Recent Advances in Theoretical and Computational Modeling of Composite Materials and Structures

The advancement in manufacturing technology and scientific research has improved the development of enhanced composite materials with tailored properties depending on their design requirements in many engineering fields, as well as in thermal and energy management. Some representative examples of advanced materials in many smart applications and complex structures rely on laminated composites, functionally graded materials (FGMs), and carbon-based constituents, primarily carbon nanotubes (CNTs), and graphene sheets or nanoplatelets, because of their remarkable mechanical properties, electrical conductivity and high permeability. For such materials, experimental tests usually require a large economical effort because of the complex nature of each constituent, together with many environmental, geometrical and or mechanical uncertainties of non-conventional specimens. At the same time, the theoretical and/or computational approaches represent a valid alternative for designing complex manufacts with more flexibility. In such a context, the development of advanced theoretical and computational models for composite materials and structures is a subject of active research, as explored here for a large variety of structural members, involving the static, dynamic, buckling, and damage/fracturing problems at different scales

Advanced Theoretical and Computational Methods for Complex Materials and Structures

The broad use of composite materials and shell structural members with complex geometries in technologies related to various branches of engineering has gained increased attention from scientists and engineers for the development of even more refined approaches and investigation of their mechanical behavior. It is well known that composite materials are able to provide higher values of strength stiffness, and thermal properties, together with conferring reduced weight, which can affect the mechanical behavior of beams, plates, and shells, in terms of static response, vibrations, and buckling loads. At the same time, enhanced structures made of composite materials can feature internal length scales and non-local behaviors, with great sensitivity to different staking sequences, ply orientations, agglomeration of nanoparticles, volume fractions of constituents, and porosity levels, among others. In addition to fiber-reinforced composites and laminates, increased attention has been paid in literature to the study of innovative components such as functionally graded materials (FGMs), carbon nanotubes (CNTs), graphene nanoplatelets, and smart constituents. Some examples of smart applications involve large stroke smart actuators, piezoelectric sensors, shape memory alloys, magnetostrictive and electrostrictive materials, as well as auxetic components and angle-tow laminates. These constituents can be included in the lamination schemes of smart structures to control and monitor the vibrational behavior or the static deflection of several composites. The development of advanced theoretical and computational models for composite materials and structures is a subject of active research and this is explored here for different complex systems, including their static, dynamic, and buckling responses; fracture mechanics at different scales; the adhesion, cohesion, and delamination of materials and interfaces

Nonlinear scale-dependent deformation behaviour of beam and plate structures

Improving the knowledge of the mechanics of small-scale structures is important in many microelectromechanical and nanoelectromechanical systems. Classical continuum mechanics cannot be utilised to determine the mechanical response of small-scale structures, since size effects become significant at small-scale levels. Modified elasticity models have been introduced for the mechanics of ultra-small structures. It has recently been shown that higher-order models, such as nonlocal strain gradient and integral models, are more capable of incorporating scale influences on the mechanical characteristics of small-scale structures than the classical continuum models. In addition, some scaledependent models are restricted to a specific range of sizes. For instance, nonlocal effects on the mechanical behaviour vanish after a particular length. Scrutinising the available literature indicates that the large amplitude vibrations of small-scale beams and plates using two-parameter scaledependent models and nonlocal integral models have not been investigated yet. In addition, no twoparameter continuum model with geometrical nonlinearity has been introduced to analyse the influence of a geometrical imperfection on the vibration of small-scale beams. Analysing these systems would provide useful results for small-scale mass sensors, resonators, energy harvesters and actuators using small-scale beams and plates. In this thesis, scale-dependent nonlinear continuum models are developed for the time-dependent deformation behaviour of beam-shaped structures. The models contain two completely different size parameters, which make it able to describe both the reduction and increase in the total stiffness. The first size parameter accounts for the nonlocality of the stress, while the second one describes the strain gradient effect. Geometrical nonlinearity on the vibrations of small-scale beams is captured through the strain-displacement equations. The small-scale beam is assumed to possess geometrical imperfections. Hamilton’s approach is utilised for deriving the corresponding differential equations. The coupled nonlinear motion equations are solved numerically employing Galerkin’s method of discretisation and the continuation scheme of solution. It is concluded that geometrical imperfections would substantially alter the nonlinear vibrational response of small-scale beams. When there is a relatively small geometrical imperfection in the structure, the small-scale beam exhibits a hardeningtype nonlinearity while a combined hardening- and softening-type nonlinearity is found for beams with large geometrical imperfections. The strain gradient influence is associated with an enhancement in the beam stiffness, leading to higher nonlinear resonance frequencies. By contrast, the stress nonlocality is related to a remarkable reduction in the total stiffness, and consequently lower nonlinear resonance frequencies. In addition, a scale-dependent model of beams is proposed in this thesis to analyse the influence of viscoelasticity and geometrical nonlinearity on the vibration of small-scale beams. A nonlocal theory incorporating strain gradients is used for describing the problem in a mathematical form. Implementing the classical continuum model of beams causes a substantial overestimation in the beam vibrational amplitude. In addition, the nonlinear resonance frequency computed by the nonlocal model is less than that obtained via the classical model. When the forcing amplitude is comparatively low, the linear and nonlinear damping mechanisms predict almost the same results. However, when forcing amplitudes become larger, the role of nonlinear viscoelasticity in the vibrational response increases. The resonance frequency of the scale-dependent model with a nonlinear damping mechanism is lower than that of the linear one. To simulate scale effects on the mechanical behaviour of ultra-small plates, a novel scale-dependent model of plates is developed. The static deflection and oscillation of rectangular plates at small-scale levels are analysed via a two-dimensional stress-driven nonlocal integral model. A reasonable kernel function, which fulfil all necessary criteria, is introduced for rectangular small-scale plates for the first time. Hamilton and Leibniz integral rules are used for deriving the non-classical motion equations of the structure. Moreover, two types of edge conditions are obtained for the linear vibration. The first type is the well-known classical boundary condition while the second type is the nonclassical edge condition associated with the curvature nonlocality. The differential quadrature technique as a powerful numerical approach for implementing complex boundary conditions is used. It is found that while the Laplacian-based nonlocal model cannot predict size influences on the bending of small-scale plates subject to uniform lateral loading, the bending response is remarkably size-dependent based on the stress-driven plate model. When the size influence increases, the difference between the resonance frequency obtained via the stress-driven model and that of other theories substantially increases. Moreover, the resonance frequency is higher when the curvature nonlocality increases due to an enhancement in the plate stiffness. It is also concluded that more constraint on the small-scale plate causes the system to vibrate at a relatively high frequency. In addition to the linear vibration, the time-dependent large deformation of small-scale plates incorporating size influences is studied. The stress-driven theory is employed to formulate the problem at small-scale levels. Geometrical nonlinearity effects are taken into account via von Kármán’s theory. Three types of edge conditions including one conventional and two nonconventional conditions are presented for nonlinear vibrations. The first non-classical edge condition is associated with the curvature nonlocality while the second one is related to nonlocal in-plane strain components. A differential quadrature technique and an appropriate iteration method are used to compute the nonlinear natural frequencies and maximum in-plane displacements. Molecular dynamics simulations are also performed for verification purposes. Nonlinear frequency ratios are increased when vibration amplitudes increase. Furthermore, the curvature nonlocality would cause the small-scale pate to vibrate at a lower nonlinear frequency ratio. By contrast, the nonlocal in-plane strain has the opposite effect on the small-scale system. The outcomes from this thesis will be useful for engineers to design vibrating small-scale resonators and sensors using ultra-small plates.Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 202

Advances in Micro- and Nanomechanics

This book focuses on recent advances in both theoretical and experimental studies of material behaviour at the micro- and nano-scales. Special attention is given to experimental studies of nanofilms, nanoparticles and nanocomposites as well as tooth defects. Various experimental techniques were used. Magneto- and thermoelastic coupling were considered, as were nonlocal models of thin structures

Continuum models for the dynamic behavior of 1D nonlinear structured solids

Mención Internacional en el título de doctorThe main objective of this thesis is to propose and validate generalized continuum models for analyzing and predicting the free vibrations of 1D linear elastic structured solids subjected to finite deformations. With this aim, two different generalized continuum models that account for geometric nonlinearities have been proposed: a nonlocal nonlinear model and a gradient velocity nonlinear one, here referred to as the inertia gradient nonlinear model. These models contain one or more microstructural parameters. The formulation of the cited theories has been devised for general 3D solids, but in this thesis they have been applied to the study of nonlinear axial and nonlinear axial-transverse coupled vibrations of a kind of 1D structured solids. The 1D structured solids chosen as reference are such that, under certain conditions, the classical nonlinear continuum model adequately reproduces its main features. However, it is well known that the classical theory is not able to capture the size effect presented in this kind of solids. Moreover, a non-standard continualization technique has been applied to the discrete system in order to get appropriate continuous equations of motion. Unlike the postulated generalized continuum models, this continualization technique permits to derive, from the characteristics of the solid structure, the additional parameters appearing in the formulation. The results for the two nonlinear analyzed problems (axial vibrations and axialtransverse coupled vibrations) obtained from the classical, generalized nonlinear continuum, and continualized models have been compared to those derived from the discrete solution taken as reference. From this critical comparison, the advantages and shortcomings of the different theories have been pointed out clearly showing the ability of the generalized continuum models to adequately address the size effects in structured solids, observed in many practical applications.El objetivo principal de esta tesis es proponer y validar modelos del continuo generalizado para analizar y predecir el comportamiento de vibraciones libres de sólidos estructurados unidimensionales elásticos y lineales sometidos a deformaciones finitas. Con este objetivo, se han propuesto dos modelos del continuo generalizado diferentes que consideran las no linealidades geométricas: un modelo no lineal no local y otro no lineal de gradiente de la velocidad, aquí referido como modelo con gradiente de inercia. Estos modelos contienen uno o más parámetros microestructurales. Las formulaciones de dichas teorías se han planteado para sólidos tridimensionales, pero en esta tesis se han aplicado al estudio de las vibraciones no lineales longitudinales y las vibraciones no lineales acopladas axiales-transversales en un tipo de sólidos 1D estructurados. El sólido 1D estructurado elegido como referencia es tal que, bajo ciertas condiciones, el modelo continuo no lineal clásico reproduce adecuadamente sus características principales. Sin embargo, es bien sabido que la teoría clásica no es capaz de capturar los efectos de tamaño que presentan este tipo de sólidos. Por otra parte, se ha aplicado una técnica de continualización no estándar al sistema discreto con el fin de obtener las ecuaciones continuas del movimiento. A diferencia de los modelos del continuo generalizado postulados, esta técnica de continualización permite derivar, a partir de las características del sólido estructurado, los parámetros adicionales que aparecen en la formulación del problema. Los resultados para los dos problemas no lineales analizados (vibraciones axiales y axiales-transversales acopladas) obtenidos mediante los modelos continuo clásico, continuos no lineales generalizados, y los continualizados se han comparado con los derivados de la solución discreta que se toma como referencia. A partir de esta comparación crítica, se han señalado las ventajas y los inconvenientes de las diferentes teorías, mostrando claramente la capacidad de los modelos del continuo generalizado para tratar adecuadamente los efectos de tamaño en los sólidos estructurados, observados ´estos en muchas aplicaciones prácticas.The financial support of the Ministerio de Ciencia e Innovación de España (Project DPI/2014-57989-P) is greatly acknowledged. The subject of this Thesis is a core part of the research project.Programa Oficial de Doctorado en Ingeniería Mecánica y de Organización IndustrialPresidente: Enrique Barbero Pozuelo.- Secretario: Eugenio Giner Maravilla.- Vocal: Julian J. Rimol

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Numerical modelling of additive manufacturing process for stainless steel tension testing samples

Nowadays additive manufacturing (AM) technologies including 3D printing grow rapidly and they are expected to replace conventional subtractive manufacturing technologies to some extents. During a selective laser melting (SLM) process as one of popular AM technologies for metals, large amount of heats is required to melt metal powders, and this leads to distortions and/or shrinkages of additively manufactured parts. It is useful to predict the 3D printed parts to control unwanted distortions and shrinkages before their 3D printing. This study develops a two-phase numerical modelling and simulation process of AM process for 17-4PH stainless steel and it considers the importance of post-processing and the need for calibration to achieve a high-quality printing at the end. By using this proposed AM modelling and simulation process, optimal process parameters, material properties, and topology can be obtained to ensure a part 3D printed successfully