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Applied Mechanics Commons

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Articles 1 - 9 of 9

Full-Text Articles in Applied Mechanics

Finite Strain Micromorphic Elasticity, Elastoplasticity, And Dynamics For Multiscale Finite Element Analysis, Farhad Shahabi Jan 2017

Finite Strain Micromorphic Elasticity, Elastoplasticity, And Dynamics For Multiscale Finite Element Analysis, Farhad Shahabi

Civil Engineering Graduate Theses & Dissertations

This study stands as an attempt to consider the micro-structure of materials in a continuum framework by the aid of micromorphic continuum theory in the sense of Eringen. Since classical continuum mechanics do not account for the micro-structural characteristics of materials, they cannot be used to address the macroscopic mechanical response of all micro-structured materials. In the "representative volume element (RVE)" based methods, classical continuum mechanics may be applied to analyze mechanical deformation and stresses of materials at the relevant micro-structural length-scale (such as grains of a polycrystalline metal, or sand, or metal matrix composite, etc), but when applying standard ...


Hierarchical Multiscale Modeling To Inform Continuum Constitutive Models Of Soils, Erik Wallace Jensen Jan 2017

Hierarchical Multiscale Modeling To Inform Continuum Constitutive Models Of Soils, Erik Wallace Jensen

Civil Engineering Graduate Theses & Dissertations

The behavior of soils is fundamentally the combined interactions between billions and billions of individual particles and particle matrices. For computational tractability and despite this fact, many soil models assume the material is a continuum essentially averaging the inter-particle interactions to predict the behavior of the bulk material. In recent years, multiscale modeling techniques have been developed to reintroduce the effect of the grain-scale interactions to help model situations where the continuum assumption fails, such as shear band development in triaxial tests or soil disaggregation under blast loading. One of such multiscale models called hierarchical upscaling, or global-local analysis, model ...


Dimensionality Detection And The Geometric Median On Data Manifolds, Lukas Ruediger Nelson Goetz-Weiss Jan 2017

Dimensionality Detection And The Geometric Median On Data Manifolds, Lukas Ruediger Nelson Goetz-Weiss

Applied Mathematics Graduate Theses & Dissertations

In many applications high-dimensional observations are assumed to arrange on or near a low-dimensional manifold embedded in an ambient Euclidean space. In this thesis, ideas from differential geometry are extended to equation-free data analysis to better understand high-dimensional datasets. In particular, two questions are addressed: (1) how can the intrinsic dimensionality of a manifold-valued dataset be determined? and (2) how can this intrinsic dimensionality be leveraged to obtain a better notion of centrality? For (1), two common methods for estimating global dimensionality are stated and a novel approach is proposed to obtain an estimator for local dimensionality. Then, for (2 ...


Effects Of Multilayer Network Interactions On Neural Network Dynamics, Yogesh Virkar Jan 2017

Effects Of Multilayer Network Interactions On Neural Network Dynamics, Yogesh Virkar

Computer Science Graduate Theses & Dissertations

Networks of excitable units are found in varied disciplines such as social science, neuroscience, genetics, epidemiology, etc. Previous studies have shown that some aspects of network function can be optimized when the network operates in the 'critical regime', i.e., at the boundary between order and disorder where the statistics of node excitations correspond to those of a classical branching process. In this thesis, we introduce and study a mathematical model of a neural network with the goal of understanding the long-standing problem of determining the mechanisms by which a neural network regulates its activity so as to operate in ...


Algebraic Multigrid(Amg) For Graph Laplacian Linear Systems: Extensions Of Amg For Signed, Undirected And Unsigned, Directed Graphs, Alyson Lindsey Fox Jan 2017

Algebraic Multigrid(Amg) For Graph Laplacian Linear Systems: Extensions Of Amg For Signed, Undirected And Unsigned, Directed Graphs, Alyson Lindsey Fox

Applied Mathematics Graduate Theses & Dissertations

Relational datasets are often modeled as an unsigned, undirected graph due the nice properties of the resulting graph Laplacian, but information is lost if certain attributes of the graph are not represented. This thesis presents two generalizations of Algebraic Multigrid (AMG) solvers with graph Laplacian systems for different graph types: applying Gremban’s expansion to extend unsigned graph Laplacian solvers to signed graph Laplacian systems and generalizing techniques in Lean Algebraic Multigrid (LAMG) to a new multigrid solver for unsigned, directed graph Laplacian systems.

Signed graphs extend the traditional notion of connections and disconnections to in- clude both favorable and ...


On The Role Of Cell Distribution In Hydrolytically Degradable Hydrogels For Tissue Engineering, Gaspard De Roucy Jan 2016

On The Role Of Cell Distribution In Hydrolytically Degradable Hydrogels For Tissue Engineering, Gaspard De Roucy

Civil Engineering Graduate Theses & Dissertations

Degradable hydrogels have recently become prominent materials in the field of tissue engineering. They can be submitted to two degradation process: hydrolytic and enzymatic. For hydrolytically degradable systems, results seem to differ between samples. Yet the reasons for such a phenomenon have not been clearly understood. The objective of this thesis is to establish a multiscale model for such hydrogels. With the hypothesis that cross-linking density varies within a cell-seeded hydrogel, the present thesis aims to interpret experimental results to model and predict their behavior. First, a three-dimensional cell distribution is generated based on the analysis of experimental microscopy images ...


Smart Surface Wrinkling Enabled By Shape Memory Polymers, Yu Wang Jan 2016

Smart Surface Wrinkling Enabled By Shape Memory Polymers, Yu Wang

Mechanical Engineering Graduate Theses & Dissertations

In this dissertation, we demonstrate self-assembly fabrication methods for programmable global and localized surface wrinkling by utilizing the shape memory effects of shape memory polymers (SMPs). Heat responsive SMPs, due to their capability of memorizing and recovering different shapes, can provide unique opportunities to realize smart surface wrinkling, and therefore were used as smart substrates or films. To build the bilayer film-substrate system, thin films, such as Si ribbons and aluminum films, were transferred or deposited on the surface of programmed SMP substrates. In the Si ribbon-SMP system, time and temperature dependent wrinkling formation and evolution were observed and systematically ...


Developing Optimal Mass Matrices For Membrane Triangles With Corner Drilling Freedoms, Qiong Guo Jan 2012

Developing Optimal Mass Matrices For Membrane Triangles With Corner Drilling Freedoms, Qiong Guo

Aerospace Engineering Sciences Graduate Theses & Dissertations

This thesis studies the construction of improved mass matrices for dynamic structural analysis using the finite element method (FEM) for spatial discretization. Two kinetic-energy discretization methods described in FEM textbooks since the mid-1960s lead to diagonally-lumped and consistent mass matrices, respectively. While these well-known models are sufficient to cover many engineering applications, they may fail to satisfy customized optimality conditions, such as delivering better accuracy in the low frequency (long wavelength) limit, which is important in structural dynamics and vibrations. Such gaps can be filled with a more general approach that relies on the use of mass templates. These are ...


Characterization Of Viscoelastic Behaviors In Bovine Pulmonary Arterial Tissue, Gregory James Pelkie Jan 2011

Characterization Of Viscoelastic Behaviors In Bovine Pulmonary Arterial Tissue, Gregory James Pelkie

Mechanical Engineering Graduate Theses & Dissertations

This work presents a characterization of the influence of viscoelasticity on the mechanical behavior of bovine pulmonary arteries. Stress relaxation tests are used to determine the time dependent response of bovine pulmonary tissue. Fitting this data to a modified standard linear solid model, allows a total of five independent time constants are attained, each of which describe individual time scales on which the medium has a viscoelastic response to an applied strain. These time constants are applied to an analytical model through the Boltzmann integral in order to describe the stress response to a prescribed loading strain. These results were ...