There are multibody systems whose physics are partially known owing to their complexity and nonlinearity. Therefore, motion equations are not utterly available to be utilized for the prediction, control, design, and monitoring of these systems. To alleviate this issue, this study aims at developing a hybrid modeling procedure to discover respective unidentified physics and, subsequently, provide a holistic governing model of the original mechanism. For approach development, a vehicle with unmodeled tires is thoroughly considered in this research work. Tires profoundly impact the dynamics of vehicles, influencing their handling, drivability, and ride comfort. Advanced chassis control systems used to improve vehicles’ safety, performance, and reliability also require knowledge of tire behavior. Nevertheless, tires are very challenging to model as they are very complex and nonlinear components. Although simplified models are often employed, they are incapable of fully capturing tire behaviors. Using neural networks, i.e., black-box models, of the tire represents a common alternative. However, these approaches do not work outside the training data distribution, and they need costly and hard-to-measure experimental data for training purposes. Thus, this research study proposes a hybrid method by combining partially known physics of vehicle dynamics and a neural network to compensate for the unknown physics of tires. The developed approach learns the tire dynamics automatically from vehicle responses without requiring costly measured tire forces but solely relying on signals from an inertial measuring unit. The suggested methodology is validated experimentally, providing accurate and stable results. The time-depending behaviors of tires during cornering are also discovered and reported. The developed model is generic and can handle either linear or nonlinear physics-based models. However, the linear tire model integrated into the hybrid procedure in this study limits the simulation to stationary trajectories and cannot address the physics of tires when a vehicle undergoes nonstationary maneuvers.

The value of unknown parameters of multibody systems is crucial for prediction, monitoring, and control, sometimes estimated using a biased physics-based model leading to incorrect outcomes. Discovering motion equations of multibody systems from time-series data is challenging as they consist of complex rational functions, constants as function arguments, and diverse function terms, which are not trivial to guess. This study aims at developing an evolutionary symbolic sparse regression approach for the system identification of multibody systems. The procedure discovers equations of motion and system parameters appearing as either constant values in function arguments or coefficients of function expressions. A genetic programming algorithm is written to generate symbolic function expressions, in which a hard-thresholding regression method is embedded. In an evolutionary manner, the complex functional forms, constant arguments, and unknown coefficients are identified to eventually discover the governing equation of a given system. A fitness measure is presented to promote parsimony in distilled equations and reduction in fit-to-data error. Hybrid discrete-continuous dynamical systems are also investigated, for which an approach is suggested to determine both mode number and system submodels. The performance and efficiency of the suggested evolutionary symbolic sparse regression methodology are evaluated in a simulation environment. The capability of the developed approach is also demonstrated by studying several multibody systems. The procedure is efficient and gives the possibility to estimate system parameters and distill the respective governing equations. This technique reduces the risk that the function dictionary does not cover all functionality required to unravel hidden physical laws and the need for prior knowledge of the mechanism of interest.

The present study aims at developing a forward dynamics methodology to specify the micro- and macro-motion of the tibiofemoral joint where the ligament behavior is simulated employing an asymmetric nonlinear elastic model. Point clouds associated with the knee components are smoothed using a Laplacian smoothing procedure. Two phases of the contact search, i.e., spatial contact search and contact detection, are in turn performed to determine nodes and elements in contact while a bounding box technique is implemented to reduce associated computational time. External loads and moment due to the presence of all soft tissues are acquired using a musculoskeletal approach and fed into the forward dynamic model. Archard wear law is also integrated in the model allowing for wear prediction of total knee arthroplasty (TKA). A mesh density analysis is performed and the developed approach is assessed against outcomes available in the literature. Trajectory and wear occurrence of TKA are obtained, and it is shown that friction can lead to changes in both of them.

The effect of friction on nonlinear dynamics and vibration of total knee arthroplasties is yet to be investigated and understood. This research work aims at studying the influence of friction on nonlinear dynamics, friction-induced vibration, and damage of tibiofemoral joints. For this purpose, a spatial dynamic knee model is developed using an asymmetric nonlinear elastic model accounting for knee joint ligaments and a penalty contact model to compute normal contact stresses in the joint while contact detection is treated such that the associated computational time is reduced. Several friction models are considered and embedded in the dynamic model to estimate tangential friction forces in the knee joint. External loads and moments, due to the presence of all soft tissues, e.g., muscles and hip-joint reaction forces, applied to the femoral bone are determined using a musculoskeletal approach. In the post-processing stage, damage, i.e., wear and creep, are estimated using three wear models and an empirical creep formulation, respectively. In addition, a FFT analysis is performed to evaluate likely friction-induced vibration of tibiofemoral joints. Mesh density analysis is performed and the methodology is assessed against outcomes available in the literature. It can be concluded that friction influences not only the tribology, but also dynamics of the knee joint, and friction-induced vibration is likely to take place when the friction coefficient increases.

The present study aims at developing a three-dimensional forward dynamics methodology to compute the micro- and macro-motion of the tibiofemoral joint where the ligament behavior is simulated employing an asymmetric nonlinear elastic model. Point clouds associated with the knee components are smoothed using the Laplacian smoothing technique. A specific contact detection is also developed in which a bounding box procedure, one-by-one surface function based scheme, and a memory module along with a minimum distance technique are integrated, leading to a significant reduction of computational time while the accuracy is preserved. External loads and moments imposed on the femoral bone from all surrounding soft issues are acquired using a musculoskeletal modeling approach, fed into the forward dynamic model for the in-detail modeling of the total knee arthroplasty. Archard wear law is in turn embedded in the presented dynamic model allowing for wear prediction of total knee arthroplasty. A mesh density analysis is performed and the developed approach is assessed against outcomes available in the literature. The efficiency of the proposed approach is evaluated and consequently, it can be concluded that the model is promising, robust, and efficient. The dynamic model is subsequently employed to study the trajectory of the knee joint under different friction coefficients. Predicted wear values and distribution are also acquired showing friction can cause changes in both of them along with the knee motion.

Although wear is known as the primary cause of long-time failure of total knee arthroplasty (TKA), it can be vital in short- and midterm TKA failure due to laxity. One of the reasons leading to joint laxity and instability is ligamentous insufficiency. This study, therefore, aims to investigate the effects of insufficient ligaments-related knee laxity on both nonlinear dynamics and wear of TKA. The study hypothesizes (a) ligamentous insufficiency can increase TKA damage; (b) stiffness reduction of each of the posterior cruciate ligament (PCL) and medial-lateral collateral ligaments (MCL-LCL) can differently contribute to TKA damage. A forward dynamics methodology is developed and the ligament behavior is simulated employing an asymmetric nonlinear elastic model. External loads and moment, due to the presence of all soft tissues, e.g., muscles and hip joint reaction forces, applied to the femoral bone are determined using a musculoskeletal approach linked to the developed model. A mesh density analysis is performed and comparing outcomes with that available in the literature allows for the assessment of our approach. From the results acquired, reduced PCL stiffness leads to an increase in linear wear rates and results in the maximum damage in TKAs. However, the maximum linear wear rates on both condyles occur once the stiffness of all ligaments is reduced. Moreover, the worn area of the tibia surface increases with the reduction in MCL-LCL stiffness on the medial condyle. The joint with insufficient PCL also shows a considerable increase in ligament forces right after toe-off.

In soft and conformal contacts, the assumptions made in the Hertz theory are violated to some extent, leading to inaccurate outcomes. An alternative contact approach is the Kelvin-Voigt model that suffers from a discontinuity existing in its constitutive law. The fi-nite element method is also expensive computationally to be used for contact simulation. The present study introduces a concept to simulate either soft or conformal contacts and develops mathematically closed-form contact models, which are nonlinear, promising, and easy-to-implement while resolving the discontinuity issue with the Kelvin-Voigt model. Two demonstrative applications, i.e. a ball-on-plate contact and a spherical joint, are considered. The developed approaches are integrated into forward dynamics algorithms to be assessed and compared against available contact approaches in the literature. Moreover, a finite element analysis is constructed for comparison purposes. It can be concluded that the proposed contact models are robust and easy-to-implement for non-Hertzian soft and conformal contacts. (c) 2020 Elsevier Inc. All rights reserved.

A new approach of coupling multibody dynamics and fluid dynamics is developed to model hydrodynamic lubrication of spherical clearance joints with thin fluid film and relative multidirectional motion. The model accounts for dynamics motion of articulating components as well as both squeeze- and wedge-film actions of the synovial fluid. Multibody dynamics methodology is employed to derive the motion equations and Reynolds equation governs the fluid dynamics. The finite difference method is utilized to discretize the governing equation of lubricant and the multi-grid method augments computational efficiency to acquire outcomes employing a Gauss–Seidel relaxation scheme. Fluid–structure interaction is incorporated into the methodology using a partitioned formulation embedded in a high-order Runge–Kutta time integrators for integrating the nonlinear equations of the coupled system over time of interest. A demonstrative example of total hip arthroplasty is considered and the developed model is assessed against outcomes available in the literature. The effect of initial conditions on the pressure, film thickness and dynamics of the lubricated spherical joint is analyzed and discussed. It is illustrated that maximum fluid pressure is undergone by the hip implant at the first walking cycle of movement due to an unstable state, which is strongly dependent upon the initial condition. Finally, the approach presented in this research work is a robust dynamic model to study hydrodynamic lubrication of spherical joints.

A mathematical method is proposed to study fluid-coupled vibration of axisymmetric plate structures with asymmetries due to either imperfection or practical reasons, e.g. the weight reduction of structure, natural frequency shifting, and accessibility. The suggested approach makes use of the separation of variables to determine general solutions of the partial differential equation of the plate transverse displacement, whilst defining multiple polar coordinate systems, each of which offers its own formulation of the plate deformation with respect to its coordinate system. Moreover, closed-form geometric equations and the chain rule for determining derivatives are implemented to move from one coordinate system to the other in order to satisfy boundary conditions. The mode shapes of the vibrating plate in the dry condition are determined and in turn used in the Rayleigh–Ritz method to characterize vibrational properties of the fluid-coupled plate structure. While implementing such an energy method, the fluid motion is formulated employing the velocity potential and solved using the separation of variables. Fluid–structure interaction is also taken into account satisfying the compatibility condition on the fluid–plate​ interface. The developed methodology to predict natural frequencies has been validated by comparison with results obtained by a commercial finite element program. It is also found that the eccentricity tends to reduce natural frequencies of the fluid-coupled system for the lower serial mode, but increases them for the higher serial modes regardless of the presence of liquid.

Vibration analysis of nominally axisymmetric plate structures with either imperfections or geometric asymmetries due to practical motivations is of interest in designing and developing some mechanical structures. Semi-analytical methods to model such structures suffer from either choosing inappropriate admissible functions or both plausible convergence issues and additional computations owing to employing the addition theorem of Bessel functions. Therefore, the present study aims at developing a new mathematical method to analyze the vibrational behavior of circular plates with geometric asymmetries. The suggested approach makes use of the separation of variables to determine general solutions of the partial differential equation of the plate transverse displacement while defining multiple polar coordinate systems each of which offers a formulation of the plate deformation. Moreover, closed-form geometric equations and the chain rule for determining derivatives are implemented to move from one coordinate system to the other to satisfy boundary conditions without any need for the cumbersome transformation involved in using the addition theorem. A finite element model is also constructed to evaluate the validity of the proposed method before studying the effects of the cutout location and size on natural frequencies and mode shapes of eccentric annular plates.

The present study aims at developing a computational framework with experimental validation to determine the mechanical properties of zirconia foams for bone tissue engineering. A micro-CT based finite element model that allows characterizing the mechanical property of such cellular structures is developed. Micro-CT images are filtered to vanish noises and smooth boundaries before constructing 3D zirconia foams using an adaptive Body-Centered Cubic background lattice. In addition to micro-CT images, the local material property at the scaffold struts is measured using a micro-indentation test, which shows a considerable difference with that of common zirconia owing to the manufacturing process. The computational model also takes the plastic deformation of material into account employing the Voce law, a nonlinear isotropic hardening law, as well as Von-mises yield criterion. Zirconia foams with different pore sizes are manufactured using the replica method and their mechanical properties determined experimentally. Such experimental outcomes are to validate and demonstrate the capability of the developed model, which can be used for pre-operational evaluations and preclinical tests of zirconia scaffolds. The stress magnitude and distribution within the scaffold as well as plastic strains and flow stress of the zirconia scaffold are computed and analysed. Using the proposed approach, a deep insight into the association of macroscopic behaviour of the scaffold to microscopic features, e.g. strut waviness, Plateau border, thickness variation of cells, irregularity, microstructural variability, imperfections and strut's material property associated with to the manufacturing procedure, can be gained.

The creep and wear of ultra-high-weight polyethylene hip prostheses under physiological conditions are studied in the present research work. A fully integrated contact-coupled dynamic model based upon multibody dynamics methodology is developed, allowing the evaluation of not only sliding distance, but also contact mechanics as well as cross-shear effects and both average pressure and in-service duration associated with the creep phenomenon. In vivo forces and motions of hip joint are used as input for the dynamic simulation, which result in more realistic contact point trajectory and contact pressure, and consequently wear and creep, compared to simplified inputs. The analysis also takes into account inertia forces due to hip motion, tribological properties of bearing bodies, and energy loss owing to contact-impact events. The principal molecular orientation (PMO) of the polyethylene cup is determined through an iterative algorithm and dynamic outcomes. Archard’s wear law is also integrated into the multibody dynamics model for wear prediction in hip implants. Creep, besides wear, is attributed to polyethylene damage, which is investigated by implementing a creep model extracted from experimental data. The model is validated using clinical data and numerical results available from previously published studies. It is shown that creep plays a significant role in hip damage along with wear, both of which can be influenced by hip parameters, e.g., hip and clearance sizes. Moreover, the creep mechanism according to creep experiment is discussed, and contributing factors to the wear phenomenon are analyzed throughout this study.

The widely-used Reynolds equation to simulate fluid lubrication in hip implants by Goenka and Booker has velocity terms accounting just for the rotational motion of the femoral head. The present study, therefore, hypothesizes that modifying velocity terms being used in Reynolds equation, which capture both translation and rotation of the femoral head, can affect resultant fluid pressure, fluid-film thickness and friction force. To assess such hypothesis, a computational model of a hip implant based on multibody dynamics methodology and Reynold equation is developed. It is illustrated that modifying velocities can cause friction forces to increase, significantly, compared to Goenker and Booker's. Moreover, the minimum film thickness and maximum fluid pressure undergo notable decreases during the swing and stance phases, respectively.

Using Hertz contact law results in inaccurate outcomes when applied to the soft conformal hip implants. The finite element method also involves huge computational time and power. In addition, the sliding distance computed using the Euler rotation method does not incorporate tribology of bearing surfaces, contact mechanics and inertia forces. This study, therefore, aimed to develop a nonlinear dynamic model based on the multibody dynamic methodology to predict contact pressure and sliding distance of metal-on-polyethylene hip prosthesis, simultaneously, under normal walking condition. A closed-form formulation of the contact stresses distributed over the articulating surfaces was derived based upon the elastic foundation model, which reduced computational time and cost significantly. Three-dimensional physiological loading and motions, inertia forces due to hip motion and energy loss during contact were incorporated to obtain contact properties and sliding distance. Comparing the outcomes with that available in the literature and a finite element analysis allowed for the validation of our approach. Contours of contact stresses and accumulated sliding distances at different instants of the walking gait cycle were investigated and discussed. It was shown that the contact point at each instant was located within the zone with the corresponding highest accumulated sliding distance. In addition, the maximum contact pressure and area took place at the stance phase with a single support. The stress distribution onto the cup surface also conformed to the contact point trajectory and the physiological loading.

The aim of this study is to develop a semi-analytical method to investigate fluid-structure coupling of concentric double shells with different lengths and elastic behaviours. Co-axial shells constitute a cylindrical circular container and a baffle submerged inside the stored fluid. The container shell is made of functionally graded materials with mechanical properties changing through its thickness continuously. The baffle made of steel is fixed along its top edge and submerged inside fluid such that its lower edge freely moves. The developed approach is verified using a commercial finite element computer code. Although the model is presented for a specific case in the present work, it can be generalized to investigate coupling of shell-plate structures via fluid. It is shown that the coupling between concentric shells occurs only when they vibrate in a same circumferential mode number, n. It is also revealed that the normalized vibration amplitude of the inner shell is about the same as that of the outer shell, for narrower radial gaps. Moreover, the natural frequencies of the fluid-coupled system gradually decrease and converge to the certain values as the gradient index increases.

The thermal residual stresses (TRSs) generated owing to the cooling down from the processing temperature in layered ceramic systems can lead to crack formation as well as influence the bending stress distribution and the strength of the structure. The purpose of this study is to minimize the thermal residual and bending stresses in dental ceramics to enhance their strength as well as to prevent the structure failure. Analytical parametric models are developed to evaluate thermal residual stresses in zirconia-porcelain multi-layered and graded discs and to simulate the piston-on-ring test. To identify optimal designs of zirconia-based dental restorations, a particle swarm optimizer is also developed. The thickness of each interlayer and compositional distribution are referred to as design variables. The effect of layers number constituting the interlayer between two based materials on the performance of graded prosthetic systems is also investigated. The developed methodology is validated against results available in literature and a finite element model constructed in the present study. Three different cases are considered to determine the optimal design of graded prosthesis based on minimizing (a) TRSs; (b) bending stresses; and (c) both TRS and bending stresses. It is demonstrated that each layer thickness and composition profile have important contributions into the resulting stress field and magnitude.

The occurrence of audible squeaking in some patients with ceramic-on-ceramic (CoC) hip prostheses is a cause for concern. Great effort has been dedicated to understand the mechanics of the hip squeaking to gain a deeper insight into factors contributing to sound emission from CoC hip articulation. Disruption of fluid-film lubrication and friction were reported as the main potential cause, while patient and surgical factors, and design and material of hip implants, were also identified as leading factors. This article summarizes the recent available literature on this subject to provide a platform for future research and development. Moreover, high wear rates and ceramic liner fracture as viable consequences of hip squeaking are discussed.

Poly-ether-ether-ketone (PEEK) veneers are attractive materials for biomedical contacting surfaces. In the present study, PEEK veneers with thicknesses between 0.1 and 2mm were synthesized on Ti6Al4V substrates by hot pressing. The influence of PEEK thicknesses on the friction and wear behavior of veneering PEEK to Ti6Al4V structures was studied under reciprocating sliding conditions against an alumina counterbody immersed in artificial saliva at 37°C. Additionally, numerical simulations were carried out to evaluate the influence of PEEK thickness on the contact stress. The results revealed that the coefficient of friction and the wear rate increased with decreasing the PEEK thickness. It was revealed that the increase of both coefficient of friction and wear rate are correlated with increased contact stress level on PEEK veneer. Such factors are determinant on the long term success of veneering biomedical PEEK to Ti6Al4V for oral applications.

Wear can influence the lifetime and performance of implants and has been found to be a key factor in primary failure of artificial hip joints. The present study aims to present a spatial multibody dynamic model to predict wear in ceramic- on-ceramic hip implants. The problem was formulated by developing a spatial multibody dynamic model of a hip prosthesis taking three-dimensional physiological loading and motion of the human body into account. Then, the Archard wear model was integrated into the dynamic calculation of the hip implant to predict wear. Additionally, geometries of the cup and head were updated throughout the simulation to generate a more realistic wear simulation. The results were validated against current literature. Finally it was illustrated that friction-induced vibration caused excessive wear of hip implant components.