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A novel nonlocal lattice particle framework for modeling of solids

Description

Fracture phenomena have been extensively studied in the last several decades. Continuum mechanics-based approaches, such as finite element methods and extended finite element methods, are widely used for fracture simulation. One well-known issue of these approaches is the stress singularity

Fracture phenomena have been extensively studied in the last several decades. Continuum mechanics-based approaches, such as finite element methods and extended finite element methods, are widely used for fracture simulation. One well-known issue of these approaches is the stress singularity resulted from the spatial discontinuity at the crack tip/front. The requirement of guiding criteria for various cracking behaviors, such as initiation, propagation, and branching, also poses some challenges. Comparing to the continuum based formulation, the discrete approaches, such as lattice spring method, discrete element method, and peridynamics, have certain advantages when modeling various fracture problems due to their intrinsic characteristics in modeling discontinuities.

A novel, alternative, and systematic framework based on a nonlocal lattice particle model is proposed in this study. The uniqueness of the proposed model is the inclusion of both pair-wise local and multi-body nonlocal potentials in the formulation. First, the basic ideas of the proposed framework for 2D isotropic solid are presented. Derivations for triangular and square lattice structure are discussed in detail. Both mechanical deformation and fracture process are simulated and model verification and validation are performed with existing analytical solutions and experimental observations. Following this, the extension to general 3D isotropic solids based on the proposed local and nonlocal potentials is given. Three cubic lattice structures are discussed in detail. Failure predictions using the 3D simulation are compared with experimental testing results and very good agreement is observed. Next, a lattice rotation scheme is proposed to account for the material orientation in modeling anisotropic solids. The consistency and difference compared to the classical material tangent stiffness transformation method are discussed in detail. The implicit and explicit solution methods for the proposed lattice particle model are also discussed. Finally, some conclusions and discussions based on the current study are drawn at the end.

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Date Created
2015

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The C++ implementation of refined level set grid (RLSG) method

Description

In this thesis, a FORTRAN code is rewritten in C++ with an object oriented ap-

proach. There are several reasons for this purpose. The first reason is to establish

the basis of a GPU programming. To write programs that utilize GPU hardware,

CUDA

In this thesis, a FORTRAN code is rewritten in C++ with an object oriented ap-

proach. There are several reasons for this purpose. The first reason is to establish

the basis of a GPU programming. To write programs that utilize GPU hardware,

CUDA or OpenCL is used which only support C and C++. FORTRAN has a feature

that lets its programs to call C/C++ functions. FORTRAN sends relevant data to

C/C++, which in turn sends that data to OpenCL. Although this approach works,

it makes the code messy and bulky and in the end more difficult to deal with. More-

over, there is a slight performance decrease from the additional data copy. This is

the motivation to have the code entirely written in C++ to make it more uniform,

efficient and clean. The second reason is the object oriented feature of the C++. The

“abstraction”, “inheritance” and “run-time polymorphism” features of C++ provide

some form of classes and objects, the ability to build new abstractions, and some

form of run-time binding, respectively. In recent years, some of popular codes has

been rewritten in C++ which were initially in FORTRAN. One of these softwares is

LAMMPS.

In this code the level set equation is solved by RLSG method to track the interface in

two phase flow. In gas/fluid flows, the surface tension is important and only exists at

the interface. Therefore, the location and some geometric features of interface need

to be evaluated which can be achieved by solving the level set equation.

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Date Created
2015

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A critical plane-energy model for multiaxial fatigue life prediction of homogeneous and heterogeneous materials

Description

A new critical plane-energy model is proposed in this thesis for multiaxial fatigue life prediction of homogeneous and heterogeneous materials. Brief review of existing methods, especially on the critical plane-based and energy-based methods, are given first. Special focus is on

A new critical plane-energy model is proposed in this thesis for multiaxial fatigue life prediction of homogeneous and heterogeneous materials. Brief review of existing methods, especially on the critical plane-based and energy-based methods, are given first. Special focus is on one critical plane approach which has been shown to work for both brittle and ductile metals. The key idea is to automatically change the critical plane orientation with respect to different materials and stress states. One potential drawback of the developed model is that it needs an empirical calibration parameter for non-proportional multiaxial loadings since only the strain terms are used and the out-of-phase hardening cannot be considered. The energy-based model using the critical plane concept is proposed with help of the Mroz-Garud hardening rule to explicitly include the effect of non-proportional hardening under fatigue cyclic loadings. Thus, the empirical calibration for non-proportional loading is not needed since the out-of-phase hardening is naturally included in the stress calculation. The model predictions are compared with experimental data from open literature and it is shown the proposed model can work for both proportional and non-proportional loadings without the empirical calibration. Next, the model is extended for the fatigue analysis of heterogeneous materials integrating with finite element method. Fatigue crack initiation of representative volume of heterogeneous materials is analyzed using the developed critical plane-energy model and special focus is on the microstructure effect on the multiaxial fatigue life predictions. Several conclusions and future work is drawn based on the proposed study.

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Date Created
2016

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Mechanisms for kink band evolution in polymer matrix composites: a digital image correlation and finite element study

Description

Polymer matrix composites (PMCs) are attractive structural materials due to their high stiffness to low weight ratio. However, unidirectional PMCs have low shear strength and failure can occur along kink bands that develop on compression due to plastic microbuckling that

Polymer matrix composites (PMCs) are attractive structural materials due to their high stiffness to low weight ratio. However, unidirectional PMCs have low shear strength and failure can occur along kink bands that develop on compression due to plastic microbuckling that carry strains large enough to induce nonlinear matrix deformation. Reviewing the literature, a large fraction of the existing work is for uniaxial compression, and the effects of stress gradients, such as those present during bending, have not been as well explored, and these effects are bound to make difference in terms of kink band nucleation and growth. Furthermore, reports on experimental measurements of strain fields leading to and developing inside these bands in the presence of stress gradients are also scarce and need to be addressed to gain a full understanding of their behavior when UDCs are used under bending and other spatially complex stress states.

In a light to bridge the aforementioned gaps, the primary focus of this work is to understand mechanisms for kink band evolution under an influence of stress-gradients induced during bending. Digital image correlation (DIC) is used to measure strains inside and around the kink bands during 3-point bending of samples with 0°/90° stacking made of Ultra-High Molecular Weight Polyethylene Fibers. Measurements indicate bands nucleate at the compression side and propagate into the sample carrying a mixture of large shear and normal strains (~33%), while also decreasing its bending stiffness. Failure was produced by a combination of plastic microbuckling and axial splitting. The microstructure of the kink bands was studied and used in a microstructurally explicit finite element model (FEM) to analyze stresses and strains at ply level in the samples during kink band evolution, using cohesive zone elements to represent the interfaces between plies. Cohesive element properties were deduced by a combination of delamination, fracture and three-point bending tests used to calibrate the FEMs. Modeling results show that the band morphology is sensitive to the shear and opening properties of the interfaces between the plies.

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Date Created
2016

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Effects of dynamic material strength on hydrodynamic instability and damage evolution in shock loaded copper

Description

Characterization and modeling of deformation and failure in metallic materials under extreme conditions, such as the high loads and strain rates found under shock loading due to explosive detonation and high velocity-impacts, are extremely important for a wide variety of

Characterization and modeling of deformation and failure in metallic materials under extreme conditions, such as the high loads and strain rates found under shock loading due to explosive detonation and high velocity-impacts, are extremely important for a wide variety of military and industrial applications. When a shock wave causes stress in a material that exceeds the elastic limit, plasticity and eventually spallation occur in the material. The process of spall fracture, which in ductile materials stems from strain localization, void nucleation, growth and coalescence, can be caused by microstructural heterogeneity. The analysis of void nucleation performed from a microstructurally explicit simulation of a spall damage evolution in a multicrystalline copper indicated triple junctions as the preferred sites for incipient damage nucleation revealing 75% of them with at least two grain boundaries with misorientation angle between 20-55°. The analysis suggested the nature of the boundaries connecting at a triple junction is an indicator of their tendency to localize spall damage. The results also showed that damage propagated preferentially into one of the high angle boundaries after voids nucleate at triple junctions. Recently the Rayleigh-Taylor Instability (RTI) and the Richtmyer-Meshkov Instability (RMI) have been used to deduce dynamic material strength at very high pressures and strain rates. The RMI is used in this work since it allows using precise diagnostics such as Transient Imaging Displacement Interferometry (TIDI) due to its slower linear growth rate. The Preston-Tonks-Wallace (PTW) model is used to study the effects of dynamic strength on the behavior of samples with a fed-thru RMI, induced via direct laser drive on a perturbed surface, on stability of the shock front and the dynamic evolution of the amplitudes and velocities of the perturbation imprinted on the back (flat) surface by the perturbed shock front. Simulation results clearly showed that the amplitude of the hydrodynamic instability increases with a decrease in strength and vice versa and that the amplitude of the perturbed shock front produced by the fed-thru RMI is also affected by strength in the same way, which provides an alternative to amplitude measurements to study strength effects under dynamic conditions. Simulation results also indicate the presence of second harmonics in the surface perturbation after a certain time, which were also affected by the material strength.

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Date Created
2016

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On the Role of the Corner Radius in the Mechanical Behavior of the Hexagonal Honeycomb

Description

The hexagonal honeycomb is a bio-inspired cellular structure with a high stiffness-to-weight ratio. It has contributed to its use in several engineering applications compared to solid bodies with identical volume and material properties. This characteristic behavior is mainly attributed to

The hexagonal honeycomb is a bio-inspired cellular structure with a high stiffness-to-weight ratio. It has contributed to its use in several engineering applications compared to solid bodies with identical volume and material properties. This characteristic behavior is mainly attributed to the effective nature of stress distribution through the honeycomb beams that manifests as bending, axial, and shear deformation mechanisms. Inspired by the presence of this feature in natural honeycomb, this work focuses on the influence of the corner radius on the mechanical properties of a honeycomb structure subjected to in-plane compression loading. First, the local response at the corner node interface is investigated with the help of finite element simulation of a periodic unit cell within the linear elastic domain and validated against the best available analytical models. Next, a parametric design of experiments (DOE) study with the unit cell is defined with design points of varying circularity and cell length ratios towards identifying the optimal combination of all geometric parameters that maximize stiffness per unit mass while minimizing the stresses induced at the corner nodes. The observed trends are then compared with compression tests of 3D printed Nylon 12 honeycomb specimens of varying corner radii and wall thicknesses. The study concluded that the presence of a corner radius has a mitigating effect on peak stresses but that these effects are dependent on thickness while also increasing specific stiffness in all cases. It also points towards an optimum combination of parameters that achieve both objectives simultaneously while shedding some light on the functional benefit of this radius in wasp and bee nests that employ a hexagonal cell.

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Date Created
2021

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Multiscale Modeling of Structure-Property Relationships in Polymers with Heterogenous Structure

Description

The exceptional mechanical properties of polymers with heterogeneous structure, such as the high toughness of polyethylene and the excellent blast-protection capability of polyurea, are strongly related to their morphology and nanoscale structure. Different polymer microstructures, such as semicrystalline morphology

The exceptional mechanical properties of polymers with heterogeneous structure, such as the high toughness of polyethylene and the excellent blast-protection capability of polyurea, are strongly related to their morphology and nanoscale structure. Different polymer microstructures, such as semicrystalline morphology and segregated nanophases, lead to coordinated molecular motions during deformation in order to preserve compatibility between the different material phases. To study molecular relaxation in polyethylene, a coarse-grained model of polyethylene was calibrated to match the local structural variable distributions sampled from supercooled atomistic melts. The coarse-grained model accurately reproduces structural properties, e.g., the local structure of both the amorphous and crystalline phases, and thermal properties, e.g., glass transition and melt temperatures, and dynamic properties: including the vastly different relaxation time scales of the amorphous and crystalline phases. A hybrid Monte Carlo routine was developed to generate realistic semicrystalline configurations of polyethylene. The generated systems accurately predict the activation energy of the alpha relaxation process within the crystalline phase. Furthermore, the models show that connectivity to long chain segments in the amorphous phase increases the energy barrier for chain slip within crystalline phase. This prediction can guide the development of tougher semicrystalline polymers by providing a fundamental understanding of how nanoscale morphology contributes to chain mobility. In a different study, the macroscopic shock response of polyurea, a phase segregated copolymer, was analyzed using density functional theory (DFT) molecular dynamics (MD) simulations and classical MD simulations. The two models predict the shock response consistently up to shock pressures of 15 GPa, beyond which the DFT-based simulations predict a softer response. From the DFT simulations, an analysis of bond scission was performed as a first step in developing a more fundamental understanding of how shock induced material transformations effect the shock response and pressure dependent strength of polyurea subjected to extreme shocks.

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Date Created
2017

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Reduced order modeling with variable spatial fidelity for the linear and nonlinear dynamics of multi-bay structures

Description

This investigation develops small-size reduced order models (ROMs) that provide an accurate prediction of the response of only part of a structure, referred to as component-centric ROMs. Four strategies to construct such ROMs are presented, the first two of which

This investigation develops small-size reduced order models (ROMs) that provide an accurate prediction of the response of only part of a structure, referred to as component-centric ROMs. Four strategies to construct such ROMs are presented, the first two of which are based on the Craig-Bampton Method and start with a set of modes for the component of interest (the β component). The response in the rest of the structure (the α component) induced by these modes is then determined and optimally represented by applying a Proper Orthogonal Decomposition strategy using Singular Value Decomposition. These first two methods are effectively basis reductions techniques of the CB basis. An approach based on the “Global - Local” Method generates the “global” modes by “averaging” the mass property over α and β comp., respectively (to extract a “coarse” model of α and β) and the “local” modes orthogonal to the “global” modes to add back necessary “information” for β. The last approach adopts as basis for the entire structure its linear modes which are dominant in the β component response. Then, the contributions of other modes in this part of the structure are approximated in terms of those of the dominant modes with close natural frequencies and similar mode shapes in the β component. In this manner, the non-dominant modal contributions are “lumped” onto the dominant ones, to reduce the number of modes for a prescribed accuracy. The four approaches are critically assessed on the structural finite element model of a 9-bay panel with the modal lumping-based method leading to the smallest sized ROMs. Therefore, it is extended to the nonlinear geometric situation and first recast as a rotation of the modal basis to achieve unobservable modes. In the linear case, these modes completely disappear from the formulation owing to orthogonality. In the nonlinear case, however, the generalized coordinates of these modes are still present in the nonlinear terms of the observable modes. A closure-type algorithm is then proposed to eliminate the unobserved generalized coordinates. This approach, its accuracy and computational savings, was demonstrated on a simple beam model and the 9-bay panel model.

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Date Created
2017

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Numerical study on cohesive zone elements for static and time dependent damage and its application in pipeline failure analysis

Description

Cohesive zone model is one of the most widely used model for fracture analysis, but still remains open ended field for research. The earlier works using the cohesive zone model and Extended finite element analysis (XFEM) have been briefly

Cohesive zone model is one of the most widely used model for fracture analysis, but still remains open ended field for research. The earlier works using the cohesive zone model and Extended finite element analysis (XFEM) have been briefly introduced followed by an elaborate elucidation of the same concepts. Cohesive zone model in conjugation with XFEM is used for analysis in static condition in order to check its applicability in failure analysis. A real time setup of pipeline failure due to impingement is analyzed along with a detailed parametric study to understand the influence of the prominent design variable. After verifying its good applicability, a creep model is built for analysis where the cohesive zone model with XFEM is used for a time dependent creep loading. The challenge in this simulation was to achieve coupled behavior of cracks initiation and propagation along with creep loading. By using Design of Experiment, the results from numerical simulation were used to build an equation for life prediction for creep loading condition. The work was further extended to account for fatigue damage accumulation for high cycle fatigue loading in cohesive elements. A model was conceived to account for damage due to fatigue loading along within cohesive zone model for cohesive elements in ABAQUS simulation software. The model was verified by comparing numerical modelling of Double cantilever beam under high cycle fatigue loading and experiment results from literature. The model was also applied to a major industrial problem of blistering in Cured-In-Plane liner pipelines and a demonstration of its failure is shown. In conclusion, various models built on cohesive zone to address static and time dependent loading with real time scenarios and future scope of work in this field is discussed.

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Date Created
2016

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Estimation of J-integral for a non-local particle model using atomistic finite element method and coupling between non-local particle and finite element methods

Description

In this paper, at first, analytical formulation of J-integral for a non-local particle model (VCPM) using atomic scale finite element method is proposed for fracture analysis of 2D solids. A brief review of classical continuum-based J-integral and anon-local lattice particle

In this paper, at first, analytical formulation of J-integral for a non-local particle model (VCPM) using atomic scale finite element method is proposed for fracture analysis of 2D solids. A brief review of classical continuum-based J-integral and anon-local lattice particle method is given first. Following this, detailed derivation for the J-integral in discrete particle system is given using the energy equivalence and stress-tensor mapping between the continuum mechanics and lattice-particle system.With the help of atomistic finite element method, the J-integral is expressed as a summation of the corresponding terms in the particle system.

Secondly, a coupling algorithm between a non-local particle method (VCPM) and the classical finite element method (FEM) is discussed to gain the advantages of both methods for fracture analysis in large structures. In this algorithm, the discrete VCPM particle and the continuum FEM domains are solved within a unified theoretical framework. A transitional element technology is developed to smoothly link the 10-particles element with the traditional FEM elements to guaranty the continuity and consistency at the coupling interface. An explicit algorithm for static simulation is developed.

Finally, numerical examples are illustrated for the accuracy, convergence, and path-independence of the derived J-integral formulation. Discussions on the comparison with alternative estimation methods and potential application for fracture simulation are given. The accuracy and efficiency of the coupling algorithm are tested by several benchmark problems such as static crack simulation.

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Agent

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Date Created
2016