin aerofoil and clarifies numerical flutter results available in the literature for the typical section of a flexible wing; inviscid, two-dimensional, incompressible, potential flow is considered in all test cases. The latter are investigated using the exact theory for small airflow perturbations, which involves both circulatory and non-circulatory effects of different nature, complemented by the p-k flutter analysis. Starting from unsteady aerodynamics and ending with steady aerodynamics, quasi-unsteady and quasi-steady aerodynamic models are systematically derived by successive simplifications within a unified approach. The influence of the aerodynamic approximations on the aeroelastic stability boundary is then rigorously assessed from both physical and mathematical perspectives. All aerodynamic models are critically discussed and compared in the light of the numerical results as well, within a comprehensive theoretical framework in practice. In all cases, results accuracy depends on the aero-structural arrangement of the flexible wing; however, simplified unsteady and simplified quasi-unsteady aerodynamic approximations are suggested for robust flutter analysis whenever the wing’s elastic axis lies ahead of the aerofoil’s control point. Full article

Steel fibers and their aspect ratios are important parameters that have significant influence on the mechanical properties of ultrahigh-performance fiber-reinforced concrete (UHPFRC). Steel fiber dosage also significantly contributes to the initial manufacturing cost of UHPFRC. This study presents a comprehensive literature review of the effects of steel fiber percentages and aspect ratios on the setting time, workability, and mechanical properties of UHPFRC. It was evident that (1) an increase in steel fiber dosage and aspect ratio negatively impacted workability, owing to the interlocking between fibers; (2) compressive strength was positively influenced by the steel fiber dosage and aspect ratio; and (3) a faster loading rate significantly improved the mechanical properties. There were also some shortcomings in the measurement method for setting time. Lastly, this research highlights current issues for future research. The findings of the study are useful for practicing engineers to understand the distinctive characteristics of UHPFRC. Full article

A common form of damage encountered in marine structures is the accumulation of corrosion in susceptible areas, which leads to material wastage. As a result, the structural strength of the members affected is compromised, endangering their safe operation in design loads. Consequently, structural instabilities may occur, such as buckling due to compressive or/and shear loads. An alternative repair practice for preventing such phenomena, approved for secondary load-carrying members, is the application of composite patches to the damaged area. In this preliminary study, this technique is examined in the scope of developing a framework that can be used to find the optimal solution for restoring the buckling strength of a corroded plate. The methods used to achieve this are based on finite element analysis (FEA) and design of experiments (DoE) to statistically analyze the aforementioned numerical calculations. By introducing the composite patch’s percentage coverage of its metal substrate and number of plies as design parameters, a response surface is generated with respect to the obtained factor of safety (regarding its reference uncorroded buckling strength). This list of data points is then evaluated, and an acceptable surface/list of design parameters’ combinations is generated. Full article

Uncertainty is a common feature in first-principles models that are widely used in various engineering problems. Uncertainty quantification (UQ) has become an essential procedure to improve the accuracy and reliability of model predictions. Polynomial chaos expansion (PCE) has been used as an efficient approach for UQ by approximating uncertainty with orthogonal polynomial basis functions of standard distributions (e.g., normal) chosen from the Askey scheme. However, uncertainty in practice may not be represented well by standard distributions. In this case, the convergence rate and accuracy of the PCE-based UQ cannot be guaranteed. Further, when models involve non-polynomial forms, the PCE-based UQ can be computationally impractical in the presence of many parametric uncertainties. To address these issues, the Gram–Schmidt (GS) orthogonalization and generalized dimension reduction method (gDRM) are integrated with the PCE in this work to deal with many parametric uncertainties that follow arbitrary distributions. The performance of the proposed method is demonstrated with three benchmark cases including two chemical engineering problems in terms of UQ accuracy and computational efficiency by comparison with available algorithms (e.g., non-intrusive PCE). Full article

The present work is focused on the investigation of the aerodynamic performances of a novedous bioinspired morphing Micro Air Vehicle (MAV) with an adaptive wing structure geometry. For this purpose, a numerical study of Computational Fluid Dynamics (CFD) implemented by Ansys Fluent 15.0 was performed in order to obtain insight about the aerodynamic effect of wing structure deformation when morphing devices are used, and its influence on the global aerodynamic parameters related with aircraft performances. On the other hand, an experimental study using the Particle Image Velocimetry technique and balance measurements in a Low-Speed Wind Tunnel was conducted to obtain experimental information about performances measured to establish a comparison between both, experimental and numerical results. The Micro Air Vehicle (MAV) presents a Zimmerman wing with an Eppler 61 airfoil. Three different wing configurations according to curvature and thickness variations and for all angles of attack have been studied. A comparative analysis based on aerodynamic features is performed by an assessment of lift coefficient (C_L), total aerodynamic drag coefficient (C_D) and aerodynamic efficiency as lift/drag ratio (C_L/C_D) in order to conclude the best wing configuration in terms of aerodynamic performance. Full article

In previous works we developed a methodology of deriving variational integrators to provide numerical solutions of systems having oscillatory behavior. These schemes use exponential functions to approximate the intermediate configurations and velocities, which are then placed into the discrete Lagrangian function characterizing the physical system. We afterwards proved that, higher order schemes can be obtained through the corresponding discrete Euler–Lagrange equations and the definition of a weighted sum of “continuous intermediate Lagrangians” each of them evaluated at an intermediate time node. In the present article, we extend these methods so as to include Lagrangians of split potential systems, namely, to address cases when the potential function can be decomposed into several components. Rather than using many intermediate points for the complete Lagrangian, in this work we introduce different numbers of intermediate points, resulting within the context of various reliable quadrature rules, for the various potentials. Finally, we assess the accuracy, convergence and computational time of the proposed technique by testing and comparing them with well known standards. Full article