Sharif Digital Repository

A Polygonal finite element method without conforming mesh was introduced by the authors for modeling large deformation elastoplastic problems. In this method, the geometry and interfaces of the problem are modeled on a uniform mesh. The boundaries are defined on the uniform background mesh using the level set method. Different polygonal elements will be created at the intersection of the interface and the uniform mesh. Polygonal element shape functions are used for the interpolation. In this paper, the capability of this polygonal finite element approach for modeling large deformational frictionless dynamic contact-impact problems is investigated. Contact interfaces are modeled independent... 

In addition to chemical stability and biocompatibility, because of the characteristics of quantum dimensions, gold nanoparticles are used in detecting cancers, imaging and therapeutics .Atomic interactions between gold particles and bioparticles are influenced by the dimensions of gold particles .Therefore, in this project, after introduction of various water models and used potentials for modeling by the method of TIP3P, we studied gold clusters in different dimensions and densities, by using EAM potential in the aquatic environment .Then we can pave the way for studying proteins besides gold nanoparticles, in the future studies. Besides, gold particles were studied as colloid, so as to... 

Fracture is one of the most important engineering problems, and the lack of knowledge about this phenomenon will result in loss of life and property. Before the computer age, fracture mechanics has been studied by many analytical mechanics researchers; and after that, lots of attempts have been done to accurately model this phenomenon.
Finite element method, one of the best methods in Computational Mechanics, is common in computational fracture mechanics. Polygonal finite element is a new concept which has been recently applied in finite element analysis. This research utilized this concept in com-putational fracture mechanics. In another word, the crack discontinuity and crack tip... 

Isogeometric Analysis method is a newly introduced method for the analysis of problems governed by partial differential equations. The method has some features in common with the finite element method and some in common with the mesh-less methods. This method uses the Non-Uniform Rational B-Splines (NURBS) functions as basis function for analysis. With this basis functions, the refinement procedure is much easier than the classical finite element method by eliminating the need to communicate with the CAD model. Modeling cracks in classical finite element method requires very fine mesh near the crack tip. One can model crack propagation by means of classical finite element, using an updating... 

Contact between different parts of a system and their interactions on each other is one of the most important phenomena that we face in modeling a variety of mechanical issues which should be carefully considered. Sometimes, this phenomenon occurs between different components in a phase and some other times between several phases, which, causes changes in the performance and response of the system. Therefore, in order to investigate its effect in particular on dynamic problems that are subject to severe changes over a short period of time, and to provide more effective methods for dealing with it, the subject of this research has been devoted to dynamic contact modeling with large... 

In this thesis, a coarse-grained multi-scale method for 2D crystallyn solids based-on finite element consepts has presented. In this method, both scales are atomic scale and similar to what we see in non-local QC method, the entire atomic structure will be intact. Accordingly, calculations of potential functions and forces in the domain will have the atomic accuracy. In the presented method to reduce the domain’s degrees of freedom, the classical finite-element meshing concept to mesh the elastic linear areas in the domain is used and the MD calculations will done on the mesh nodes. Therefore, degrees of freedom in the system will reduce and consequently, the computational cost will reduce.... 

In this thesis, a fully coupled numerical model is developed for the modeling of dynamic cohesive crack propagation and hydraulic fracture in saturated porous media using extended finite element method. Many engineering structures like concrete or soil dams and buildings foundation are built with porous materials like concrete, rock and soil. Behavior of these materials in which void among the solid particles are filled with one or more fluids are so complicated rather than single solid phase. Dynamic analysis of porous mediums containing a discontinuity has many applications in various civil engineering fields including structure, earthquake, hydraulic structures, etc. For instance... 

The band gap offset is an effect of coordination numbers (CNs) of atoms reduction at the edge of transversal cross-section Si nanowires (SiNWs) which would be of increasingly important for greater shell-core ratio sections. In this paper, a hierarchical multi-scale modeling has been developed to simulate edge effect on the band gap shift of SiNWs due to geometry effect induced strain in the self-equilibrium state. Classical Molecular Dynamics (MD) approach and Finite Element Method (FEM) are used in the micro (atomic) and macro scale levels, respectively. Using the Cauchy-Born (CB) hypothesis as a correlator of continuum and atomic properties, the atomic positions are related to the... 

Contact happens when two bodies collide. Depending on our assumption, it can be considered as a frictional or frictionless contact. Here we have assumed that friction accompanies the contact phenomenon, hence it is called a frictional contact. For modeling contact problems, different procedures can be used such as node-to-node or node-to-surface patterns. Here we want to use the node-to-surface procedure to model the contact problem. The node-to-surface pattern has the capability to model interface behavior between different materials. By using the finite element method through numerical computations and also by applying constraint conditions which are related to contact conditions, we can... 

Nanotechnology is the knowledge of future. Some people Compare the initialization of nanotechnology to the beginning of the industrial revolution. Experimental modeling of nano-materials can be so expensive, but, with the aid of computational nanomechanics, we can perform less experiments and more numerical simulation. In the past decades, applications of nanotubes in medicine, electrical engineering, mechanical engineering, building nano sensors, nano engines and etc caused a pervasive study on the mechanics of carbon nanotubes. In this Thesis, the writer has implemented the Tersoff interatomic potential to perform molecular dynamics simulations of carbon nanotubes. In this work, tensile... 

One of the most important problems that challenge the researchers in modeling physical phenomena is the Impact Problem. The complexity of impact problems is due to the fact that this problem consists of various sub-problems, each of which of high complexity and in order to have a clear understanding and correct modeling of the problem, one needs to address each and every one of these problems with great effort, severity and punctuality.Impact problems often involve one or more dynamic systems that can also be subjected to dynamic loading. This loading could be a result of external agents or dynamic interaction of the two bodies with each other. In cases where the problem involves interaction... 

In continuum mechanics, the constitutive models are usually based on the Cauchy-Born (CB) hypothesis which seeks the intrinsic characteristics of the material via the atomistic information and it is valid in small deformation. The main purpose of this thesis is to investigate the temperature effect on the stability and size dependency of Cauchy-Born hypothesis and a novel temperature-dependent multi-scale method is developed to investigate the role of temperature on surface effects in the analysis of nano-scale materials. Three-dimensional temperature-related Cauchy-Born formulation are developed for crystalline structure and the stability and size dependency of temperature-related... 

Mindboggling advances in nanotechnology have urged researchers to develop state-of-the-art numerical methods to enable them to simulate and to interpret phenomena at this scale. Unfortunately, Classical models have numerous shortcomings which hinder their applications in new contexts. For instance, classical Continuum Mechanics fails to appropriately depict material behavior at small scales, and, on the other hand, Molecular Dynamics simulations are computationally prohibitive. As a consequence, researchers have devised multi-scale methods during the past decade to overcome these obstacles. In fact, in multi-scale methods information is passed from one mathematical description to the other.... 

In present research forming process of nanopowders, which is a part of powder metallurgy was investigated by molecular dynamics method. Powder metallurgy is a relatively new method for production of industrial parts by pouring powder into die and compaction to desired density. One can reach parts with higher quality and strength by decreasing size of powder’s particles and entering the nano scale. Particle with smaller size have higher specific surface and due more intensity to react. Classic methods for investigation of this process don’t cover the atomic scale effects, so using newer procedures such as molecular dynamics is highly recommended. In present research, at first compaction of... 

We carry out computer simulations in the hope of understanding the properties of assemblies of molecules in terms of their structure and the microscopic interactions between them. This serves as a complement to conventional experiments, enabling us to learn something new, something that cannot be found out in other ways. One of the main families of simulation technique are molecular dynamics (MD). Over the last decade , nanoscience and nanotechnology have emerged as two of the pillars of the research that will lead us to the next industrial revolution. The fundamental entities of interest to nanoscience and nanotechnology are the isolated individual nanostructures and their assemblies. Nano... 

During the last decade, thanks to a combination of exploding computational power and improved physical insight into material behavior, continuum and atomistic simulations improved greatly. Both classes of methods are now used to solve problems, which are more complicated than ever with greater accuracy than ever before. Nevertheless, there still exist problems for which neither method alone is sufficient. In general, atomistic simulations cannot be used for such length scales due to the restrictions on the number of atoms that can be simulated, along with the time scales, which they can be simulated for. In contrast, continuum simulations tend to fail at the atomic scale, for example due to... 

Due to high cost and ineffectiveness of molecular models a new method for coupling continuum models with molecular models is used. In this method, the continuum and molecular domains are overlapped. Comparing the results obtained from the concurrent simulations and molecular dynamic simulations proves the accuracy of the method used. The method is used for modeling single layered graphene sheets, stress contours are presented for multiscale and both static and dynamic simulations of concurrent. For multiscale simulations two different carbon nano tubes are investigated and strees-bond angle and strees-bond length are also presented  

In this study, a novel multiscale analysis is proposed to utilize atomistic properties of crystalline nano-materials as an input to continuum problems in the range of large deformation. The main purpose of presented work is investigating the capability of different hyperelasticity models based on molecular statics (MS) and molecular dynamics methods to attain proper hyperelastic strain energy density function to illustrate atomistic information under various types of deformation loadings. Also, the proficiency of hyperelastic model is investigated for nano-structure including different percentages of voids. The material parameters of hyperelastic strain energy density can be obtained from... 

In this study, the hierarchical multiscale method is presented to model macro-scale materials with considering large and plastic deformations. Since the classic methods such as continuum mechanics were unable to model defects such as dislocations, voids, and etc. at nano scale. Also, the molecular dynamics methods have high computational costs; hence, recearchers try to develop multiscale methods in order to utilize them. Multiscale modeling in which two scales are considered and some information be transferred from fine scale to coarse scale. In this work, the coarse scale is modeled by finite element method (FEM) and the fine scale is analysed by molecular dynamics (MD). In fact, two... 

Lattice modeling is one of the most effective methods of simulation of crack initiation and propagation in heterogeneous materials. In this method, not only the impurities can be modeled in detail, but also micro crack initiations and crack ramifications can be observed. Lattice model simulations have shown remarkable results in both force-displacement charts and visual crack formations in heterogeneous materials, especially concrete. Simulation of mechanical behavior of concrete has always been a controversial issue in lattice modeling; and, so far, many researchers have proposed different methods. However, high computation demands, has preserved researchers from any major work on the...