The classical continuum mechanics, which studies the mechanical behavior of structures based on partial differential equations, shows its deficiencies when it encounters a discontinuity. Peridynamics based on integral equations can simulate fracture but suffers from high computational costs. A hybrid local/nonlocal model combining the advantages of peridynamics with those of classical continuum mechanics can simulate fracture and reduce the computational cost. Under the framework of the hybrid local/nonlocal model, this research developed an approach and computational codes for fracture simulations. First, we developed the computational codes based on the hybrid model with a priori partition of the domain between local and nonlocal models to tackle engineering problems with relevant level of difficulty. Second, we developed a strength-induced approach to enhance the capability of the computational codes because the strength-induced approach can limit the peridynamic model to necessary computational steps at the time level and a relatively small zone at the space level during a simulation. The strength-induced approach also improved the hybrid models by enabling an automatic partition of the domain without manual involvement. At last, a strength-induced computational code was developed based on this research. This dissertation complemented and illustrated numerically some previous work of Cohmas laboratory, in which a new route was introduced toward simulating the whole process of material behaviors including elastic deformation, crack nucleation and propagation until structural failure.

This work explores the computational modeling of electromechanical problems using peridynamics and in particular, its application in studying the potential of carbon nanotube (CNT) reinforced nanocomposites for the purpose of sensing deformation and damage in materials. Peridynamics, a non-local continuum theory which was originally formulated for modeling problems in solid mechanics, has been extended in this research to electromechanical fields and applied to study the electromechanical properties of CNT nanocomposites at multiple length scales. Piezoresistivity is the coupling between the electrical properties of a material and applied mechanical loads, more specifically the change in resistance in response to deformation. This can include both, a geometric effect due to change in dimensions as well as the change in resistivity of the material itself. Nanocomposites referred to in this work are materials which consist of CNTs dispersed in a binding polymer matrix. The origins of the extraordinary piezoresistive properties of nanocomposites lie at the nanoscale where the non-local phenomenon of electron hopping plays a significant role in establishing the properties of the nanocomposite along with CNT network formation and inherent piezoresistivity of CNTs themselves. Electron hopping or tunneling allows for a current to flow between neighboring CNTs even when they are not in contact, provided the energy barrier for electrons to hop is small enough. This phenomenon is highly nonlinear with respect to the intertube distance and is also dependent on other factors such as the potential barrier of the polymer matrix. To investigate this in more detail, peridynamic simulations are first employed to study the piezoresistivity at the CNT bundle scale by considering a nanoscale representative volume element (RVE) of CNTs within polymer matrix, and by explicitly modeling electron hopping effects. This is done by introducing electron hopping bonds and it is shown that the conductivity and the non-local length scale parameter in peridynamics (the horizon) can be derived from a purely physics based model rather than assuming an ad-hoc value. Piezoresistivity can be characterized as a function of the deformation and damage within the material and thereby used as an in-situ indicator of the structural health of the material. As such, a material system for which real time in-situ monitoring may be useful is polymer bonded explosives. While these materials are designed for detonation under conditions of a strong shock, they can be damaged or even ignited under certain low magnitude impact scenarios such as during accidental drop or transportation. Since these materials are a heterogeneous system consisting of explosive grains within a polymer matrix binder, it is proposed that CNTs can be dispersed within the binder medium leading to an inherently piezoresistive hybrid nanocomposite bonded explosive material (NCBX) material which can then be monitored for a continuous assessment of deformation and damage within the material. To explore the potential use of CNT nanocomposites for this novel application, peridynamic simulations are carried out at the microscale level, first under quasistatic conditions and subsequently under dynamic conditions to allow the propagation of elastic waves. Peridynamics equations, which can be discretized to obtain a meshless method are particularly suited to this problem as the explicit modeling of crack initiation and propagation at the microscale is essential to understanding the properties of this material. Moreover, many other parameters such as electrical conductivity of the grain and the properties of the grain-binder interface are studied to understand their effect on the piezoresistive response of the material. For example, it is found that conductivity of the grain plays a major role in the piezoresistive response since it affects the preferential pathways of current density depending on the relative ease of flow through grain vs. binder. The results of this work are promising and are two fold. Peridynamics is found to be an effective method to model such materials, both at the nanoscale and the microscale. It alleviates some of difficulties faced by traditional finite element methods in the modeling of damage in materials and can be extended to coupled fields with relative ease. Secondly, simulations presented in this work show that there is much promise in this novel application of nanocomposites in the field of structural health monitoring of polymer bonded explosives. / Ph. D.

Since the last century a lot of effort has been spent trying to analyze damage and crack evolution in solids. This field is of interest because of the many applications that require the study of the behavior of materials at the micro- or nanoscale, i.e. modeling of composites and advanced aerospace applications. Peridynamics is a recently developed theory that substitutes the differential equations that constitute classical continuum mechanics with integral equations. Since integral equations are valid at discontinuities and cracks, peridynamics is able to model fracture and damage in a more natural way, without having to work around mathematical singularities present in the classical continuum mechanics theory. The objective of the present work is to show how peridynamics can be implemented in finite element analysis (FEA) using a mesh of one-dimensional truss elements instead of 2-D surface elements. The truss elements can be taken as a representation of the bonds between molecules or particles in the body and their strength is found according to the physical properties of the material. The possibility implementing peridynamics in a finite element framework, the most used method for structural analysis, is critical for expanding the range of problems that can be analyzed, simplifying the verification of the code and for making fracture analysis computationally cheaper. The creation of an in-house code allows for easier modifications, customization and enrichment if more complex cases (such as multiscale modeling of composites or piezoresistive materials) are to be analyzed. The problems discussed in the present thesis involve plates with holes and inclusions subjected to tension. Displacement boundary conditions are applied in all cases. The results show good agreement with theory as well as with empirical observation. Stress concentrations reflect the behavior of materials in real life, cracks spontaneously initiate and debonding naturally happens at the right locations. Several examples clearly show this behavior and prove that peridynamics is a promising tool for stress and fracture analysis. / Master of Science

The classical continuum theory is not capable of predicting failure without an external crack growth criteria and treats the interface having zero thickness. Alternatively, a nonlocal continuum theory referred to as peridynamic theory eliminates these shortcomings by utilizing formulation that uses displacements, rather than derivatives of displacements, and including material failure in its constitutive relations through the response functions. This study presents a new response function as part of the peridynamic theory to include thermal loading. Furthermore, an efficient numerical algorithm is presented for solution of peridynamic equations. Solution method relies on the discretization of peridynamic equations at collocation points resulting in a set of ordinary differential equations with respect to time. These differential equations are then integrated using explicit methods. In order to improve numerical efficiency of the computations, spatial partitioning is introduced through uniform grids as arrays of linked lists. Furthermore, the domain of interest is divided into subunits each of which is assigned to a specific processor to utilize parallel processing using OpenMP. In order to obtain the static solutions, the adaptive dynamic relaxation method is developed for the solution of peridynamic equations. Furthermore, an approach to couple peridynamic theory and finite element analysis is introduced to take advantage of their salient features. The regions in which failure is expected are modeled using peridynamics while the remaining regions are modeled utilizing finite element method. Finally, the present solution method is utilized for damage prediction of many problems subjected to mechanical, thermal and buckling loads.

Orientador: Edison Zacarias da Silva / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-23T16:18:47Z (GMT). No. of bitstreams: 1 Pereira_ZennerSilva_D.pdf: 11614247 bytes, checksum: d882692dfdab010e889cb1717d250a1f (MD5) Previous issue date: 2013 / Resumo: Nas últimas décadas uma geração de nanodispositivos foi desenvolvida. Estes dispositivos nanoeletrônicos são fabricados por novas técnicas fundamentadas em física, química e engenharia. Muitos desses nanomateriais têm suas propriedades físicas alteradas pelo efeito de tamanho, por causa desses novos efeitos é importante entender como estes dispositivos trabalham propriamente a fim de encontrarmos formas de obter novas aplicações baseadas nestes novos efeitos. Nanofios metálicos estão sendo largamente estudados tanto teoricamente como experimentalmente. Recentemente uma nova possibilidade de soldagem foi mostrada experimentalmente entre nanofios de ouro em temperatura ambiente, sem necessidade de aplicação de calor adicional e com baixa pressão, chamada de solda fria (cold welding). Usando Dinâmica Molecular (MD) com potenciais efetivos, nós simulamos o processo de soldagem fria em nanofios de ouro, prata e ouro-prata com diâmetros de 4.3nm em 300 K. Nós mostramos que a soldagem fria é um processo possível até mesmo quando os nanofios sofrem fortes deformações e defeitos antes do processo de soldagem. Durante o processo de soldagem os nanofios resultaram com poucos defeitos. Pequenas pressões foram necessárias para que a soldagem fosse atingida. Nós também realizamos cálculos de Dinâmica Molecular com embedded-atom-method para modelar o crescimento de filmes-finos de paládio depositados em um substrato de ouro para um sistema de aproximadamente 100 mil átomos. Nós mostramos que o filmes-finos de paládio cresceu sob stress sobre o substrato de ouro. Após a deposição de 9 monocamadas o stress armazenado no filmes de paládio relaxou formando defeitos na estrutura do cristal. Defeitos do tipo falhas de empilhamento surgiram nos filmes de paládio formando um padrão de deformação no mesmo. Para quantificar o stress nós também calculamos a evolução do tensor de stress durante o crescimento. Existem fenômenos físicos como fraturas em materiais que são caracterizados pela quebra das ligações atômicas que levam a efeitos macroscópicos. Para estudarmos este tipo de problema, nós desenvolvemos um código inicial que acopla Dinâmica Molecular com Peridyvii namics (PD) (uma recente teoria de contínuo). A ideia básica para acoplar Dinâmica Molecular e Peridynamics está baseada no teorema de Schwarz. Este teorema fornece uma maneira de resolver equações diferenciais em diferentes subdomínios conectados por uma interface. O acoplamento é feito trocando condições de contorno entre subdomínios conectados por esta interface. A parte mais difícil deste acoplamento encontra-se em tratar os dados com ruídos oriundos da Dinâmica Molecular e passá-los para a Peridynamics. Para isto nós usamos uma interpolação estatística chamada interpolação de Kriging. Desta forma nós pudemos alcançar um acoplamento entre MD e PD / Abstract: Over the last decades a new generation of nanoeletronic devices have been developed. These nanoeletronic devices have been made by new techniques based on physics, chemistry and engineering. Many of these nanomaterials have shown changes in their physical properties and therefore, it is very important to understand how they work properly in order to find ways to obtain new applications supported by these new effects. Metallic nanowires have been largely studied theoretical and experimentally. Recently a new possibility of welding was experimentally shown in the case of gold and silver nanowires (NWs) at ambient temperatures, without need of additional heat and with low pressures, called cold welding. Using molecular dynamics with effective potentials, we simulated cold welding of gold, silver, and silver-gold NWs with diameters of 4.3 nm at 300 K. We show the cold welding is a possible process in metal NWs and that these welded NWs, even after losing their crystalline structure after breaking, can reconstruct their face-centered-cubic structure during the welding process with the result of very few defects in the final cold welded NWs. The stress tensor shows a low average value during welding with oscillations indicating tension and relaxation stages. Small pressures are required for the process to occur, resulting in a fairly perfect crystal structure for the final NW after being broken and welded. We have also performed Molecular Dynamics calculations with embedded-atom-method to model the growth of a Pd thin film deposited on Au(100) for a system with approximately 100,000 atoms. We showed that the Pd film grew under stress on the Au substrate. After the deposition of 9 monolayers, the stress stored in the Pd film relaxed with the formation of defects, stacking faults in the structure of Pd forming a pattern of deformation in the film. To quantitatively access the defect formation we also measured the stress tensor evolution during growth. There are physical phenomena like brittle fracture that is characterized by breaking of atomic bonds leading to macroscopic effects. In order to study this kind of problems, we developed the initial programming code that couples molecular dynamics (MD) and Peridyix namics (PD) (a new model to continuum). The basic idea to coupling Molecular Dynamics and Peridynamics is based on a mathematical theorem that is known as Schwarz theorem. It gives a way to solve differential equations in different subdomains that are connected by an interface (overlap). The coupling is made by exchanging boundary conditions through of the interface between subdomains. The hardest part is to treat noise molecular dynamics data and after that to pass those data to continuum theories. In order to pass data from MD to Peridynamics we have used a statistical interpolation called Kriging interpolation. This way we can achieve an algorithm to coupling DM with PD / Doutorado / Física / Doutor em Ciências

In this work we study peridynamics, a non-local model in continuum me- chanics introduced by Silling (2000). The non-locality is reflected in the fact that points at finite distance exert a force upon each other. If, however, these points are more distant than a characteristic length called horizon, it is customary to assume that they do not interact. We compare peridynamics with elasticity, especially in the limit of small horizon. We restrict ourselves, concerning this vanishing non-locality, to variational formulation of time- independent processes. We compute a Γ-limit for homogeneous and isotropic solid in linear peridynamics. In some cases this Γ-limit coincides with linear elasticity and the Poisson ratio is equal to 1 4. We conclude by clarifying why in some situation the computed Γ-limit can differ from the linear elasticity. 1

This study proposes an approach for solving density-based multi-material topology optimization of cracked structures using Peridynamics. The alternating active-phase algorithm is utilized to transform the multi-material problem into a series of binary phase topology optimization sub-problems. Instead of the conventional mesh-based methods, the Peridynamics theory (PD) is used as a tool to model the behaviour of the materials and solve for the displacement field. The most significant advantage of PD is its ability to model discontinuities in a relatively straightforward manner. Thus, in the present work, the effect of cracks as a discontinuity is investigated on the optimal multi-material topologies. The Solid Isotropic Material with Penalty (SIMP) method is utilized to define the material properties as a function of the design variables. Also, the optimization problem is solved through the Optimality Criteria (OC) approach. The proposed method is compared to the results reported in the literature by executing three numerical examples that investigate the effect of the direction of an interior crack on the optimal topologies. Moreover, the efficiency of the proposed approach is verified by solving several examples where we aim at minimizing the compliance of the structure with and without initial cracks. / Graduate

Recent advances in non-local continuum models, notably peridynamics, have spurred a paradigm shift in solid mechanics simulation by allowing accurate mathematical representation of singularities and discontinuities. This doctoral work attempts to extend the use of this theory to a community more familiar with local continuum models. In this communication, a coupling strategy - the morphing method -, which bridges local and non-local models, is presented. This thesis employs the morphing method to ease use of the non-local model to represent problems with failure-induced discontinuities. First, we give a quick review of strategies for the simulation of discrete degradation, and suggest a hybrid local/non-local alternative. Second, we present the technical concepts involved in the morphing method and evaluate the quality of the coupling. Third, we develop a numerical tool for the simulation of the hybrid model for fracture and damage and demonstrate its capabilities on numerical model examples

Several aspects of fracture nucleation and growth in brittle porous ceramics and in thin films are investigated, through analytical, numerical modelling, and experimental validation. A mechanical experimental characterization has been developed for a porous ceramic, namely, a 3D apatite, characterised by an oriented porosity and used for biomedical applications. The ceramic is produced from wood, so that the resulting porosity evidences a multi-scale nature, a feature determining peculiar failure mechanisms and an unprecedented porosity/strength ratio. In particular, the material exhibits an exfoliation-type failure, resulting in a progressive loss in mechanical properties, occurring for compression tests parallel to the grains and for highly slender specimens. Similar cohesive-brittle behaviour is also found when the compression is applied in the direction orthogonal to the porous channels, regardless of the shape ratio of the specimen. An in-depth analysis of this response is performed by means of a phase-field model. After calibrating the model, stress-strain curves and fracturing patterns are accurately reproduced. Furthermore, the effects of multi-scale porosity on mechanical behaviour are determined. Various strategies available in the literature for evaluating the properties of porous materials are compared to the proposed phase-field approach. The results open new possibilities for the prediction and characterization of complex fracturing phenomena occurring in highly porous ceramics, so to facilitate medical applications as structural bone repair. An application of the peridynamic theory of continuum mechanics is developed to obtain a dimensional reduced formulation for the characterisation of through-thickness delamination of plates. The kinematic of the plate is carefully chosen to be composed of an absolutely continuous part and a zone where jumps in the displacements are allowed; in this way, the reduced form of the elastic bond-based peridynamic energy and the reduced Lagrangian are explicitly retrieved in a closed-form. The reduction generates a hierarchy of terms, characterizing the energy stored inside the plane element. A semi-analytical solution, obtained by means of a minimization procedure, is obtained for a test case and compared with finite element simulations. Despite the fact that the numerical model is fully three-dimensional (in other words, it is not reduced), this model leads to the same moment-curvature diagrams and nucleation/growth of the delamination surface found with the reduced formulation. Finally, the convergence of the proposed reduced model to local elastic theory at vanishing internal length is determined, so that a reduced-localized cohesive model for fracture is retrieved.

Polymer bonded explosives (PBXs) are composites comprised of energetic crystals with a very high energy density surrounded by a polymer binder. The formation of hotspots within polymer bonded explosives can lead to the thermal decomposition and initiation of the energetic material. A frictional heating model is applied at the mesoscale to assess the potential for the formation of hotspots under low velocity impact loadings. Monitoring of the formation and growth of damage at the mesoscale is considered through the inclusion of a piezoresistive carbon nanotube network within the energetic binder providing embedded strain and damage sensing. A coupled multiphysics thermo-electro-mechanical peridynamics framework is developed to perform computational simulations on an energetic material microstructure subject to these low velocity impact loads. With increase in impact energy, the model predicts larger amounts of sensing and damage thereby supporting the use of carbon nanotubes to assess damage growth and subsequent formation of hotspots. The framework is also applied to assess the combined effects of thermal loading due to prescribed hotspots with inertial effects due to low velocity impact loading. It has been found that the present model is able to detect the presence of hotspot dominated regions within the energetic material through the piezoresistive sensing mechanism. The influence of prescribed hotspots on the thermo-electro-mechanical response of the energetic material under a combination of thermal and inertial loading was observed to dominate the lower velocity impact response via thermal shock damage. In contrast, the higher velocity impact energies demonstrated an inertially dominated damage response. Quantifying the piezoresistive effect derived from embedding carbon nanotubes in polymers remains a challenge since these nanocomposites exhibit significant variation in their electro-mechanical properties depending upon factors such as CNT volume fraction, CNT dispersion, CNT alignment and properties of the polymer. Of interest is electrical percolation where the electrical conductivity of the CNT/polymer nanocomposite increases through orders of magnitude with increase in CNT volume fraction. Estimates and distributions for the electrical conductivity and piezoresistive coefficients of the CNT/polymer nanocomposite are obtained and analyzed with increasing CNT volume fraction and varying barrier potential, which is a parameter that controls the extent of electron tunneling. The effect of CNT alignment is analyzed by comparing the electro-mechanical properties in the alignment direction versus the transverse direction for different orientation conditions. Estimates of piezoresistive coefficients are converted into gage factors and compared with experimental sources in literature. The methodology for this work uses automated scripts which are used in conjunction with high performance computing to generate several 5 μm ×5 μm realizations for different CNT volume fractions. These realizations are then analyzed using finite elements to obtain volume averaged effective values, which are then subsequently used to generate measures of central tendency (estimated mean) and variability (standard deviation, coefficient of variation, skewness and kurtosis) in a descriptive statistical analysis. / Doctor of Philosophy / Carbon nanotubes or CNTs belong to a class of novel materials known as nanomaterials which are materials with length scales on the order of nanometers. CNTs have been widely studied due to their unique mechanical, electrical and thermal properties in comparison to traditional materials such as metals or plastics. Often times, research and applications concerning the use of CNTs involves embedding the CNTs as a filler within a larger composite material system. In the present work, CNTs are considered to be embedded within a polymer. It is known that the electrical properties of such a CNT/polymer composite change in response to the application of a mechanical force. This change in electrical properties is caused due to the presence of CNTs and is used as a means of sensing the mechanical state of the composite, i.e. real time structural monitoring. The extent of the change in electrical properties, also known as sensing, depends upon a number of different factors such as the amount of CNTs used per unit volume of the polymer, how well dispersed or clumped together the CNTs are within the polymer and the type of polymer material used, among other factors. A statistical analysis is performed with several case studies where these factors are varied and the resulting change in the sensing response is monitored. Several important conclusions were made from the statistical analysis with some of the results providing new insights into the sensing behavior of CNT/polymer composites. For example, it was found that a key parameter known as barrier potential, which directly influences the extent of sensing achieved through a mechanism known as electrical tunneling, needs to be several orders of magnitude lower than previously reported values to accurately capture the sensing effects. Key metrics quantifying the extent of sensing from the analysis were found to be in agreement with previously reported experimental results. The significance of such a statistical study lies in the fact that CNT embedded composites are increasingly being proposed and used for sensing applications. The use of CNT embedded polymers to encase explosive crystalline grains such as HMX or RDX is one such example. These explosive grains are used in a number of different civil and military applications such as fuel rocket propellants, industry explosives, military munitions etc. The grains possess extremely high energy densities and are susceptible to undergo violent chemical reaction if a trigger is provided through thermal or mechanical means. As such, the monitoring of the structural state of these explosives is crucial for their safe handling and processing. In this work, the sensing response of a composite material comprising of explosive grains surrounded by polymer material containing CNTs is studied in response to different types of mechanical loads, ranging from mild stimuli to impact. It was found that the sensing mechanism was capable of tracking mechanical damage as well as the resulting temperature increases interior to the composite. In addition to its application to safety and preventative measures, the use of CNTs in this context also provided insight into the mechanisms related to the sudden release of energy in these explosive grains which is of significant interest since this is an active area of research as well.