Search results for: continuum model

Authors: Gürkan Şakar, Fevzi Çakmak Bolat

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In this study free vibration analysis of aluminum honeycomb sandwich structures were carried out experimentally and numerically. The natural frequencies and mode shapes of sandwich structures fabricated with different configurations for clamped-free boundary condition were determined. The effects of lower and upper face sheet thickness, the core material thickness, cell diameter, cell angle and foil thickness on the vibration characteristics were examined. The numerical studies were performed with ANSYS package. While the sandwich structures were modeled in ANSYS the continuum model was used. Later, the numerical results were compared with the experimental findings.

Keywords: sandwich structure, free vibration, numeric analysis, 3D model, continuum model

Procedia PDF Downloads 397

Authors: J. Ismail, F. Zaïri, M. Naït-Abdelaziz, Z. Azari

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In this work, a combined approach of continuum damage mechanics (CDM) and fracture mechanics is applied to model a glass plate behavior under static indentation. A spherical indenter is used and a CDM based constitutive model with an anisotropic damage tensor was selected and implemented into a finite element code to study the damage of glass. Various regions with critical damage values were predicted in good agreement with the experimental observations in the literature. In these regions, the directions of crack propagation, including both cracks initiating on the surface as well as in the bulk, were predicted using the strain energy density factor.

Keywords: finite element modeling, continuum damage mechanics, indentation, cracks

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Authors: Francisco Velez, Juan David Gomez

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Dispersion effects on the Scattering for a semicircular canyon in a micropolar continuum are analyzed, by using a computational finite element scheme. The presence of microrotational waves and the dispersive SV waves affects the propagation of elastic waves. Here, a contrast with the classic model is presented, and the dependence with the micropolar parameters is studied.

Keywords: scattering, semicircular canyon, wave dispersion, micropolar medium, FEM modeling

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Authors: A. Amar

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The angular distributions of the nuclear systems under consideration have been analyzed in the framework of the optical model (OM), where the real part was taken in the crystal model form. A crystal model (CM) has been applied to deuteron elastically scattered by ⁶,⁷Li and ⁹Be. A crystal model (CM) + distorted-wave Born approximation (DWBA) + dynamic polarization potential (DPP) potential has been applied to deuteron elastically scattered by ⁶,⁷Li and 9Be. Also, a crystal model has been applied to ⁶Li elastically scattered by ¹⁶O and ²⁸Sn in addition to the ⁷Li+⁷Li system and the ¹²C(alpha,⁸Be) ⁸Be reaction. The continuum-discretized coupled-channels (CDCC) method has been applied to the ⁷Li+⁷Li system and agreement between the crystal model and the continuum-discretized coupled-channels (CDCC) method has been observed. In general, the models succeeded in reproducing the differential cross sections at the full angular range and for all the energies under consideration.

Keywords: optical model (OM), crystal model (CM), distorted-wave born approximation (DWBA), dynamic polarization potential (DPP), the continuum-discretized coupled-channels (CDCC) method, and deuteron elastically scattered by ⁶, ⁷Li and ⁹Be

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Authors: Yogesh D. Bansod, Jiri Bursa

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The quantitative study of cell mechanics is of paramount interest since it regulates the behavior of the living cells in response to the myriad of extracellular and intracellular mechanical stimuli. The novel experimental techniques together with robust computational approaches have given rise to new theories and models, which describe cell mechanics as a combination of biomechanical and biochemical processes. This review paper encapsulates the existing continuum-based computational approaches that have been developed for interpreting the mechanical responses of living cells under different loading and boundary conditions. The salient features and drawbacks of each model are discussed from both structural and biological points of view. This discussion can contribute to the development of even more precise and realistic computational models of cell mechanics based on continuum approaches or on their combination with microstructural approaches, which in turn may provide a better understanding of mechanotransduction in living cells.

Keywords: cell mechanics, computational models, continuum approach, mechanical models

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Authors: Qijiao He

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MicroElectrical-Mechanical System (MEMS) is one of the most rapidly developing frontier research field both in theory study and applied technology. Micro-channel is a very important link component of MEMS. With the research and development of MEMS, the size of the micro-devices and the micro-channels becomes further smaller. Compared with the macroscale flow, the flow characteristics of gas in the micro-channel have changed, and the rarefaction effect appears obviously. However, for the rarefied gas and microscale flow, Navier-Stokes-Fourier (NSF) equations are no longer appropriate due to the breakup of the continuum hypothesis. A Nonlinear Coupled Constitutive Model (NCCM) has been derived from the Boltzmann equation to describe the characteristics of both continuum and rarefied gas flows. We apply the present scheme to simulate continuum and rarefied gas flows in a micro-channel structure. And for comparison, we apply other widely used methods which based on particle simulation or direct solution of distribution function, such as Direct simulation of Monte Carlo (DSMC), Unified Gas-Kinetic Scheme (UGKS) and Lattice Boltzmann Method (LBM), to simulate the flows. The results show that the present solution is in better agreement with the experimental data and the DSMC, UGKS and LBM results than the NSF results in rarefied cases but is in good agreement with the NSF results in continuum cases. And some characteristics of both continuum and rarefied gas flows are observed and analyzed.

Keywords: continuum and rarefied gas flows, discontinuous Galerkin method, generalized hydrodynamic equations, numerical simulation

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Authors: Rasikha Ramanand, Priyanka Dixit

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Background: Continuum of maternal care which includes antenatal care, delivery care and postnatal care aids in averting maternal deaths. The objective of this paper is to identify the association between previous experiences of child death on Continuum of Care (CoC) of recent child. Further, the study aimed at understanding where the drop-out rate was high in the continuum. Methods: The study was based on the Nation-wide District Level Household and Facility Survey (DLHS-4) conducted during 2012-13, which provides information on antenatal care, delivery care, percentage of women who received JSY benefits, percentage of women who had any pregnancy, delivery, the place of delivery etc. The sample included women who were selected from the non-EAG states who delivered at least two children. The data were analyzed using SPSS 20.Binary Logistic regression was applied to the data in which the Continuum of Care (CoC) was the dependent variable while the independent variables were entered as the covariates. Results: A major finding of the study was the antenatal to delivery care period where the drop-out rates were high. Also, it was found that a large proportion of women did not receive any of the services along the continuum. Conclusions: This study has clearly established the relationship between previous history of child loss and continuum of maternal care.

Keywords: antenatal care, continuum of care, child loss, delivery care, India, maternal health care, postnatal care

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Authors: Temesgen Takele Kasa

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The main aim of this paper is to suggest one active slip based continuum dislocation approach to matrix dominated MMC plasticity analysis. The approach centered the free energy principles through the continuum behavior of dislocations combined with small strain continuum kinematics. The analytical derivation of this method includes the formulation of one active slip system, the thermodynamic approach of dislocations, determination of free energy, and evolution of dislocations. In addition zero and non-zero energy dissipation analysis of dislocation evolution is also formulated by using varational energy minimization method. In general, this work shows its capability to analyze the plasticity of matrix dominated MMC with inclusions. The proposed method is also found to be capable of handling plasticity of MMC.

Keywords: active slip, continuum dislocation, distortion, dominated, energy dissipation, matrix dominated, plasticity

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Authors: Ladislav Écsi, Roland Jančo

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Contemporary multiplicative plasticity models assume that the body's intermediate configuration consists of an assembly of locally unloaded neighbourhoods of material particles that cannot be reassembled together to give the overall stress-free intermediate configuration since the neighbourhoods are not necessarily compatible with each other. As a result, the plastic deformation gradient, an inelastic component in the multiplicative split of the deformation gradient, cannot be integrated, and the material particle moves from the initial configuration to the intermediate configuration without a position vector and a plastic displacement field when plastic flow occurs. Such behaviour is incompatible with the continuum theory and the continuum physics of elastoplastic deformations, and the related material models can hardly be denoted as truly continuum-based. The paper presents a proper continuum-based reformulation of current problems in finite strain plasticity. It will be shown that the incompatible neighbourhoods in real material are modelled by the product of the plastic multiplier and the yield surface normal when the plastic flow is defined in the current configuration. The incompatible plastic factor can also model the neighbourhoods as the solution of the system of differential equations whose coefficient matrix is the above product when the plastic flow is defined in the intermediate configuration. The incompatible tensors replace the compatible spatial plastic velocity gradient in the former case or the compatible plastic deformation gradient in the latter case in the definition of the plastic flow rule. They act as local imperfections but have the same position vector as the compatible plastic velocity gradient or the compatible plastic deformation gradient in the definitions of the related plastic flow rules. The unstressed intermediate configuration, the unloaded configuration after the plastic flow, where the residual stresses have been removed, can always be calculated by integrating either the compatible plastic velocity gradient or the compatible plastic deformation gradient. However, the corresponding plastic displacement field becomes permanent with both elastic and plastic components. The residual strains and stresses originate from the difference between the compatible plastic/permanent displacement field gradient and the prescribed incompatible second-order tensor characterizing the plastic flow in the definition of the plastic flow rule, which becomes an assignment statement rather than an equilibrium equation. The above also means that the elastic and plastic factors in the multiplicative split of the deformation gradient are, in reality, gradients and that there is no problem with the continuum physics of elastoplastic deformations. The formulation is demonstrated in a numerical example using the regularized Mooney-Rivlin material model and modified equilibrium statements where the intermediate configuration is calculated, whose analysis results are compared with the identical material model using the current equilibrium statements. The advantages and disadvantages of each formulation, including their relationship with multiplicative plasticity, are also discussed.

Keywords: finite strain plasticity, continuum formulation, regularized Mooney-Rivlin material model, compatibility

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Authors: Anny Zambrano, German Gonzalez, Yair Quintero

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The continuum damage concept is used to study the interaction between hydraulic fractures and natural fractures, the objective is representing the path and relation among this two fractures types and predict its complex behavior without the need to pre-define their direction as occurs in other finite element applications, providing results more consistent with the physical behavior of the phenomenon. The approach uses finite element simulations through Abaqus software to model damage fracturing, the fracturing process by damage propagation in a rock. The modeling the phenomenon develops in two dimensional (2D) so that the fracture will be represented by a line and the crack front by a point. It considers nonlinear constitutive behavior, finite strain, time-dependent deformation, complex boundary conditions, strain hardening and softening, and strain based damage evolution in compression and tension. The complete governing equations are provided and the method is described in detail to permit readers to replicate all results. The model is compared to models that are published and available. Comparisons are focused in five interactions between natural fractures (NF) and hydraulic fractures: Fractured arrested at NF, crossing NF with or without offset, branching at intersecting NFs, branching at end of NF and NF dilation due to shear slippage. The most significant new finding is, that is not necessary to use pre-defined addresses propagation and stress condition can be evaluated as a dominant factor in the process. This is important because it can model in a more real way the generated complex hydraulic fractures, and be a valuable tool to predict potential problems and different geometries of the fracture network in the process of fracturing due to fluid injection.

Keywords: continuum damage, hydraulic fractures, natural fractures, complex fracture network, stiffness

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Authors: Pakhapoom Sarapat, James M. Hill, Duangkamon Baowan

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Carbon nanotori provide several properties such as high tensile strength and heat resistance. They are promised to be ideal structures for encapsulation, and their encapsulation ability can be determined by the interaction energy between the carbon nanotori and the encapsulated nanostructures. Such interaction energy is evaluated using Lennard-Jones potential and continuum approximation. Here, four problems relating to toroidal molecules are determined in order to find the most stable configuration. Firstly, the interaction energy between a carbon nanotorus and an atom is examined. The second problem relates to the energy of a fullerene encapsulated inside a carbon nanotorus. Next, the interaction energy between two symmetrically situated and parallel nanotori is considered. Finally, the classical mechanics is applied to model the interaction energy between the toroidal structure of cyclodextrin and the spherical DNA molecules. These mathematical models might be exploited to study a number of promising devices for future developments in bio and nanotechnology.

Keywords: carbon nanotori, continuum approximation, interaction energy, Lennard-Jones potential, nanotechnology

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Authors: Gyula I. Tóth, Shaho Abdalla

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Even though numerical simulations indeed have a significant precursory/supportive role in exploring the disordered phase displaying no long-range order in pattern formation models, studying the stability properties of this phase and determining the order of the ordered-disordered phase transition in these models necessitate an analytical description of the disordered phase. First, we will present the results of a comprehensive statistical analysis of a large number (1,000-10,000) of numerical simulations in the Swift-Hohenberg model, where the bulk disordered (or amorphous) phase is stable. We will show that the average free energy density (over configurations) converges, while the variance of the energy density vanishes with increasing system size in numerical simulations, which suggest that the disordered phase is a thermodynamic phase (i.e., its properties are independent of the configuration in the macroscopic limit). Furthermore, the structural analysis of this phase in the Fourier space suggests that the phase can be modeled by a colored isotropic Gaussian noise, where any instant of the noise describes a possible configuration. Based on these results, we developed the general mathematical framework of finding a pool of solutions to partial differential equations in the sense of continuous probability measure, which we will present briefly. Applying the general idea to the Swift-Hohenberg model we show, that the amorphous phase can be found, and its properties can be determined analytically. As the general mathematical framework is not restricted to continuum theories, we hope that the proposed methodology will open a new chapter in studying disordered phases.

Keywords: fundamental theory, mathematical physics, continuum models, analytical description

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Authors: Vincent Iacobellis, Kamran Behdinan

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A finite element cohesive zone model is used to predict the temperature dependent material properties of a polyimide matrix composite with unidirectional carbon fiber arrangement. The cohesive zone parameters have been obtained from previous research involving an atomistic-to-continuum multiscale simulation of the fiber-matrix interface using the bridging cell multiscale method. The goal of the research was to both investigate the effect of temperature change on the composite behavior with respect to transverse loading as well as the validate the use of cohesive parameters obtained from atomistic-to-continuum multiscale modeling to predict fiber-matrix interfacial cracking. From the multiscale model cohesive zone parameters (i.e. maximum traction and energy of separation) were obtained by modeling the interface between the coarse-grained polyimide matrix and graphite based carbon fiber. The cohesive parameters from this simulation were used in a cohesive zone model of the composite microstructure in order to predict the properties of the macroscale composite with respect to changes in temperature ranging from 21 ˚C to 316 ˚C. Good agreement was found between the microscale RUC model and experimental results for stress-strain response, stiffness, and material strength at low and high temperatures. Examination of the deformation of the composite through localized crack initiation at the fiber-matrix interface also agreed with experimental observations of similar phenomena. Overall, the cohesive zone model was shown to be both effective at modeling the composite properties with respect to transverse loading as well as validated the use of cohesive zone parameters obtained from the multiscale simulation.

Keywords: cohesive zone model, fiber-matrix interface, microscale damage, multiscale modeling

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Authors: Noe Brice Nkoumbou Kaptchouang, Pierre-Guy Vincent, Yann Monerie

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The present work addresses the modelling and the simulation of crack initiation and propagation in ductile materials which failed by void nucleation, growth, and coalescence. One of the current research frameworks on crack propagation is the use of cohesive-volumetric approach where the crack growth is modelled as a decohesion of two surfaces in a continuum material. In this framework, the material behavior is characterized by two constitutive relations, the volumetric constitutive law relating stress and strain, and a traction-separation law across a two-dimensional surface embedded in the three-dimensional continuum. Several cohesive models have been proposed for the simulation of crack growth in brittle materials. On the other hand, the application of cohesive models in modelling crack growth in ductile material is still a relatively open field. One idea developed in the literature is to identify the traction separation for ductile material based on the behavior of a continuously-deforming unit cell failing by void growth and coalescence. Following this method, the present study proposed a semi-analytical cohesive model for ductile material based on a micromechanical approach. The strain localization band prior to ductile failure is modelled as a cohesive band, and the Gurson-Tvergaard-Needleman plasticity model (GTN) is used to model the behavior of the cohesive band and derived a corresponding traction separation law. The numerical implementation of the model is realized using the non-smooth contact method (NSCD) where cohesive models are introduced as mixed boundary conditions between each volumetric finite element. The present approach is applied to the simulation of crack growth in nuclear ferritic steel. The model provides an alternative way to simulate crack propagation using the numerical efficiency of cohesive model with a traction separation law directly derived from porous continuous model.

Keywords: ductile failure, cohesive model, GTN model, numerical simulation

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Authors: Katharina Kargel, Frederic Vobbe

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The present study examines how offenders targeting children and adolescents strategically use digital media when committing acts of sexualised violence along the online-offline continuum. Even offenders who are previously known to their victims use digital media extensively. The choice to instrumentalise digital media in order to initiate, threaten, exploit and humiliate victims demonstrates the rationale of offenders when committing acts of digitally supported violence. Through digital media, offenders can assume the power of interpretation over their victims’ situations. The ways in which digital media is used to commit violence along the online-offline continuum are a direct manifestation of the hedonistic utilitarianism demonstrated by offenders: a disposition characterised by the weighing of pleasures (“mental states”) and intrinsic value expected from using digital media against the risk of an outcome subjectively experienced as uncomfortable. Thus, sexualised violence using digital media goes beyond the traditional understanding of sexual online grooming.

Keywords: sexualized violence, offender strategy, grooming, children and adolescents, qualitative research, methodology

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Authors: Theddeus Tochukwu Akano, Omotayo Abayomi Fakinlede

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Proper understanding of the behavior of compliant mechanisms use by athletes is important in order to avoid catastrophic failure. Such compliant mechanisms like the flex-run require the knowledge of their dynamic response and deformation behavior under quickly varying loads. The modeling of finite deformations of the compliant athletic system is described by Neo-Hookean model under contact-impact conditions. The dynamic impact-contact governing equations for both the target and impactor are derived based on the updated Lagrangian approach. A method where contactor and target are considered as a united body is applied in the formulation of the principle of virtual work for the bodies. In this paper, methods of continuum mechanics and nonlinear finite element method were deployed to develop a model that could capture the behavior of the compliant athletic system under quickly varying loads. A hybrid system of symbolic algebra (AceGEN) and a compiled back end (AceFEM) were employed, leveraging both ease of use and computational efficiency. The simulated results reveal the effect of the various contact-impact conditions on the deformation behavior of the impacting compliant mechanism.

Keywords: eigenvalue problems, finite element method, robin boundary condition, sturm-liouville problem

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Authors: Sara Mosallanejad, Bogdan Z. Dlugogorski, Jeff Gore, Mohammednoor Altarawneh

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Ammonium nitrate (NH­₄NO₃, AN) is commonly used as the main component of AN emulsion and fuel oil (ANFO) explosives, that use extensively in civilian and mining operations for underground development and tunneling applications. The emulsion formulation and wettability of AN prills, which affect the physical stability and detonation of ANFO, highly depend on the surface tension, density, viscosity of the used liquid. Therefore, for engineering applications of this material, the determination of density and surface tension of concentrated aqueous solutions of AN is essential. The molecular dynamics (MD) simulation method have been used to investigate the density and the surface tension of high concentrated ammonium nitrate solutions; up to its solubility limit in water. Non-polarisable models for water and ions have carried out the simulations, and the electronic continuum correction model (ECC) uses a scaling of the charges of the ions to apply the polarisation implicitly into the non-polarisable model. The results of calculated density and the surface tension of the solutions have been compared to available experimental values. Our MD simulations show that the non-polarisable model with full-charge ions overestimates the experimental results while the reduce-charge model for the ions fits very well with the experimental data. Ions in the solutions show repulsion from the interface using the non-polarisable force fields. However, when charges of the ions in the original model are scaled in line with the scaling factor of the ECC model, the ions create a double ionic layer near the interface by the migration of anions toward the interface while cations stay in the bulk of the solutions. Similar ions orientations near the interface were observed when polarisable models were used in simulations. In conclusion, applying the ECC model to the non-polarisable force field yields the density and surface tension of the AN solutions with high accuracy in comparison to the experimental measurements.

Keywords: ammonium nitrate, electronic continuum correction, non-polarisable force field, surface tension

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Authors: Ratchada Sopakayang, Gerhard A. Holzapfel

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In this study, a new constitutive model is developed to describe the hyperelastic behavior of collagenous tissues with a parallel arrangement of collagen fibers such as ligaments and tendons. The model is formulated using a continuum approach incorporating the structural changes of the main tissue components: collagen fibers, proteoglycan-rich matrix and fiber-matrix interaction. The mechanical contribution of the interaction between the fibers and the matrix is simply expressed by a coupling term. The structural change of the collagen fibers is incorporated in the constitutive model to describe the activation of the fibers under tissue straining. Finally, the constitutive model can easily describe the stress-stretch nonlinearity which occurs when a ligament/tendon is axially stretched. This study shows that the interaction between the fibers and the matrix contributes to the mechanical tissue response. Therefore, the model may lead to a better understanding of the physiological mechanisms of ligaments and tendons under axial loading.

Keywords: constitutive model, fiber-matrix, hyperelasticity, interaction, ligament, tendon

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Authors: Nikolaos Reppas, Yilin Gui, Ben Wetenhall, Colin Davie

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Injection of CO2 inside wellbore can induce different kind of loadings that can lead to thermal, hydraulic, and mechanical changes on the surrounding rock. A dual-porosity theoretical constitutive model will be presented for the stability analysis of the wellbore during CO2 injection. An elastoplastic damage response will be considered. A bounding yield surface will be presented considering damage effects on sandstone. The main target of the research paper is to present a theoretical constitutive model that can help industries to safely store CO2 in geological rock formations and forecast any changes on the surrounding rock of the wellbore. The fully coupled elasto-plastic damage Thermo-Hydraulic-Mechanical theoretical model will be validated from existing experimental data for sandstone after simulating some scenarios by using FEM on MATLAB software.

Keywords: carbon capture and storage, rock mechanics, THM effects on rock, constitutive model

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Authors: Francesco Marotti de Sciarra, Raffaele Barretta

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Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement are presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.

Keywords: Bernoulli-Euler beams, nanobeams, nonlocal elasticity, closed-form solutions

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Authors: Manoj K. Kumar, Deepthi Bathala

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Man has the need to know and feel as a part of the historical continuum and it is this continuum that reinforces his identity. Architecture and the built environment contribute to this identity as established by the various identity theories exploring the relationship between the two. Architecture which is organic has been successful in maintaining a continuum of identity until the advent of globalization when the world saw a drastic shift to architecture of ‘placelessness’. The answer to the perfect synthesis of ‘universalization’ and ‘regionalism’ is an ongoing quest. However, history has established a smooth transition from vernacular to colonial to modern unlike the architecture of today. The traditional Kerala architecture has evolved from the tropical climate, geography, local needs, materials, skills and foreign influences. It is unique in contrast to the architecture of the neighboring states as a result of the geographical barriers however influenced by the architecture of the Orient due to trade relations. Through 1805 to 1950, the European influence on the architecture of Kerala resulted in the emergence of the colonial style which managed to establish a continuum of the traditional architecture. The paper focuses on the identification of the components of architecture that established the continuity of place-identity in the architecture of Kerala and examines the transition from the traditional Kerala architecture to colonial architecture during the colonial period. Visual surveys based on the principles of urban design, cognitive mapping, typology analysis followed by the strong understanding of the morphological and built environment along with the matrix method are the research tools used. The understanding of these components of continuity can be useful in creating buildings which people can relate to in the present day. South-Asia shares the history of colonialism and the understanding of these components can pave the way for further research on how to establish a regional identity in the era of globalization.

Keywords: colonial, identity, place, regional

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Authors: Masoud Safdari, Jacob Fish

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Despite vast amount of existing theoretical knowledge, the implementation of a universal multiscale modeling, analysis, and simulation software framework remains challenging. Existing multiscale software and solutions are often domain-specific, closed-source and mandate a high-level of experience and skills in both multiscale analysis and programming. Furthermore, tools currently existing for Atomistic-to-Continuum (AtC) multiscaling are developed with the assumptions such as accessibility of high-performance computing facilities to the users. These issues mentioned plus many other challenges have reduced the adoption of multiscale in academia and especially industry. In the current work, we introduce Multiscale Hub (MsHub), an effort towards making AtC more accessible through cloud services. As a joint effort between academia and industry, MsHub provides a universal web-enabled framework for practical multiscaling. Developed on top of universally acclaimed scientific programming language Python, the package currently provides an open-source, comprehensive, easy-to-use framework for AtC coupling. MsHub offers an easy to use interface to prominent molecular dynamics and multiphysics continuum mechanics packages such as LAMMPS and MFEM (a free, lightweight, scalable C++ library for finite element methods). In this work, we first report on the design philosophy of MsHub, challenges identified and issues faced regarding its implementation. MsHub takes the advantage of a comprehensive set of tools and algorithms developed for AtC that can be used for a variety of governing physics. We then briefly report key AtC algorithms implemented in MsHub. Finally, we conclude with a few examples illustrating the capabilities of the package and its future directions.

Keywords: atomistic, continuum, coupling, multiscale

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Authors: Eda Gök

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Peridynamics is a new modeling concept of non-local interactions for solid structures. The formulations of Peridynamic (PD) theory are based on integral equations rather than differential equations. Through, undefined equations of associated problems are avoided. PD theory might be defined as continuum version of molecular dynamics. The medium is usually modeled with mass particles bonded together. Particles interact with each other directly across finite distances through central forces named as bonds. The main assumption of this theory is that the body is composed of material points which interact with other material points within a finite distance. Although, PD theory developed for discontinuities, it gives good results for structures which have no discontinuities. In this paper, displacement control of the isotropic plate under the effect of tensile and bending loading has been investigated by means of PD theory. A MATLAB code is generated to create PD bonds and corresponding surface correction factors. Using generated MATLAB code the geometry of the specimen is generated, and the code is implemented in Finite Element Software. The results obtained from non-local continuum theory are compared with the Finite Element Analysis results and analytical solution. The results show good agreement.

Keywords: non-local continuum mechanics, peridynamic theory, solid structures, tensile loading, flexural loading

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Authors: Dua K. S. Y. Klaas, Monzur A. Imteaz, Ika Sudiayem, Elkan M. E. Klaas, Eldav C. M. Klaas

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Due to its porous nature, karst terrains – geomorphologically developed from dissolved formations, is vulnerable to water shortage and deteriorated water quality. Therefore, a solid comprehension on sub-surface flow of karst landscape is essential to assess the long-term availability of groundwater resources. In this paper, a single-continuum model using a finite difference model, MODLFOW, was constructed to represent an unconfined carbonate aquifer in a tropical karst island of Rote in Indonesia. The model, spatially discretized in 20 x 20 m grid cells, was calibrated and validated using available groundwater level and atmospheric variables. In the calibration and validation steps, Parameter Estimation (PEST) and geostatistical pilot point methods were employed to estimate hydraulic conductivity and specific yield values. The results show that the model is able to represent the sub-surface flow indicated by good model performances both in calibration and validation steps. The final model can be used as a robust representation of the system for future study on climate and land use scenarios.

Keywords: carbonate aquifer, karst, sub-surface flow, groundwater model

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Authors: Alper T. Celebi, Ali Beskok

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Electroosmotic (EO) slip flows in nanochannels are investigated using non-equilibrium molecular dynamics (MD) simulations, and the results are compared with analytical solution of Poisson-Boltzmann and Stokes (PB-S) equations with slip contribution. The ultimate objective of this study is to show that well-known continuum flow model can accurately predict the EO velocity profiles in nanochannels using the slip lengths and apparent viscosities obtained from force-driven flow simulations performed at various liquid-wall interaction strengths. EO flow of aqueous NaCl solution in silicon nanochannels are simulated under realistic electrochemical conditions within the validity region of Poisson-Boltzmann theory. A physical surface charge density is determined for nanochannels based on dissociations of silanol functional groups on channel surfaces at known salt concentration, temperature and local pH. First, we present results of density profiles and ion distributions by equilibrium MD simulations, ensuring that the desired thermodynamic state and ionic conditions are satisfied. Next, force-driven nanochannel flow simulations are performed to predict the apparent viscosity of ionic solution between charged surfaces and slip lengths. Parabolic velocity profiles obtained from force-driven flow simulations are fitted to a second-order polynomial equation, where viscosity and slip lengths are quantified by comparing the coefficients of the fitted equation with continuum flow model. Presence of charged surface increases the viscosity of ionic solution while the velocity-slip at wall decreases. Afterwards, EO flow simulations are carried out under uniform electric field for different liquid-wall interaction strengths. Velocity profiles present finite slips near walls, followed with a conventional viscous flow profile in the electrical double layer that reaches a bulk flow region in the center of the channel. The EO flow enhances with increased slip at the walls, which depends on wall-liquid interaction strength and the surface charge. MD velocity profiles are compared with the predictions from analytical solutions of the slip modified PB-S equation, where the slip length and apparent viscosity values are obtained from force-driven flow simulations in charged silicon nano-channels. Our MD results show good agreements with the analytical solutions at various slip conditions, verifying the validity of PB-S equation in nanochannels as small as 3.5 nm. In addition, the continuum model normalizes slip length with the Debye length instead of the channel height, which implies that enhancement in EO flows is independent of the channel height. Further MD simulations performed at different channel heights also shows that the flow enhancement due to slip is independent of the channel height. This is important because slip enhanced EO flow is observable even in micro-channels experiments by using a hydrophobic channel with large slip and high conductivity solutions with small Debye length. The present study provides an advanced understanding of EO flows in nanochannels. Correct characterization of nanoscale EO slip flow is crucial to discover the extent of well-known continuum models, which is required for various applications spanning from ion separation to drug delivery and bio-fluidic analysis.

Keywords: electroosmotic flow, molecular dynamics, slip length, velocity-slip

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Authors: Shruti Motiwale, Xianlin Zhou, Reuben H. Kraft

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Military and sports personnel are often required to wear heavy helmets for extended periods of time. This leads to excessive cyclic loads on the neck and an increased chance of injury. Computational models offer one approach to understand and predict the time progression of disc degeneration under severe cyclic loading. In this paper, we have applied an analytic non-linear damage evolution model to estimate damage evolution in an intervertebral disc due to cyclic loads over decade-long time periods. We have also proposed a novel strategy for inclusion of recovery in the damage model. Our results show that damage only grows 20% in the initial 75% of the life, growing exponentially in the remaining 25% life. The analysis also shows that it is crucial to include recovery in a damage model.

Keywords: cervical spine, computational biomechanics, damage evolution, intervertebral disc, continuum damage mechanics

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Authors: Ho Young Son, Bu Seog Ju, Woo Young Jung

Abstract:

This study presents the seismic safety evaluation of weir structure subjected to strong earthquake ground motions, as a flood defense structure in civil engineering structures. The seismic safety analysis procedure was illustrated through development of Finite Element (FE) and InFinite Element (IFE) method in ABAQUS platform. The IFE model was generated by CINPS4, 4-node linear one-way infinite model as a sold continuum infinite element in foundation areas of the weir structure and then nonlinear FE model using friction model for soil-structure interactions was applied in this study. In order to understand the complex behavior of weir structures, nonlinear time history analysis was carried out. Consequently, it was interesting to note that the compressive stress gave more vulnerability to the weir structure, in comparison to the tensile stress, during an earthquake. The stress concentration of the weir structure was shown at the connection area between the weir body and stilling basin area. The stress both tension and compression was reduced in IFE model rather than FE model of weir structures.

Keywords: seismic, numerical analysis, FEM, weir, boundary condition

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Authors: Zhao Wang, Hong Yan

Abstract:

In this paper, a unified-gas kinetic scheme (UGKS) for the gas-particle flow is constructed. UGKS is a direct modeling method for both continuum and rarefied flow computations. The dynamics of particle and gas are described as rarefied and continuum flow, respectively. Therefore, we use the Bhatnagar-Gross-Krook (BGK) equation for the particle distribution function. For the gas phase, the gas kinetic scheme for Navier-Stokes equation is solved. The momentum transfer between gas and particle is achieved by the acceleration term added to the BGK equation. The new scheme is tested by a 2cm-in-thickness dense bed comprised of glass particles with 1.5mm in diameter, and reasonable agreement is achieved.

Keywords: gas-particle flow, unified gas-kinetic scheme, momentum transfer, shock-induced fluidization

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Authors: M. L. Burnwal, P. Raychowdhury

Abstract:

Earthquake leads to adverse effects on buildings resting on soft soils. Mitigating the response of shallow foundations on soft soil with different methods reduces settlement and provides foundation stability. Few methods such as the rocking foundation (used in Performance-based design), deep foundation, prefabricated drain, grouting, and Vibro-compaction are used to control the pore pressure and enhance the strength of the loose soils. One of the problems with these methods is that the settlement is uncontrollable, leading to differential settlement of the footings, further leading to the collapse of buildings. The present study investigates the utility of geosynthetics as a potential improvement of the subsoil to reduce the earthquake-induced settlement of structures. A steel moment-resisting frame building resting on loose liquefiable dry soil, subjected to Uttarkashi 1991 and Chamba 1995 earthquakes, is used for the soil-structure interaction (SSI) analysis. The continuum model can simultaneously simulate structure, soil, interfaces, and geogrids in the OpenSees framework. Soil is modeled with PressureDependentMultiYield (PDMY) material models with Quad element that provides stress-strain at gauss points and is calibrated to predict the behavior of Ganga sand. The model analyzed with a tied degree of freedom contact reveals that the system responses align with the shake table experimental results. An attempt is made to study the responses of footing structure and geosynthetics with unreinforced and reinforced bases with varying parameters. The result shows that geogrid reinforces shallow foundation effectively reduces the settlement by 60%.

Keywords: settlement, shallow foundation, SSI, continuum FEM

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Authors: Smriti, Ajeet Kumar

Abstract:

We present a variant of the Irving-Kirkwood procedure to obtain the microscopic expressions of the cross-section averaged continuum fields such as internal force and moment in one-dimensional nanostructures in the non-equilibrium setting. In one-dimensional continuum theories for slender bodies, we deal with quantities such as mass, linear momentum, angular momentum, and strain energy densities, all defined per unit length. These quantities are obtained by integrating the corresponding pointwise (per unit volume) quantities over the cross-section of the slender body. However, no well-defined cross-section exists for these nanostructures at finite temperature. We thus define the cross-section of a nanorod to be an infinite plane which is fixed in space even when time progresses and defines the above continuum quantities by integrating the pointwise microscopic quantities over this infinite plane. The method yields explicit expressions of both the potential and kinetic parts of the above quantities. We further specialize in these expressions for helically repeating one-dimensional nanostructures in order to use them in molecular dynamics study of extension, torsion, and bending of such nanostructures. As, the Irving-Kirkwood procedure does not yield expressions of stiffnesses, we resort to a thermodynamic equilibrium approach to obtain the expressions of axial force, twisting moment, bending moment, and the associated stiffnesses by taking the first and second derivatives of the Helmholtz free energy with respect to conjugate strain measures. The equilibrium approach yields expressions independent of kinetic terms. We then establish the equivalence of the expressions obtained using the two approaches. The derived expressions are used to understand the extension, torsion, and bending of single-walled carbon nanotubes at non-zero temperatures.

Keywords: thermoelasticity, molecular dynamics, one dimensional nanostructures, nanotube buckling

Procedia PDF Downloads 106