Sharif Digital Repository

Stress tensors and their rates are fundamental quantities in modeling the behavior of materials in the field of nonlinear continuum mechanics. One of the most remarkable applications of stress rates is their presence in the rate type constitutive equations of materials.
Co-rotational rates are corresponding to the rates which are measured by an observer who is in a reference rotating coordinate system. In general, under some specific conditions for the spin of a co-rotational rate, the rate of an Eulerian tensor would be objective. In this thesis, the objective co-rotational rates of Eulerian stress tensors for isotropic elastic materials under large deformations are obtained for the... 

The concept of generalized strains is a well-established subject in the classical continuum mechanics. The characteristics and various applications of the generalized strains have been the point of interest of many researchers in the classical continuum mechanics. The aim of this thesis is the introduction of generalized strains in the micropolar theory, as a non-classical continuum theory. A set of generalized strains is suggested for the deformation of macro-elements. Moreover, a set of generalized strains is proposed for the micro-structures. Since the rate of strains possesses a significant importance in the constitutive equations of nonlinear analysis of solids, expressions for the rate... 

The micropolar theory is a nonclassical continuum theory which considers a microstructure associated to each particle. This microstructure has three degrees of freedom and can rigidly rotate in the three dimensional space. Beside the classical or force stress tensor, in the micropolar theory the couple stress tensor is also considered.This research is devoted to deriving energy pair tensors for material strain measures in micropolar continuum. The subject of strains and their conjugate stresses is one of the major topics in the field of solid mechanics which has greatly been dealt with in the literature. This concept was introduced for investigating structural inequalities in solid... 

In this project, a size-dependent formulation is presented for mechanical analyses of inhomogeneous micro-plates based on the modified couple stress theory. The modified couple stress theory as a non-classical continuum theory has the ability to consider the small size effects in the mechanical behavior of the structures.The material properties are supposed arbitrarily to vary through the thickness of the plate. The governing differential equations of motion are derived for functionally graded plates utilizing variational approach. Based on the derived formulation, the static and free-vibration behaviors as well as buckling analysis of a rectangular functionally graded micro-plate are... 

Vibration analysis of micro-structures has been a major topic in recent years. Among them micro-plates play an important role in micro- and nano-electromechanical systems (MEMS and NEMS), e.g. micropumps, micromirrors, and microresonators. Some experimental observations revealed the size-dependent mechanical behavior in micro-scaled structures. Because of the incapability of the classical continuum theory to interpret the experimentally-detected small-scale effects in mechanical behavior of micro-scaled systems, non-classical theories should be used to deal with micron and sub-micron structures. Couple stress theory is one of the non-classical theories with only one length scale parameter. A... 

Micro-rotating machinery with compact energy sources and high power density has been developed in the recent decade to run portable electronic devices. To achieve efficiency targets, these miniaturized turbo-machinery must spin at elevated rotational speeds which sometimes can reach up to one million revolutions per minute. At this relatively high spinning rate, the rotordynamic behavior of these systems plays an important role in the stage of design. On the other hand, the classical continuum theory has been proven not to be able to appropriately predict the mechanical behavior of the small-scale structures. To overcome overall mentioned weakness, in this thesis the rotor of micro-engines... 

The present study deals with the analysis of Atomic Microscope with crack by making use of Strain Gradient Elasticity theory. Empirical observations represent that in micro dimensions, materials show behaviors, which the classic continuum mechanics theories are not able to explain. Thus, taking advantage of non-classic theories, which are capable of explaining such phenomena or behaviors in analyzing materials in micro dimensions seems necessary and of much significance. In this direction, by applying an Euler-Bernoulli beam assumption and neglecting the shear effects, governing equations and boundary conditions of the problem were obtained via taking advantage of variations in Hamilton... 

In recent years, the world has seen a great progress in micro electro-mechanical systems (MEMS). Small size, low weight, high accuracy and low energy consumption have made these devices applicable in a variety of usages. In MEMS devices, mechanical components are used for specific purposes among which one of the most widely used are micro plates. Microplates are used in the structure of many devices such as microswitchs and atomic force microscopes. Therefore, studying of static and dynamic behavior of microplates is important. As the object gets smaller (to the scale of micro and nano meters), the classic theory of mechanics of continuous media cannot predict the behavior due to its... 

The analysis of nonlinear forced vibration of micro-rotors (rotating micro-shafts with disks) is carried out under loads of mass eccentricity distribution and in the presence of internal damping. For the analysis, the non-classical continuum theories of couple stress and strain gradient are employed. Vibrational behavior of micro-rotors is extremely sensitive due to the very high rotational speed, which is at the order of several millions per minute speed. The considered nonlinearity is of geometrical type due to the mid-plane stretching. First, the governing equations of motion of micro-rotors are derived by utilizing the Hamilton principle. In the next step, the Galerkin and multiple scale... 

Incapability of the classical continuum mechanics theory to justify the experimental observations of the mechanical response of the small-scale structures and parts motivated the researchers to pursue the introduction and utilization of the non-classical continuum theories for analysis and design of such structures and parts. In this paper, utilizing the modified couple stress theory and the strain gradient theory as well-known and powerful non-classical continuum theories, the mechanical response, including the displacement and stress fields, for micro-rotating disks with angular acceleration is investigated. The governing differential equations of motion and the corresponding boundary... 

Todays, advances in manufacturing technologies have led to design and production of micro-scale elements, including the elements employed in micro-electro-mechanical systems (MEMS). Micro-rotating systems like the micro-turbines are that kind of systems at which the high rotational speeds and the complexity of design and analysis have led to a special attention in modeling and investigating of their dynamic-vibrational behavior. In addition, in small scales, using the non-classical continuum mechanics theories such as the couple stress theory and the strain gradient theory is required to obtain the high precise results. On the other hand, attention to the torsional deformation of rotors... 

Heart failure is one of the leading causes of death around the world and diastolic dysfunction is the main culprit behind about 30 percent of them. End-diastolic pressure-volume relationship is one of the most important indices of ventricles diastolic function, however invasive nature of assessment, has hindered its use in clinical applications. Despite the advances in computational modeling and bio-mechanical simulations, computational cost of these procedures often renders the computational methods unsuitable for clinical implications. Machine learning methods are usually the proper substitute in such cases. However, this method requires a large set of pre-calculated data for training,... 

Experimental observations on multilayer graphene structures show that interlayer interactions including compressive and shear effects between layers are very important in their mechanical behavior. Existing analytical investigations have generally addressed the issue of pressure interactions between layers using interatomic potentials, while the models which consider the interlayer shear effect are rarely found in the literature. To address this shortcoming, this thesis presents a new formulation for multilayer graphene structures with desired shapes and boundaries, taking into account the interlayer shear effect according to the classical continuum mechanics theory. Next, size-dependent... 

Throughout history, engineers have always been searching for ways to increase the strength-to-weight ratio in the design of engineering structures. Using lattice structures has been a method implemented in different applications to achieve this goal. Herein, two novel hybrid lattice structures are designed, and their compressive quasi-static mechanical behavior is evaluated experimentally and numerically. In one of the designed structures, using dual-phase strengthening, FCC unit cells are incorporated as a reinforcement phase into a BCC matrix. In the multifunctional lattice structure, FCC and BCC unit cells are combined with their central nodes connected. All of the designed structures are... 

In the present study, by considering the damage effects, the governing equations for elastoplastic behavior of a rotating disk are derived. Then several numerical solutions are presented for specific examples. First, by means of elastic strain energy functions along with the damage appearing in the literature and irreversible Thermodynamics laws, an analytical solution is generated for a rotating disk undergoing elastic deformations. For this purpose, the components of strain tensor are obtained in terms of the damage variable and the stress tensor components. Then, by employing the damage evolution relations mixed with the damage surface relation, damage variable is derived as a function of... 

Due to the features like small dimensions, low manufacturing cost and low power consumption, micro-electromechanical systems (MEMS) are widely utilized in engineering applications. Many experimental investigations have indicated that the mechanical behavior of constructive microelements of these systems isn’t predictable by classical continuum theory. Therefore, to analyze the behavior of microelements, the non-classical continuum theories which can capture size effects should be utilized. On the other hand, various experimental observations have confirmed that thermoelastic damping (TED) is a dominant source of energy dissipation in microelements, in contrast to the non-small parts and... 

Engineering of properties was previously not possible. With the advent of additive manufacturing, it became possible to produce structures with architected microstructures, known as lattice structures. The popularity of these structures, due to their lightweight and tunable properties, has increased the importance of their optimal mechanical analysis. Since direct analysis of these structures is computationally prohibitive due to their high level of detail, homogenization methods have been proposed as an alternative. Since these methods couldn't capture size effects, higher-order homogenization methods were introduced. However, despite their good accuracy, these methods are still rarely used... 

Strong van der Waals (vdW) potential fields of carbon nanotubes (CNTs) makes them capable to encapsulate some nanostructures inside their hollow space, which leads to the construction of new hybrid nanostructures under specific conditions. Carbon nano-peapods, carbon nanowires and the hybrid of DNA and CNT are the main categories of hybrid nanostructures of CNT. Characteristics of hybrid nanotubes are unique and different from those of CNT. In nanostructures, the lattice spacing between individual atoms is considerable with respect to the structural dimensions. Also, the range of internal characteristic length is relatively close to external ones. So that utilizing the classical continuum... 

In this thesis, equations related to large deformation of a polymer were derived by considering viscoelastic effects. To express type of material behavior which includes elastoplastic and viscoelastic property at the same time, two-layer viscoplastic model was used. An axisymmetric model was used for modeling problem in finite element software. By derivation of parameters related to two layer model and entering them in finite element software and also entering other properties required to model the forming process, modeling was performed by special profile connecting input and output sections. Due to favorable properties of spline functions, profiles used in die geometry, were selected from... 

In the present study, we analyzed the mechanical behavior of micro rotating disk based on the most general form of strain gradient elasticity. According to the fact that micro rotating disks have an important role in MEMS, it is necessary to present an exact analysis of their mechanical behavior. It is noticed experimentally that materials behave stronger in deformation as they get smaller. The classical continuum theory is not capable to predict such behavior; therefore, it is essential to use one of the non-classical continuum theories to analyze the material in micro scales, which can capture this phenomenon. In this work, the strain gradient theory is utilized to derive the governing...