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Aerospace and Mechanical Engineering
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AEM Solid Mechanics Research Seminar

The Solid Mechanics Research Seminar is a tradition in the AEM department going back to the mid 1980s. This is an informal seminar where the talks are often given on the board (although slides are fine). The speaker reports on some new and interesting topic related to solid mechanics in some depth and the audience is strongly encouraged to ask questions.

“The Solid Mechanics Research Seminar was the single most important educational experience of my graduate studies.” — Prof. Kaushik Bhattacharya (Caltech), AEM alumnus.

Talks take place in Room 321 of Mechanical Engineering, biweekly on Tuesdays at 12:00pm, unless otherwise specified. Feel free to bring your lunch!

To be informed of upcoming seminars, join the AEM Solid Mechanics Research Seminar mailing list.


Summer 2018


17-Jul-2017 — Special place: Tuesday 12:00-1:00pm, AkerH 313

Mr. Shrinidhi Pandurangi, Graduate Student, Field of Theoretical and Applied Mechanics, Cornell University
Localization of deformation in a Beam on an Elastic Foundation: Long length asymptotics and computations
Abstract: With the broader objective of understanding the phenomenon of localization of deformation in nonlinearly elastic systems, the problem of stability of a classical Euler-Bernoulli beam on a nonlinear elastic foundation under axial compressive load is considered. In the first part of the talk, the initial post-critical behaviour of long length beams near the primary bifurcation point is discussed using a multi-scale perturbative expansion. Asymptotic analysis of the symmetric and the antisymmetric modes of deformation of the beam is presented for the limiting cases when the beam lengths become very large but stay finite.

In the second part, the global post-buckling regime of an infinitely long beam is investigated by applying a systematic numerical continuation method. Using a finite element discretization of the beam-foundation system subjected to appropriate periodic boundary conditions, a computational approach is discussed to calculate bifurcation paths leading to stable localized deformations. A parametric study is used to explore the effects of different nonlinear foundations (hardening, softening and restabilising). A representative sample of the resulting bifurcation diagrams and stability results are presented.


Spring 2018


01-May-2018

Dr. Ashley Bucsek, Postdoctoral Fellow, University of Minnesota (James group)
Elucidating deformation mechanisms in shape memory alloys using 3D X-ray diffraction
Abstract: In the case of shape memory alloys (SMAs), fundamental micromechanical theory has been an active area of research for more than 70 years. However, experiments to validate these theories on the microstructural scale are relatively new, challenging, and often limited to two-dimensional surface measurements. To address this open area, I utilize cutting-edge in situ synchrotron X-ray techniques such as near-field and far-field 3D X-Ray Diffraction (3DXRD) and Dark-Field X-Ray Microscopy (DFXM). Using these techniques, I present results from three particular experiments on NiTi SMAs: (1) A forward model algorithmic approach to indexing martensite in two-phase 3DXRD data is used to inform the use of martensite prediction criteria in modeling; (2) A full understanding of the relationships between microstructure evolution, deformation mechanisms, and macroscopic behavior is reported for reversible twin rearrangement (a.k.a. martensite reorientation); (3) The topology, misorientation, and elastic strains inside an austenite single crystal during thermally-induced transformation are shown with a spatial resolution of 100 nm. These three studies demonstrate how three-dimensional in situ diffraction techniques can be used to make huge leaps in our understanding of advanced materials and advanced deformation mechanisms.

24-Apr-2018

Mr. Jiadi Fan, Graduate Student, University of Minnesota (Tadmor group)
Molecular dynamics simulation of the epoxy crosslinking process
Abstract: A methodology to build cross-linked atomistic structures for epoxy is presented. The methodology is based on a polymerization molecular dynamics (MD) scheme in which monomers are allowed to react with each other during an MD simulation. The criteria for forming chemical bonds is based on distances between prespecified reactive atoms on the monomers and growing polymer chains. A brief review of force fields (FFs) is also presented, the philosophy of various kinds of FFs is introduced, the advantage and disadvantage of several commonly used FFs are also discussed. As an example, the crosslinking process of DGEBA/D230 epoxy is simulated using the LAMMPS MD code with the Dreiding FF. The density, glass transition temperature (Tg), and Young's modulus of epoxy at different crosslinking conversion are calculated and compared with experimental data.

17-Apr-2018

Mr. Andrew Vechart, Graduate Student, University of Minnesota (Elliott group)
Application of group-theoretic techniques for efficient numerical branch following and robust bifurcation analysis
Abstract: Numerical branch following techniques are employed to efficiently determine solution paths of non-linear systems as a parameter is varied.  For equivariant equations, solution paths with nontrivial symmetry lie within an invariant subspace, called the fixed point space.  At symmetry-breaking bifurcation points, the Jacobian becomes singular.  Conveniently, this singularity is orthogonal to the fixed point subspace and one can construct the symmetry reduced problem on the fixed point space to solve a lower dimensional system of equations without singularity.  However, in practice the explicit construction of the reduced problem is computationally prohibitive for many problems of interest.  As an alternative, we are investigating algorithms that operate on the complete space but exploit symmetry information to improve their efficiency.  In this context, Krylov methods are attractive because they will naturally work within the fixed point space.  The robustness of such algorithms must be carefully considered because their numerical implementation (using floating-point math) may lead to departures from the fixed point space that could adversely affect convergence near singular points.  This work considers the implications of using Krylov-based solvers (e.g. GMRES) in the typical Newton-Raphson corrector step of branch following algorithms for symmetric systems.

10-Apr-2018

Prof. Basile Audoly, Professor at LMS/École Polytechnique and Senior researcher at CNRS, France
A geometric method for simulating the dynamics of thin elastic rods and viscous threads
Abstract: Rigid bars connected by elastic hinges are a popular model for demonstrating instabilities of planar elastic beams, such as elastic buckling (with one bar, one hinge and an axial load), or flutter instabilities (with two bars, two hinges and a follower force). By extending this planar set-up to three dimensions, we derive a discrete rod model. It is primarily defined in a discrete setting, which makes it appealing for simulations; it is also consistent with the classical theory of (continuous) beams when the length of the bars goes to zero. The 3d rotations of the directors, the bending and the twisting of the rod are represented based on ideas derived from discrete differential geometry. A detailed derivation of the model is proposed, the similarity and differences with the finite-element method are highlighted, and some applications to thin elastic rods and thin viscous threads are presented.

03-Apr-2018

Dr. Kuan Zhang, Postdoctoral Fellow, University of Minnesota (Tadmor group)
Multiscale simulation of 2D heterostructures: Structural and electron diffraction scaling of twisted graphene bilayers
Abstract: Layered heterostructures formed by stacking two-dimensional (2D) materials are attracting considerable attention with remarkable properties. The registry-dependent nature of the van der Waals interactions between the layers can drive incommensurate to commensurate structural transitions complicating the mechanical and electronic behavior. We have developed a multiscale framework for simulating the mechanical response of 2D heterostructures. We use this method to study the structural relaxation in twisted graphene bilayers, which involves a localized rotation and shrinking of AA domains that scales in two regimes with the imposed twist. For small twisting angles, the localized rotation tends to a constant; for large twist, the rotation scales linearly with it. The results are validated experimentally through comparison to a simulated electron diffraction analysis of the relaxed structures. We predict a complex electron diffraction pattern involving the appearance of weak satellite peaks in the small twist regime. The mechanism of this new phenomenon is found to be intimately tied to the scaling behavior, and explained by using an analytical model in which the relaxation kinematics are described as an exponentially-decaying (Gaussian) rotation field centered on the AA domains. Both the angle-dependent scaling and diffraction patterns are in quantitative agreement with experimental observations.

27-Mar-2018

Prof. Dionisios Margetis, Professor, University of Maryland
The trouble with crystal facets: A continuum-scale problem, with a touch of discreteness
Abstract: Recent advances in materials science enable the observation and control of microstructures such as line or point defects with remarkable precision. In this talk, I will discuss recent progress and open challenges in understanding how microscopic details in the kinetics of crystal surfaces can macroscopically influence the surface morphological evolution. In particular, the talk will explore via selected examples how the kinetics of microscale defects near surface plateaus, facets, can leave their imprints at larger scales.

20-Mar-2018

Prof. John Ball, Sedleian Professor of Natural Philosophy, Mathematical Institute, University of Oxford, UK
Remarks on incompatible and compatible sets of matrices
Abstract: The talk will discuss various results (mostly drawn from joint work with R.D James) concerning compact sets of matrices that are compatible or incompatible for gradient Young measures, with connections to metastability in martensitic phase transformations.

06-Mar-2018

Prof. Brad Holschuh, Assistant Professor, University of Minnesota
Soft robotics using shape memory materials for wearable technology applications
Abstract: Soft robotics — an emerging field that seeks to create actuated systems using non-rigid materials — enables the design and characterization of broad new categories of physically-dynamic wearable systems. Traditional wearable robotic systems (e.g., rigid exoskeletons) primarily rely on hydraulic or servo-style actuators to create forces and displacements on the body; soft robotic systems eschew these rigid structures, offering similar functional benefits to the wearer in a superior, compliant, and often perceptually-invisible form factor. In this talk I will present work from the University of Minnesota's Wearable Technology Laboratory (WTL) investigating the use of soft robotic shape memory systems for on-body actuation. This talk will focus both on technology development (e.g., linear and two-dimensional actuation structures) and systems design for a variety of wearable technology applications (e.g., medical devices to improve lower body circulation, EVA/IVA systems for astronaut health and performance, behavioral interventions for autistic children, and shape-changing clothing for everyday consumer use).

27-Feb-2018

Prof. Liping Liu, Associate Professor, Rutgers University
Optimal bounds and optimal microstructures for multiphase composites
Abstract: This talk will focus on an optimal design problem for multiphase composites. Mathematically, this optimal design problem is equivalent to the quasi-convexification of a multi-well energy function and is addressed by an indirect method. That is, a microstructure-independent bound is first derived for the effective energy function, and then, an optimal microstructure is explicitly constructed to attain this bound. Both directions can be quite non-trivial and are not fully solved for composites of three or more phases.

In the first part of the talk, I will present a new method of deriving the Hashin-Shtrikman bounds for multiphase composites which turn out to be the best known bounds. This method conveniently yields the optimality conditions for microstructures. Secondly, we show the optimality conditions cannot always be satisfied for composites of three or more phases. In particular, we find an explicit necessary and sufficient conditions for the optimality of the Hashin-Shtrikman bounds for three-phase isotropic conductive composites of isotropic materials. Finally, we present a necessary condition for smooth optimal microstructures and propose some open problems that may be of interest to analysts.

20-Feb-2018

Mr. Eduardo Vitral, Postdoctoral Fellow, University of Minnesota (Leo group)
Curvature driven evolution of a smectic liquid crystal out of thermodynamic equilibrium
Abstract: We introduce a mesoscale model of a complex fluid to study the two phase interface separating a layered phase of uniaxial symmetry from an isotropic phase. The model is used to derive capillary and elastic contributions to local equilibrium conditions at deformed interfaces (generalized Gibbs-Thomson relations), extra stresses and their contribution to flow, and the nonequilibrium equations governing interfacial motion. Particular attention is paid to often neglected surface invariants such as the Gaussian curvature, and its role in driving changes of topology of the interface during its evolution. The methodology also lends itself to large scale computational analysis, with a parallel implemented pseudo-spectral approach. Focal conics are verified to be equilibrium shapes for the proposed phase field description. Our study is motivated by recent experiments on surface instabilities of toroidal focal conic domains in smectic films, and preliminary out of equilibrium results are shown to match some of the experimentally observed morphologies.

06-Feb-2018

Dr. Paul Plucinsky, Postdoctoral Fellow, University of Minnesota (James group)
"Active" thin and slender structures: A case study in nematic elastomer sheets
Abstract: Thin structures exhibit a broad range of mechanical responses as the competition between stretching and bending in these structures can result in buckling and localized deformations like folding and tension wrinkling. Active materials also exhibit a broad range of mechanical responses as features that manifest themselves at the microscale in these materials result in mechanical couplings at the engineering scale (thermal/electrical/dissipative) and novel function (e.g., the shape memory effect and piezoelectricity in select metal alloys and the immense fracture toughness of hydrogels). Given this richness in behaviors, my research broadly aims to address the following questions: What happens when active materials are incorporated into thin structures? Do phenomena inherent to these materials compete with or enhance those inherent to thin structures? Does this interplay result in entirely new and unexpected phenomena? And can all this be exploited to design new functions in engineering systems?

In this talk, we explore these questions in the context of a theoretical study of thin sheets of nematic liquid crystal elastomer. These materials are active rubbery solids made of cross-linked polymer chains that have liquid crystals either incorporated into the main chain or pendent from them. Their structure enables a coupling between the mechanical elasticity of the polymer network and the ordering of the liquid crystals, and this in turn results in fairly complex mechanical behavior including large spontaneous distortion due to temperature change, soft-elasticity and fine-scale microstructure.

We study thin sheets of nematic elastomer. First, we show that thin of sheets of a particular class of nematic elastomer can resist wrinkling when stretched. Second, we show that thin sheets of another class of nematic elastomer can be actuated into a multitude of complex shapes. In order to obtain these results, we systematically develop two dimensional theories for thin sheets starting from a well-accepted first principles theory for nematic elastomers. These characterize (i) the mechanical response due to instabilities such as structural wrinkling and fine-scale material microstructure, and (ii) thermal actuation of heterogeneously patterned sheets. For the latter, we show that the theory, which comes in the form of a two dimensional metric constraint, admits two broad classes of designable actuation in nonisometric origami and lifted surface. For the former, we show that taut and appreciably stressed sheets of nematic elastomer are capable of suppressing wrinkling by modifying the expected state of stress through the formation of microstructure. 



Previous talks appear below


Fall 2017


21-Nov-2017

Mr. Mingjian Wen, Graduate Student, University of Minnesota (Tadmor group)
Development of Interatomic Potentials for 2D Heterostructures
Abstract: Two-dimensional (2D) heterostructures created by stacking 2D materials are unique materials whose properties are controlled by the stacking order and orientation. To understand 2D heterostructures and accelerate the development of innovative nanotechnological devices based on these materials, molecular simulations with highly-accurate interatomic potentials are needed. Such potentials should not only provide an accurate description of the interactions within layers but also between layers as those play a vital role in defining the functionality of many 2D heterostructures. Using state-of-the-art data analytics, machine learning, and informatics, we are developing a fitting framework for automatically generating interatomic potentials for 2D heterostructures. In this talk I will discuss two potentials that have been developed: (1) a potential for molybdenum-disulfide based on a Fisher information theory analysis to gauge parameter sensitivity and model uncertainty; and (2) a bond-order interlayer potential for graphitic systems that accurately represents the energy and forces for stacking states that previous interlayer potentials cannot distinguish.

07-Nov-2017

Ms. Hanlin Gu, Graduate Student, University of Minnesota (James group)
Cofactor conditions in developing highly reversible martensitic phase transformations
Abstract: Highly reversible phase transformation has been studied successfully using cofactor conditions (supercompatibility conditions between austenite and martensite phases). By forming perfect interfaces between austenite and martensitic microstructure, the reversibility is tremendously improved in different metallic alloy systems, reported by Eckhard Quandt (10 million tensile cycles of NiTiCuCo alloy) and Xian Chen (100,000 compressive cycles of AuCuZn). In this talk, I will discuss our recent results about how cofactor conditions play a role in reversibility for uniaxial tensile stress induced phase transformation for polycrystalline material. And in special cases, cubic to orthorhombic and cubic to monoclinic phase transformation, a further simplified form of cofactor conditions based on eigenvalues and eigenvectors of transformation stretch matrices is investigated. The simplified form provides a visual way to understand cofactor conditions.

24-Oct-2017

Prof. Hanuš Seiner, Associate Professor, Institute of Thermomechanics, Czech Academy of Sciences, Prague
Highly mobile interfaces in shape memory alloys
Abstract: The lecture will summarize the most recent experimental and theoretical findings related to the topic of highly mobile interfaces, i.e. twin interfaces in shape memory alloys that are able to be set into motion under as small stresses as 0.01 MPa. It will be shown that these interfaces exhibit extremely complex morphologies involving many different scales of lamination, which opens new questions and new challenges for mathematical modelling. The current description of the highly mobile interfaces within the well-established mathematical theory of martensitic microstructures gives satisfying explanations of the experimentally observed morphologies, but does not provide any direct explanations of the high mobility itself. For this reason, kinematic multiscale models are nowadays developed, enlightening the relation between the morphology and the mobility. These models require deeper understanding of the mechanisms acting at all involved lengthscales, especially at the atomistic scale, where the formation of specific microstructures (modulations) is driven by quantum-mechanics effects.

10-Oct-2017

Dr. Vivek Dabade, Postdoctoral Scholar, University of Minnesota (James group)
Micromagnetics of Galfenol
Abstract: We present the micromagnetics of soft cubic ferromagnets with large magnetostriction, with the goal of understanding the single crystal Galfenol samples recently reported by Chopra and Wuttig. Taking first the no-exchange formulation of the micromagnetics energy, we construct minimizing sequences that yield local average magnetization and strain curves matching the experimental findings. Reintroducing then a sharp-interface version of the exchange energy, we pursue quantitative constructions to derive optimal energy scaling laws for the ansatz of normal and zig-zag Landau states; within the parameter regime of Galfenol, we show that the latter achieves lower energy scaling via equipartition of energy between the 90 degree wall energy, 180 degree wall energy, and the anisotropy energy. This forms the first step in adapting the program of Kohn and Müller to explain why certain magnetic microstructures are observed over others.

28-Sep-2017 — Special time: Thursday 12-1pm, Nolte Center 140

Prof. Alexander Shapeev, Assistant Professor, Center for Data-Intensive Science and Engineering, Skolkovo Institute of Science and Technology (Skoltech), Moscow, Russia
Machine-learning interatomic potentials
Abstract: Molecular simulations are the largest consumer of supercomputing time worldwide. Molecular simulations rely on one of the two models: accurate and very computationally expensive quantum-mechanical models, most notably the density functional theory, and empirical interatomic potentials that postulate a simple functional form of interatomic interaction that is fast to compute. Machine learning interatomic potentials (MLIPs) has recently been put forward as a promising methodology of combining the quantum-mechanical accuracy and the computational efficiency of the empirical potentials. MLIPs postulate a functional form that is fast to compute, yet flexible enough to be able to represent arbitrary interatomic interactions.

In my talk I will give an overview of the existing developments in the field of MLIPs, present the MLIPs developed in my group, and finally show how active learning can ensure reliability of such potentials. I will illustrate applications of such potentials in molecular dynamics, crystal structure prediction, prediction of alloy phase diagrams, and cheminformatics.

26-Sep-2017

Dr. Ananya Renuka Balakrishna, Postdoctoral Fellow, Department of Materials Science and Engineering, Massachussetts Institute of Technology (MIT)
Phase field modeling of microstructural evolution
Abstract: The current trend of miniaturization in the electronics and the energy storage device industries has advanced research interests in material properties at the fine scale. Understanding the evolution of microstructures would provide insights on how to control and engineer nanoscale material properties. In this talk, I will provide an overview on the use of phase field models to investigate microstructural evolution in two material systems: ferroelectrics and lithium battery electrodes. First, I will present phase field modeling of electro-mechanically coupled systems and demonstrate the model's application to design nanoscale ferroelectric device concepts. Second, I will introduce my recent work on transformation based phase field crystal modeling approach, which couples lattice symmetry with phase composition. I explore an application of this model to describe phase transformation in lithium battery electrodes.

12-Sep-2017

Mr. Fan Feng, PhD Student, University of Minnesota (James group)
Deformable Helical Miura Origami inspired by Phase Transformation
Abstract: Origami is an ancient art form about folding paper that originated in China, but was refined in Japan. From the point of view of solid mechanics, the deformation y: Omega -> R^3 from the reference sheet to the folded configuration, is a continuous isometric homotopy, which allows jumps of the deformation gradient at the fold lines. A helical Miura-ori (HMO) is an origami cylinder built by using an Abelian helical isometry group. An example is the Yoshimura pattern. We give a general method of constructing HMO structures, and we comment on their rigidity. Inspired by the theory of phase transformations in helical structures that we have developed, we construct compatible interfaces between two phases of an HMO. By transforming one phase to the other, and despite the generic rigidity, we can approximate deformable helical Miura-ori.


Summer 2017


21-Jul-2017 — Special day and time: Friday 1:30-2:30pm, AkerH 227

Prof. Shakti Gupta, Associate Professor, Indian Institute of Technology, Kanpur
Carbon nanostructures: Molecular simulations, continuum models and some related issues
Abstract: Continuum hypothesis based properties, for example, elastic modulli or thermal conductivity of a material at small lengths scale can be derived efficiently using molecular mechanics or dynamics. While doing so one makes a few key assumptions and develops what are called as equivalent continuum structures (ECSs). Accuracy of the derived quantity for a given structure thus depends strongly on its ECS. In this talk we will first present development of ECSs for single-walled carbon nanotubes (SWCNTs) and graphene based on the theory of linear vibrations and show instances when these ECSs may fail or behave counterintuitively. Subsequently, results from two methods leading to conflicting values of critical buckling strain in SWCNTs under compression will be presented. Lastly, we will present some very recent results on instabilities in carbon nanocone stacks.

29-Jun-2017 — Special day and time: Thursday 4:00-5:00pm, AkerH 227

Dr. Anton Muehlemann, Postdoctoral Fellow, University of California, Berkeley
New Theory for the Morphology of Lath Martensite
Abstract: Using the framework of the Ball-James model we propose a new theory to predict features of the (557) and (111) lath transformation observed in low-carbon steels. Our approach generates a one-parameter family of possible habit plane normals and a selection mechanism then identifies the (557) and (111) normals as those arising from a deformation with small atomic movement and maximal compatibility. Compared to existing theories which require 7 or more fitted parameters our theory only uses the assumption of energy minimisation and compatibility. Interestingly, the theory predicts that a type of twinning mechanism is involved - instead of the commonly proposed high dislocation density.

17-May-2017 — Special day and time: Wednesday 2:30-3:30pm, AkerH 227

Prof. Prashant Purohit, Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania
DNA phase transitions and fluctuations of lipid bilayers
Abstract: Experimental studies on single molecules of DNA have reported a rich variety of structural transitions, including coexistence of three phases, in a torsionally constrained molecule. A comprehensive knowledge of these structural transitions is useful for unraveling the in vivo and in vitro behavior of DNA. Our objective is to understand the structural transitions in a torsionally constrained DNA molecule when it is pulled using optical or magnetic tweezers. We use foundational concepts from the Zimm-Bragg helix-coil transition theory and merge them with ideas from the theory of fluctuating elastic rods to model the mechanics of DNA. We also account for the electrostatic interactions between the ions and the negatively charged phosphate backbone of DNA. Using our model we calculate the force and torque corresponding to the over-stretching transition characterized by a 70% jump in the contour length of the molecule and examine the effect of salt concentration on this transition. We also deduce conditions under which the co-existence of B-, S- and P-DNA is possible. We examine how the cooperativity parameter for each transition affects the force-extension curve or torque-rotation curve. We attempt to rationalize the non-monotonic dependence of external work done on the ion concentration by connecting it to the electrostatic dependence of the interfacial energy between two phases of DNA. As a second topic we will consider thermal fluctuations of lipid bilayer membranes. Typically, membrane fluctuations are analyzed by decomposing into normal modes or by molecular simulations. We propose a new approach to calculate the partition function of a membrane. We view the membrane as a fluctuating elastic plate and discretize it into triangular elements. We express its energy as a function of nodal displacements, and then compute the partition function and covariance matrix using Gaussian integrals. We recover well-known results for the dependence of the projected area of the membrane on the applied tension and recent simulation results on the dependence of membrane free energy on geometry, spontaneous curvature and tension. As new applications we compute elastic and entropic interactions of inclusions in membranes.


Spring 2017


21-Feb-2017

Prof. Robert Lipton, Department of Mathematics, Louisiana State University
Double Well Potentials and Nonlocal Brittle Fracture Modeling
Abstract: The dynamic fracture of brittle solids is a particularly interesting collective interaction connecting both large and small length scales. Apply enough stress or strain to a sample of brittle material and one eventually snaps bonds at the atomistic scale leading to fracture of the macroscopic specimen. We discuss a nonlocal mesoscopic model for calculating dynamic fracture. The force interaction is derived from a double well strain energy density function, resulting in a non-monotonic material model. The material properties change in response to evolving internal forces eliminating the need for a separate phase field to model the fracture set. The model can be viewed as a regularized fracture model. In the limit of zero nonlocal interaction, the model recovers a sharp interface evolution characterized by the classic Griffith free energy of brittle fracture with elastic deformation satisfying the linear elastic wave equation off the crack set. We conclude with a brief numerical analysis of the model which is joint work with Prashant Jah.

07-Mar-2017 — Special time: 1:00-2:00pm, AkerH 319

Prof. Nilima Nigam, Department of Mathematics, Simon Fraser University
Localized activation and intramuscular fat in muscle: an investigation using DG methods
Abstract: The response of the muscle-tissue unit (MTU) to activation and applied forces is affected by the architectural details as well as the material properties of this nearly-incompressible tissue. We will describe the (highly nonlinear) elastic equations governing this response for a fully three-dimensional, quasi-static, fully nonlinear and anisotropic MTU. We describe a three-field formulation for this problem, and present a DG discretization strategy. The scheme was implemented using {\tt deal.ii}. We present computational results about the effects of localized activation as well as the effects of fatty tissue on muscle response. This is joint with Sebastian Dominguez, Hadi Rahemi, David Ryan and James Wakeling.

21-Mar-2017 — Special time: 1:00-2:00pm, AkerH 319

Dr. Prashant Jha, Department of Mathematics, Louisiana State University
Coarse Graining of Electric Field Interactions with Materials
Abstract: In this work, we present our continuum limit calculations of electrical interactions in ionic crystals and dielectrics. Continuum limit calculations serve two main purposes. First, they give an idea of how the macroscopic behavior of the material is related to the interactions at the atomistic scale. Second, they help in developing a multiscale numerical method, where the goal is to model the material both at the scale of atoms and at the macroscale. We consider two important settings: nanorod-like materials, where the thickness of a material in the lateral direction is of the order of the atomic spacing, and the materials, where atoms are randomly fluctuating due to the thermal energy. Our calculations, for the nanorod-like materials, show that the electrostatics energy is not long-range in continuum limit. We also consider the discrete system of dipole moments along the straight line and along the helix. We then compute the limit of the energy as the separation between the dipole moments tends to zero. The energy, in the continuum limit, is short-range in nature. This agrees with the calculations of Gioia and James for the magnetic thin films. We consider the system of atoms which are fluctuating due to thermal energy. We model the charge density field as a random field and compute the continuum limit of the electrostatics energy.

18-Apr-2017

Prof. Ryan Elliott, AEM, University of Minnesota
A Framework for Frequently Occurring Generically Non-Generic Degeneracies
Abstract: The occurrence of generic degeneracies in physical systems is closely related to underlying symmetries of the governing equations. The occurrence of additional non-generic degeneracies which cannot be accounted for by usual symmetry arguments is usually termed as accidental. In this work, we formulate a mechanistic framework which helps identify and investigate a particular class of degeneracies associated with equivariant systems under certain common symmetry groups. We show that the existence of a first-integral for such systems (i.e., a potential function or energy functional) along with certain mathematical properties of such symmetry groups guarantees generically that non-generic degeneracies in the spectrum of the Jacobian of the governing equations (and likely other properties of the system) occurs. We apply our theory to three common physical systems and show that it successfully explains the "accidental" degeneracy found in (1) the stiffness matrix associated with truss structures having cyclic symmetry, (2) electronic properties of periodic, cyclic and helical structures without inversion symmetry, and (3) the elastic constants matrix in the theory of linear elasticity.

Last Modified: 2018-08-16 at 16:48:00 -- this is in International Standard Date and Time Notation