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In this paper, the influence of functional elastomeric substrate-supported layers for enhancing potential resistance capability against localized plastic failure of advanced high strength steels is considered based on a localized necking model of vertex theory. Application of this structure leads to postponing the plastic instability of the metallic part. By defining diffuse and localized modes of deformation in a general framework, the theoretical models are developed to predict necking limits at several stress states. In addition, the results of the Hookean and neo-Hookean elastomers are compared in terms of strain hardening with the anisotropy parameter of Hill’s yield criteria. Since necking band angle (NBA) is a principal factor for the necking prediction, its effect on bifurcation events is evaluated specifically for different ratios of stress rate, and quadratic and non-quadratic yield criteria. This analysis is performed by proposing a supported and yield-dependent necking bound angle (YD-NBA). All considerations are done by providing equilibrium conditions governed over the NBA. Finally, obtained results indicate good agreements between several theoretical considerations and experimental data.

This paper reports on an investigation into the relationship between stiffness and applied force of an advanced biological composite structure using four techniques: experimental observation; finit...

Bone is a nonlinear, inhomogeneous and anisotropic material. To predict the behavior of bones expert systems are employed to reduce the computational cost and to enhance the accuracy of simulations. In this study, an artificial neural network (ANN) was used for the prediction of displacement in long bones followed by ex-vivo experiments. Three hydrated third metacarpal bones (MC3) from 3 thoroughbred horses were used in the experiments. A set of strain gauges were distributed around the midshaft of the bones. These bones were then loaded in compression in an MTS machine. The recordings of strains, load, load exposure time, and displacement were used as ANN input parameters. The ANN which was trained using 3,250 experimental data points from two bones predicted the displacement of the third bone (R2 ≥ 0.98). It was suggested that the ANN should be trained using noisy data points. The proposed modification in the training algorithm makes the ANN very robust against noisy inputs measurements. The performance of the ANN was evaluated in response to changes in the number of input data points and then by assuming a lack of strain data. A finite element analysis (FEA) was conducted to replicate one cycle of force-displacement experimental data (to gain the same accuracy produced by the ANN). The comparison of FEA and ANN displacement predictions indicates that the ANN produced a satisfactory outcome within a couple of seconds, while FEA required more than 160 times as long to solve the same model (CPU time: 5 h and 30 min).

Dramatic advancements in interdisciplinary research with the fourth paradigm of science, especially the implementation of computer science, nourish the potential for artificial intelligence (AI), machine learning (ML), and artificial neural network (ANN) algorithms to be applied to studies concerning mechanics of bones. Despite recent enormous advancement in techniques, gaining deep knowledge to find correlations between bone shape, material, mechanical, and physical responses as well as properties is a daunting task. This is due to both complexity of the material itself and the convoluted shapes that this complex material forms. Moreover, many uncertainties and ambiguities exist concerning the use of traditional computational techniques that hinders gaining a full comprehension of this advanced biological material. This book chapter offers a review of literature on the use of AI, ML, and ANN in the study of bone mechanics research. A main question as to why to implement AI and ML in the mechanics of bones is fully addressed and explained. This chapter also introduces AI and ML and elaborates on the main features of ML algorithms such as learning paradigms, subtypes, main ideas with examples, performance metrics, training algorithms, and training datasets. As a frequently employed ML algorithm in bone mechanics, feedforward ANNs are discussed to make their taxonomy and working principles more readily comprehensible to researchers. A summary as well as detailed review of papers that employed ANNs to learn from collected data on bone mechanics are presented. Reviewing literature on the use of these data-driven tools is essential since their wider application has the potential to: improve clinical assessments enabling real-time simulations; avoid and/or minimize injuries; and, encourage early detection of such injuries in the first place.

Feedforward backpropagation artificial neural networks (ANNs) have been increasingly employed in many engineering practices concerning materials modeling. Despite their extensive applications, how to achieve successfully trained ANNs is not thoroughly explained in the literature, nor are there lucid discussions to delineate influential parameters obtained from analyses. Long bones are composite materials possessing nonhomogeneous and anisotropic properties, and their mechanical responses exhibit dependency on numerous variables. Material complexity hinders researchers from arriving at a consensus in implementing an optimal constitutive model or encourages them to adopt a simple constitutive model including many simplifying assumptions. However, such exceptional features and engineering challenges make long bones materials worth investigating, enriching our comprehension of complex engineering structures using novel techniques where traditional methods may present limitations. This paper reports on the prediction of loading, displacement, load and displacement simultaneously, and strains using feedforward backpropagation ANNs trained with experimental recordings. The technique was used to find optimum network structures (architectures) that encompass the best prediction ability. To enhance predictions, the influence of several elements such as a network training algorithm, injecting noise to datasets prior to training, the level of injected noise which directly affects model fitting and regularization, and data normalization prior to training were investigated and discussed. Essential parameters influencing decision making in identifying well-trained and well-generalized ANNs were elaborated. A considerable emphasis in this study was placed on examining the generalization ability of the already trained and tested ANNs, thus guaranteeing unbiased models that avoided overfitting. Gaining favorable outcomes in this study required three years of performing experiments and data collection before establishing the networks. The subsequent training, testing, and determination of the generalization of more than 60,000 ANNs are promising and will assist researchers in comprehending mechanical responses of complicated engineering structures that exhibit peculiar nonlinear properties.

In this paper, we attempted to measure the effect of Bach’s section, which presents a high-power coefficient in the standard Savonius model, on the performance of the helical Savonius wind turbine, by observing the parameters affecting turbine performance. Assessment methods based on the tip speed ratio, torque variation, flow field characterizations, and the power coefficient are performed. The present issue was stimulated using the turbulence model SST (k- ω) at 6, 8, and 10 m/s wind flow velocities via COMSOL software. Numerical simulation was validated employing previous articles. Outputs demonstrate that Bach-primary and Bach-developed wind turbine models have less flow separation at the spoke-end than the simple helical Savonius model, ultimately improving wind turbines’ total performance and reducing spoke-dynamic loads. Compared with the basic model, the Bach-developed model shows an 18.3% performance improvement in the maximum power coefficient. Bach’s primary model also offers a 12.4% increase in power production than the initial model’s best performance. Furthermore, the results indicate that changing the geometric parameters of the Bach model at high velocities (in turbulent flows) does not significantly affect improving performance.

The shape of the diaphysis of the equine third metacarpal bone (MC3) has a substantial influence on its mechanical properties. The connection between bone shape and bone adaptive responses is likely to be useful in forecasting the response of MC3 to a training program as well as predicting its internal loading. A variety of geometrical parameters including cortical area (A), width of dorsal cortex (D), palmar cortex (P), medial cortex (M), lateral cortex (L), medulla in dorsopalmar plane (Md), and medulla in lateromedial plane (M1) in three main cross sections (slices) within the diaphysis of 27 Thoroughbred horses aged from 12 hours to 15 years were measured using computer-aided-design and were analysed using t-tests and ANOVA test (performed in statistical MATLAB codes). Shape indices ([D/P] × [(D+P)/ Md]), H (D+Md +P), and V (M+ M1 +L) were also calculated. For all the samples, the values were plotted for a slice taken from around the mid-point of the shaft, and from two others taken at 3 cm proximally and distally from the middle slice. Cortical area decreased from proximal to distal slices in the majority of the specimens, except for all the foal samples where the area fluctuated and showed a converging-diverging shape. A similar trend was observed for one of the adult horses. To investigate converging-diverging shape configuration, a two-degree polynomial function was fitted to the plots of geometrical parameters and then the curvature (k) of these fitted curves was quantified and compared to assess the significant changes. Previous research showed that 0.5 mm differences in thickness of the midshaft dorsal cortex have a significant effect on local strain in vivo. Variations in the geometrical parameters of the midshaft metacarpus have a dramatic impact on the internal loading of the MC3 and should be considered in designing equine training programs in attempts to predict and prevent bone damage.

This paper presented a systematic approach toward localized failure inspection of internally pressurized laminated ellipsoidal woven composite domes. The domes were made of thin glass fiber reinforced polymer (GFRP) woven composite layups [0,0,0], [0,30,0], [0,45,0], and [0,75,0]. The analytical results demonstrated that the circumferential regions near meridian φ = 45° in prolate ellipsoidal domes and near meridian φ = 90° in oblate ellipsoidal domes sustain the highest deformation under internal pressure. This observation was then confirmed by the numerical and experimental results. In addition, the numerical and experimental results showed localized rather than uniform failure in those regions, irrespective of changes in laminate stacking sequence. It was observed that localized failure occurs since the woven fibers configuration in some areas of woven remains in initial geometry (square shape), while the rests are deformed into the rhombic shape. In other words, by moving along the circumferential direction from the area close to θ = 0° to θ = 45° and θ = 45° to θ = 90°, the shape of woven fibers gradually changes from square (strong area) to rhombic (weak area), and rhombic to square, respectively. Thus, to minimize failure pressure, the meridian region vulnerable to failure must initially be identified. Afterwards, the rhombic regions in the circumference corresponding to that meridian must be strengthened.

Shape is a key factor in influencing mechanical responses of bones. Considered to be smart viscoelastic and inhomogeneous materials, bones are stimulated to change shape (model and remodel) when they experience changes in the compressive strain distribution. Using reverse engineering techniques via computer-aided design (CAD) is crucial to create a virtual environment to investigate the significance of shape in biomechanical engineering. Nonetheless, data are lacking to quantify the accuracy of generated models and to address errors in finite element analysis (FEA). In the present study, reverse engineering through extrapolating cross-sectional slices was used to reconstruct the diaphysis of 15 equine third metacarpal bones (MC3). The reconstructed geometry was aligned with, and compared against, computed tomography-based models (reference models) of these bones and then the error map of the generated surfaces was plotted. The minimum error of reconstructed geometry was found to be +0.135 mm and -0.185 mm (0.407 mm ± 0.235, P > .05 and -0.563 mm ± 0.369, P > .05 for outside [convex] and inside [concave] surface position, respectively). Minor reconstructed surface error was observed on the dorsal cortex (0.216 mm ± 0.07, P > .05) for the outside surface and -0.185 mm ± 0.13, P > .05 for the inside surface. In addition, a displacement-based error estimation was used on 10 MC3 to identify poorly shaped elements in FEA, and the relations of finite element convergence analysis were used to present a framework for minimizing stress and strain errors in FEA. Finite element analysis errors of 3%-5% provided in the literature are unfortunate. Our proposed model, which presents an accurate FEA (error of 0.12%) in the smallest number of iterations possible, will assist future investigators to maximize FEA accuracy without the current runtime penalty.

An analytical solution has been developed developed in this research for electro-mechanical flexural response of smart laminated piezoelectric composite rectangular plates encompassing flexible-spring boundary conditions at two opposite edges. Flexible-spring boundary structure is introduced to the system by inclusion of rotational springs of adjustable stiffness which can vary depending on changes in the rotational fixity factor of the springs. To add to the case study complexity, the two other edges are kept free. Three advantages of employing the proposed analytical method include: (1) the electro-mechanical flexural coupling between the piezoelectric actuators and the plate’s rotational springs of adjustable stiffness is addressed; (2) there is no need for trial deformation and characteristic function—therefore, it has higher accuracy than conventional semi-inverse methods; (3) there is no restriction imposed to the position, type, and number of applied loads. The Linear Theory of Piezoelectricity and Classical Plate Theory are adopted to derive the exact elasticity equation. The higher-order Fourier integral and higher-order unit step function differential equations are combined to derive the analytical equations. The analytical results are validated against those obtained from Abaqus Finite Element (FE) package. The results comparison showed good agreement. The proposed smart plates can potentially be applied to real-life structural systems such as smart floors and bridges and the proposed analytical solution can be used to analyze the flexural deformation response.

A new analytical flexural solution based on double finite integral Fourier transform and trigonometric series differentiation procedures was developed for thick multi-layered composite hybrid rectangular plates resting on Winkler elastic foundation in air and water. The effect of material anisotropy, coupled hydro-mechanical loads, and underwater floor inclination angle,which were overlooked in the literature, is considered in this study. Furthermore, the predetermination of the shape deformation function is not required in our proposed analytical solution, which offers more accurate results. For the particular cases where the plate made of isotropic material is in air, the analytical results are compared with, and verified by the literature. Literature is lacking to investigate thick multi-layered composite hybrid rectangular plates with free edges and under hydro-mechanical load; hence our analytical results are compared with, and verified by,numerical analysis employing finite element method (FEM). The analytical results provide excellent agreement with both literature and the proposed FEM. FEM is shown to be time-intensive since the results converge after 60 seconds runtime with definition of 12159 elements during mesh refinement, yet the proposed analytical method demonstrates that the convergence can easily be achieved after 5 seconds runtime through selecting small values for Fourier terms.

Artificial intelligence (AI) and machine learning (ML) are fascinating interdisciplinary scientific domains where machines are provided with an approximation of human intelligence. The conjecture is that machines are able to learn from existing examples, and employ this accumulated knowledge to fulfil challenging tasks such as regression analysis, pattern classification, and prediction. The horse biomechanical models have been identified as an alternative tool to investigate the effects of mechanical loading and induced deformations on the tissues and structures in humans. Many reported investigations into bone fatigue, subchondral bone damage in the joints of both humans and animals, and identification of vital parameters responsible for retaining integrity of anatomical regions during normal activities in all species are heavily reliant on equine biomechanical research. Horse racing is a lucrative industry and injury prevention in expensive thoroughbreds has encouraged the implementation of various measurement techniques, which results in massive data generation. ML substantially accelerates analysis and interpretation of data and provides considerable advantages over traditional statistical tools historically adopted in biomechanical research. This paper provides the reader with: a brief introduction to AI, taxonomy and several types of ML algorithms, working principle of a feedforward artificial neural network (ANN), and, a detailed review of the applications of AI, ML, and ANN in equine biomechanical research (i.e. locomotory system function, gait analysis, joint and bone mechanics, and hoof function). Reviewing literature on the use of these data-driven tools is essential since their wider application has the potential to: improve clinical assessments enabling real-time simulations, avoid and/or minimize injuries, and encourage early detection of such injuries in the first place.

Mobility solutions offered by living creatures have inspired engineers to capture their locomotion patterns and then develop novel animal-like robots that use legs for locomotion. Exploring relationships among mechanical responses and kinematic parameters is essential for both inventing these robots and enhancing computational techniques. Establishment of accurate physical models to quantify mechanical responses of biological systems is challenging because the corresponding variables are multidimensional, dynamic and highly nonlinear. This encourages the advent of data-driven models in mechanical sciences. This paper delves into the use of feedforward and time-series (dynamic) artificial neural networks (ANN) to analyse experimental data recorded from a racing horse exercised up to 60 km/h to then relate hoof mechanical strain to kinematic parameters recorded experimentally. An inertial measurement unit that was comprised of a sensor and data acquisition system package was designed and mounted on the horse's hoof to measure linear accelerations and angular rates of motion. In addition, an instrumented Aluminium horseshoe that was designed and manufactured and contained: 1) inertial sensors including three orthogonal accelerometers and three orthogonal rate gyroscopes; and, 2) a strain gauge located at the middle of the shoe. The horse was warmed up in a steady gallop at around 35 km/h for 1 km then turned around and galloped at increasing speed to 68 km/h back to the finishing line. Nine kinematic parameters, measured during horse exercise, formed the ANNs input variables: hoof linear accelerations along three orthogonal directions (ax,ay,az), hoof angular rates of motion along three orthogonal directions (Gx, Gy, Gz), shoe linear accelerations along three orthogonal directions (axs, ays, azs), and time. Feedforward and time-series ANNs trained using 1,000,000 experimental instances offered excellent reliability for the prediction of mechanical strain from kinematic measurements, i.e. R ≥ 0.97.

Geothermal energy is among the types of renewable energies, which has variety of applications nowadays. The main purpose of this research is to design better geometry of heat exchange pipes to be placed into the construction foundation pile that can maximally use the clean energy hidden in the depths of the ground through these pipes and increase the strength and longevity of foundation piles, in terms of structural. Therefore, five heat foundation piles connected in series were exploited for four different geometries. The simulation was performed by ANSYS- FLUENT commercial software, which has high computational accuracy with validation made. The results indicate that the U6 heat exchanger at the depth of 25 m has the maximum efficiency and thermal performance capacity, illustrating the fact that its heat transfer rate is the highest compared to other geometries and then spiral, W, and U geometries have maximum efficiency respectively. Moreover, by increasing the contact area of the pipes and the concrete, the heat transfer rate will increase, and the temperature of the output fluid will be gradually reduced.

Long bones are composite materials possessing nonhomogeneous and anisotropic properties. They repair themselves (self-repairing) and adapt to changing mechanical demands by altering their shape and mechanical properties (self-adapting). Such exceptional features make long bones intriguing materials to comprehend properly. This also expands our knowledge of engineering materials and motivates researchers to employ novel techniques where conventional approaches may present limitations. This paper delves into the use of artificial neural network (ANN) expert systems to predict load-displacement curves of a long bone. Thirteen hydrated third metacarpal (MC3) bones from thoroughbred horses aged from twelve hours to three years were loaded in compression in an MTS machine. Strain readings from one three-gauge rosette and three distinct single-element gauges at different locations on the MC3 midshaft, displacement, load, load exposure time, horse age and bone side (left or right limb) were recorded for each bone. This information shaped ANNs input variables. Two in-series feedforward back-propagation ANNs were employed where the experimental recordings except for load were fed into the first ANN to predict load. Then, the predicted load along with the rest of experimental recordings were fed into the second ANN to predict displacement. Cyclic load-displacement and stiffness predicted by ANNs were plotted versus experimental counterparts. ANNs regression analyses showed R > 0.95 for training and testing datasets. To confirm their accuracy, ANNs were used to predict responses of specific bone samples that were not used in ANNs training. The ANNs trained using 17,718 experimental data points from twelve bones predicted the load (R = 0.997, RMSE = 2.44 kN), displacement (R = 0.948, RMSE = 0.321 mm), and stiffness (R = 0.982, RMSE = 1.197 kN/mm) of the thirteenth bone. The encouraging outcomes exhibit the exceptional ability of artificial neural networks in capturing the mechanical characteristics of complex structures.

The hierarchical nature of bone makes it a difficult material to fully comprehend. The equine third metacarpal (MC3) bone experiences nonuniform surface strains, which are a measure of displacement induced by loads. This paper investigates the use of an artificial neural network expert system to quantify MC3 bone loading. Previous studies focused on determining the response of bone using load, bone geometry, mechanical properties, and constraints as input parameters. This is referred to as a forward problem and is generally solved using numerical techniques such as finite element analysis (FEA). Conversely, an inverse problem has to be solved to quantify load from the measurements of strain and displacement. Commercially available FEA packages, without manipulating their underlying algebraic formulae, are incapable of completing a solution to the inverse problem. In this study, an artificial neural network (ANN) was employed to quantify the load required to produce the MC3 displacement and surface strains determined experimentally. Nine hydrated MC3 bones from thoroughbred horses were loaded in compression in an MTS machine. Ex-vivo experiments measured strain readings from one three-gauge rosette and three distinct single-element gauges at different locations on the MC3 midshaft, associated displacement, and load exposure time. Horse age and bone side (left or right limb) were also recorded for each MC3 bone. This information was used to construct input variables for the ANN model. The ability of this expert system to predict the MC3 loading was investigated. The ANN prediction offered excellent reliability for the prediction of load in the MC3 bones investigated, i.e. R2 ≥ 0.98.

This paper, in line with the previous study [23] , is concerned with the finite element implementation of nanoplates. However, in this contribution free vibration responses of multicrystalline nanoplates by considering surface effects are presented. Nanomaterials and nanostructures have been receiving widespread attentions during last decades. This fact is due largely to surprising, peculiar, and impressive mechanical; electrical; and physical behaviors of nanostructures. Currently, nanostructures such as nanoplates are being utilized in the designing and manufacturing Nanoelectromechanical systems (NEMS) and Microelectromechanical systems (MEMS). Furthermore, silicon, thanks to its exceptional mechanical, physical, and electrical properties is extensively employed in the NEMS and MEMS. The mechanical properties and responses of nanoplates are intensely size-dependent, and in contrast to plates with macro dimensions, static and free vibration responses of nanoplates strongly depend on the size of nanoplates. In this study, a rectangular multicrystalline plate with nanothickness; arbitrary geometry, and boundary conditions is analyzed. Each crystal of the nanoplate is assumed to be anisotropic, and a prominent point that must be taken into consideration is the interface region, which exists between every two crystals. The free vibration responses of nanoplate such as natural frequency are considered, and the influence of size, surface effects, interface region, and various boundary conditions over natural frequency of the nanoplate is considered. Due to the fact that geometry of the multicrystalline nanoplate is not straightforward to be dealt with the governing equations, the finite element method is employed to obtain the results of free vibration response. Moreover, we succeed to employ ANSYS software in order to attain the free vibration responses of multicrystalline nanoplates. In addition, the present finite element method results, the code of which is generated in MATLAB, are compared with those obtained from ANSYS software, and the correlation of the results is quite remarkable.

Nanostructures have been receiving extensive attention during the last two decades, due to their peculiar mechanical and other physical properties as compared with other macrostructures and macrosystems. The mechanical properties of nanostructures are intensely size-dependent. Furthermore, in the absence of external forces, nanostructures have a great tendency to deform due to their surface effects. Moreover, since the atoms on the surface have different equilibrium configuration from that of in the bulk, the elastic stiffness of the surface can be different from that of the bulk. In this study an ultra-thin plate of nanoscale thickness with an arbitrary geometry and boundary conditions is analyzed. A rectangular plate with nanoscale thickness is presented. In order to generalize the study, a multicrystalline plate with varying crystal properties has been assumed. Furthermore, the mechanical properties of the plate are dependent on the orientation. In fact the multicrystalline nanoplate is an anisotropic plate. The shapes and orientations of each crystal have been chosen haphazardly. However, the entire shape of the plate is a rectangle of microdimension with nanothickness. Due to the fact that silicon is much more applicable than any other material in Nanoelectromechanical systems (NEMS), it is assumed that the plate is made of silicon. The plate is subjected to a static load and the deformation as well as the corresponding strain is demonstrated. Due to the fact that the governing equation of the plate and its solution is not too straightforward to be solved easily, the finite element method is implemented so as to obtain the corresponding results. The results which have been achieved by the method of finite element and by employing the ANSYS software are illustrated and compared. Accordance of the results is quite remarkable.