Matching Items (7)
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- All Subjects: Finite element method
- Creators: Liu, Yongming
Description
The objective of this research is to develop robust, accurate, and adaptive algorithms in the framework of the extended finite element method (XFEM) for fracture analysis of highly heterogeneous materials with complex internal geometries. A key contribution of this work is the creation of novel methods designed to automate the incorporation of high-resolution data, e.g. from X-ray tomography, that can be used to better interpret the enormous volume of data generated in modern in-situ experimental testing. Thus new algorithms were developed for automating analysis of complex microstructures characterized by segmented tomographic images.
A centrality-based geometry segmentation algorithm was developed to accurately identify discrete inclusions and particles in composite materials where limitations in imaging resolution leads to spurious connections between particles in close contact.To allow for this algorithm to successfully segment geometry independently of particle size and shape, a relative centrality metric was defined to allow for a threshold centrality criterion for removal of voxels that spuriously connect distinct geometries.
To automate incorporation of microstructural information from high-resolution images, two methods were developed that initialize signed distance fields on adaptively-refined finite element meshes. The first method utilizes a level set evolution equation that is directly solved on the finite element mesh through Galerkins method. The evolution equation is formulated to produce a signed distance field that matches geometry defined by a set of voxels segmented from tomographic images. The method achieves optimal convergence for the order of elements used. In a second approach, the fast marching method is employed to initialize a distance field on a uniform grid which is then projected by least squares onto a finite element mesh. This latter approach is shown to be superior in speed and accuracy.
Lastly, extended finite element method simulations are performed for the analysis of particle fracture in metal matrix composites with realistic particle geometries initialized from X-ray tomographic data. In the simulations, particles fracture probabilistically through a Weibull strength distribution. The model is verified through comparisons with the experimentally-measured stress-strain response of the material as well as analysis of the fracture. Further, simulations are then performed to analyze the effect of mesh sensitivity, the effect of fracture of particles on their neighbors, and the role of a particles shape on its fracture probability.
A centrality-based geometry segmentation algorithm was developed to accurately identify discrete inclusions and particles in composite materials where limitations in imaging resolution leads to spurious connections between particles in close contact.To allow for this algorithm to successfully segment geometry independently of particle size and shape, a relative centrality metric was defined to allow for a threshold centrality criterion for removal of voxels that spuriously connect distinct geometries.
To automate incorporation of microstructural information from high-resolution images, two methods were developed that initialize signed distance fields on adaptively-refined finite element meshes. The first method utilizes a level set evolution equation that is directly solved on the finite element mesh through Galerkins method. The evolution equation is formulated to produce a signed distance field that matches geometry defined by a set of voxels segmented from tomographic images. The method achieves optimal convergence for the order of elements used. In a second approach, the fast marching method is employed to initialize a distance field on a uniform grid which is then projected by least squares onto a finite element mesh. This latter approach is shown to be superior in speed and accuracy.
Lastly, extended finite element method simulations are performed for the analysis of particle fracture in metal matrix composites with realistic particle geometries initialized from X-ray tomographic data. In the simulations, particles fracture probabilistically through a Weibull strength distribution. The model is verified through comparisons with the experimentally-measured stress-strain response of the material as well as analysis of the fracture. Further, simulations are then performed to analyze the effect of mesh sensitivity, the effect of fracture of particles on their neighbors, and the role of a particles shape on its fracture probability.
ContributorsYuan, Rui (Author) / Oswald, Jay (Thesis advisor) / Chawla, Nikhilesh (Committee member) / Liu, Yongming (Committee member) / Solanki, Kiran (Committee member) / Chen, Kangping (Committee member) / Arizona State University (Publisher)
Created2015
Description
This investigation focuses on the development of uncertainty modeling methods applicable to both the structural and thermal models of heated structures as part of an effort to enable the design under uncertainty of hypersonic vehicles. The maximum entropy-based nonparametric stochastic modeling approach is used within the context of coupled structural-thermal Reduced Order Models (ROMs). Not only does this strategy allow for a computationally efficient generation of samples of the structural and thermal responses but the maximum entropy approach allows to introduce both aleatoric and some epistemic uncertainty into the system.
While the nonparametric approach has a long history of applications to structural models, the present investigation was the first one to consider it for the heat conduction problem. In this process, it was recognized that the nonparametric approach had to be modified to maintain the localization of the temperature near the heat source, which was successfully achieved.
The introduction of uncertainty in coupled structural-thermal ROMs of heated structures was addressed next. It was first recognized that the structural stiffness coefficients (linear, quadratic, and cubic) and the parameters quantifying the effects of the temperature distribution on the structural response can be regrouped into a matrix that is symmetric and positive definite. The nonparametric approach was then applied to this matrix allowing the assessment of the effects of uncertainty on the resulting temperature distributions and structural response.
The third part of this document focuses on introducing uncertainty using the Maximum Entropy Method at the level of finite element by randomizing elemental matrices, for instance, elemental stiffness, mass and conductance matrices. This approach brings some epistemic uncertainty not present in the parametric approach (e.g., by randomizing the elasticity tensor) while retaining more local character than the operation in ROM level.
The last part of this document focuses on the development of “reduced ROMs” (RROMs) which are reduced order models with small bases constructed in a data-driven process from a “full” ROM with a much larger basis. The development of the RROM methodology is motivated by the desire to optimally reduce the computational cost especially in multi-physics situations where a lack of prior understanding/knowledge of the solution typically leads to the selection of ROM bases that are excessively broad to ensure the necessary accuracy in representing the response. It is additionally emphasized that the ROM reduction process can be carried out adaptively, i.e., differently over different ranges of loading conditions.
While the nonparametric approach has a long history of applications to structural models, the present investigation was the first one to consider it for the heat conduction problem. In this process, it was recognized that the nonparametric approach had to be modified to maintain the localization of the temperature near the heat source, which was successfully achieved.
The introduction of uncertainty in coupled structural-thermal ROMs of heated structures was addressed next. It was first recognized that the structural stiffness coefficients (linear, quadratic, and cubic) and the parameters quantifying the effects of the temperature distribution on the structural response can be regrouped into a matrix that is symmetric and positive definite. The nonparametric approach was then applied to this matrix allowing the assessment of the effects of uncertainty on the resulting temperature distributions and structural response.
The third part of this document focuses on introducing uncertainty using the Maximum Entropy Method at the level of finite element by randomizing elemental matrices, for instance, elemental stiffness, mass and conductance matrices. This approach brings some epistemic uncertainty not present in the parametric approach (e.g., by randomizing the elasticity tensor) while retaining more local character than the operation in ROM level.
The last part of this document focuses on the development of “reduced ROMs” (RROMs) which are reduced order models with small bases constructed in a data-driven process from a “full” ROM with a much larger basis. The development of the RROM methodology is motivated by the desire to optimally reduce the computational cost especially in multi-physics situations where a lack of prior understanding/knowledge of the solution typically leads to the selection of ROM bases that are excessively broad to ensure the necessary accuracy in representing the response. It is additionally emphasized that the ROM reduction process can be carried out adaptively, i.e., differently over different ranges of loading conditions.
ContributorsSong, Pengchao (Author) / Mignolet, Marc P (Thesis advisor) / Smarslok, Benjamin (Committee member) / Chattopadhyay, Aditi (Committee member) / Liu, Yongming (Committee member) / Jiang, Hanqing (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2019
Description
An integrated experimental and numerical investigation for laser-generated optoacoustic wave propagation in structural materials is performed. First, a multi-physics simulation model is proposed to simulate the pulsed laser as a point heat source which hits the surface of an aluminum sheet. The pulsed laser source can generate a localized heating on the surface of the plate and induce an in-plane stress wave. ANSYS – a finite element analysis software – is used to build the 3D model and a coupled thermal-mechanical simulation is performed in which the heat flux is determined by an empirical laser-heat conversion relationship. The displacement and stress field-histories are obtained to get the time of arrival and wave propagation speed of the stress wave. The effect of an added point mass is investigated in detail to observe the local material perturbation and remote wave signals. Following this, the experimental investigation of optoacoustic wave is also performed. A new experimental setup and control is developed and assembled in-house. Various laser firing parameters are investigated experimentally and the optimal combination is used for the experimental testing. Matrix design for different testing conditions is also proposed to include the effect of wave path, sampling procedure, and local point mass on the optoacoustic wave propagation. The developed numerical simulation results are validated with experimental observations. It is shown that the proposed experimental setup can offer a potential fast scanning method for damage detection (local property change) for plate-like structural component.
ContributorsLiu, Chen (Author) / Liu, Yongming (Thesis advisor) / Wang, Liping (Committee member) / Jiao, Yang (Committee member) / Arizona State University (Publisher)
Created2016
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 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.
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.
ContributorsZope, Jayesh (Author) / Liu, Yongming (Thesis advisor) / Oswald, Jay (Committee member) / Jiang, Hanqing (Committee member) / Arizona State University (Publisher)
Created2016
Description
Composite materials are now beginning to provide uses hitherto reserved for metals in structural systems such as airframes and engine containment systems, wraps for repair and rehabilitation, and ballistic/blast mitigation systems. These structural systems are often subjected to impact loads and there is a pressing need for accurate prediction of deformation, damage and failure. There are numerous material models that have been developed to analyze the dynamic impact response of polymer matrix composites. However, there are key features that are missing in those models that prevent them from providing accurate predictive capabilities. In this dissertation, a general purpose orthotropic elasto-plastic computational constitutive material model has been developed to predict the response of composites subjected to high velocity impacts. The constitutive model is divided into three components – deformation model, damage model and failure model, with failure to be added at a later date. The deformation model generalizes the Tsai-Wu failure criteria and extends it using a strain-hardening-based orthotropic yield function with a non-associative flow rule. A strain equivalent formulation is utilized in the damage model that permits plastic and damage calculations to be uncoupled and capture the nonlinear unloading and local softening of the stress-strain response. A diagonal damage tensor is defined to account for the directionally dependent variation of damage. However, in composites it has been found that loading in one direction can lead to damage in multiple coordinate directions. To account for this phenomena, the terms in the damage matrix are semi-coupled such that the damage in a particular coordinate direction is a function of the stresses and plastic strains in all of the coordinate directions. The overall framework is driven by experimental tabulated temperature and rate-dependent stress-strain data as well as data that characterizes the damage matrix and failure. The developed theory has been implemented in a commercial explicit finite element analysis code, LS-DYNA®, as MAT213. Several verification and validation tests using a commonly available carbon-fiber composite, Toyobo’s T800/F3900, have been carried and the results show that the theory and implementation are efficient, robust and accurate.
ContributorsHoffarth, Canio (Author) / Rajan, Subramaniam D. (Thesis advisor) / Goldberg, Robert (Committee member) / Neithalath, Narayanan (Committee member) / Mobasher, Barzin (Committee member) / Liu, Yongming (Committee member) / Arizona State University (Publisher)
Created2016
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 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.
ContributorsChandrasekhar, Vishal (Author) / Liu, Yongming (Thesis advisor) / Oswald, Jay (Committee member) / Jiang, Hanqing (Committee member) / Arizona State University (Publisher)
Created2016
Description
A method for modelling the interactions of dislocations with inclusions has been developed to analyse toughening mechanisms in alloys. This method is different from the superposition method in that infinite domain solutions and image stress fields are not superimposed. The method is based on the extended finite element method (XFEM) in which the dislocations are modelled according to the Volterra dislocation model. Interior discontinuities are introduced across dislocation glide planes using enrichment functions and the resulting boundary value problem is solved through the standard finite element variational approach. The level set method is used to describe the geometry of the dislocation glide planes without any explicit treatment of the interface geometry which provides a convenient and an appealing means for describing the dislocation. A method for estimating the Peach-Koehler force by the domain form of J-integral is considered. The convergence and accuracy of the method are studied for an edge dislocation interacting with a free surface where analytical solutions are available. The force converges to the exact solution at an optimal rate for linear finite elements. The applicability of the method to dislocation interactions with inclusions is illustrated with a system of Aluminium matrix containing Aluminium-copper precipitates. The effect of size, shape and orientation of the inclusions on an edge dislocation for a difference in stiffness and coefficient of thermal expansion of the inclusions and matrix is considered. The force on the dislocation due to a hard inclusion increased by 8% in approaching the sharp corners of a square inclusion than a circular inclusion of equal area. The dislocation experienced 24% more force in moving towards the edges of a square shaped inclusion than towards its centre. When the areas of the inclusions were halved, 30% less force was exerted on the dislocation. This method was used to analyse interfaces with mismatch strains. Introducing eigenstrains equal to 0.004 to the elastic mismatch increased the force by 15 times for a circular inclusion. The energy needed to move an edge dislocation through a domain filled with circular inclusions is 4% more than that needed for a domain with square shaped inclusions.
ContributorsVeeresh, Pawan (Author) / Oswald, Jay (Thesis advisor) / Jiang, Hanqing (Committee member) / Liu, Yongming (Committee member) / Arizona State University (Publisher)
Created2016