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 317 of Akerman Hall, every Tuesday at 12:20-1:20pm, unless otherwise specified. Feel free to bring your lunch!

This seminar can also be taken for credit as AEM 8500.

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

Spring 2019


Prof. Christelle Combescure, Maitre de Conferences (Associate Professsor), Universite Paris Est Marne-la-Vallée
Post-bifurcation analysis of lattices structures, methods and parameters of influence
Abstract: Thanks to their advantageous strength/weight ratio, lattices structures are becoming more and more important in today's industrial designs. Their manufacturing has now become possible due to the development of new additive manufacturing processes. These materials are highly symmetric and, as a consequence, are prompt to fail with unstable behaviors when subjected to compression loadings. Predicting the onset of instability and the associated possible deformation modes is nowadays quite common but going further towards post-bifurcation can be challenging when considering such highly symmetric structures. Yet, when an instability occurs, it does not necessarily leads to catastrophic behaviors and the instabilities can even be taken advantage of to trigger new physical characteristics in the material. Methods to study the post-bifurcation behavior of such structures will be presented along with some recent results on important factors influencing the deformation modes.

Fall 2018


Dr. Paul Plucinsky, Postdoctoral Fellow, University of Minnesota (James group)
Compatibility of phases in helical structures
Abstract: In bulk crystalline solids, the presence of compatible interfaces at microscopic scales is related to the lattice parameters describing the periodicity of their crystalline phases. Recent efforts in the tuning of such parameters to achieve compatibility of phases have led to remarkable macroscopic properties, including near-zero thermal hysteresis for such solids undergoing phase transformation. Can this line of thinking can be applied more generally? The structure of matter in many examples—in, for instance, nanoscience and biology—is that of discrete symmetries that are not inherently periodic: single wall carbon nanotubes of any chirality, BCN, GaN, MoS2, WS2, non-animal viruses such as the tail sheath of bacteriophage T4, bacterial flagella, and microtubules, to name a few. These are helical structures. In this talk, I will discuss phase transformations in helical structures and provide the  necessary and sufficient conditions on the structural parameters of the two helical phases such that they are compatible. These results provide a basis for the tuning of helical structural parameters so as to achieve compatibility of phases. Compatible helical transformations with low hysteresis and fatigue resistance would exhibit an unusual shape memory effect involving twist and possibly extension, and may have potential applications as new artificial muscles and actuators.

04-Dec-2018 — Special Time: Tuesday 12:45-1:45pm, Tate B55

Ms. Gunjan Pahlani, Graduate Student, University of Minnesota (James group)
Objective Molecular Dynamics
Abstract: One of the pervasive bottlenecks in science and engineering is the time-scale limitation of molecular dynamics (MD). Using accurate atomic forces, how do we perform an MD simulation on a large number of atoms for experimentally accessible time scales? In this work, we are developing the method of Objective Molecular Dynamics for this purpose. This is a method of simulation in which only a few (say 50-1000) atoms are actually simulated, but the full infinite set of atoms satisfy exactly the MD equations. We present a method, capable of simulating three parameter family of incompressible flows as well as compressible flow and unsteady flows. It allows us to calculate viscometric properties from a molecular-level simulation in the absence of constitutive equations, fluids in regime currently inaccessible to theory or experiment undergoing chemical reactions, high rates of shear, expansion or phase change which are far from equilibrium. We illustrate this method using Couette and Extensional flow. From a dynamical systems viewpoint, this is an (unstudied) invariant manifold of molecular dynamics. This invariant manifold provided by OMD is inherited by Boltzmann equation. We present fascinating connections with the Boltzmann equation and continuum mechanics.


Dr. Ashley Bucsek, Postdoctoral Fellow, University of Minnesota (James group)
Converting small temperature differences to electricity using ferroelectric capacitors
Abstract: The discovery of new methods of generating energy without adversely affecting the environment is the most compelling scientific problem of our time. Due to continuously rising societal needs, energy is being both consumed and wasted in increasing quantities. Roughly 60% of unrecovered waste heat is considered ”low grade” because of the difficulty of converting small temperature differences to electric or mechanical energy using conventional technologies. Yet, the abundance of natural and industrial waste heat at small temperature differences is a growing and drastically underutilized stockpile of convertible energy. We present a novel energy conversion device that converts small temperature differences to electricity using ferroelectric capacitors. Ferroelectrics undergo a first-order phase transformation between a phase that is strongly polarized and a phase that is not polarized. We use analogies between the ferroelectric phase transformation and the first-order phase transformation utilized in steam engines to discuss thermodynamic efficiency and power density. We also demonstrate the conversion capabilities of such a device, present a theoretical framework to model the circuit parameters, and discuss using phase engineering to achieve extreme cyclic repeatability.


Ms. Anna Gorgogianni, Graduate Student, Department of Civil, Environmental and Geo-Engineering, University of Minnesota (Le group)
Rate and Size Effects on Strength Distribution of Quasibrittle Structures
Abstract: In the design of engineering structures against extreme loading, such as explosions, impact, and blast, a key design parameter is the dynamic strength. The fracture strength of solids is known to depend on a range of factors such as the loading conditions, structure geometry, microstructural properties and inherent flaws. It has been shown that, at low strain rates, the failure of quasibrittle structures is featured by a damage localization mechanism. As a consequence, quasibrittle structures exhibit a size-dependent failure behavior, which transitions from quasi-plastic to perfectly brittle with an increasing structure size. Meanwhile, it is recognized that spatial fluctuations of microstructural properties could also lead to a size effect on the structural strength. Recent studies were able to capture the effect of this size-dependent failure behavior on the statistics of static strength, by a finite weakest link model. However, the weakest link model is a statistical representation of the damage localization mechanism, which has been shown to decrease with increasing loading rate. When subjected to dynamic loading, brittle and quasibrittle structures exhibit a strength enhancement and a diffused damage pattern with the initiation of many micro-fractures. This implies that the scaling behavior must vary with the applied strain rates, and the weakest-link model statistical representation of structural failure would need to gradually diminish in order to describe structural failure under dynamic loading conditions. This is achieved in the present study through the introduction of a rate-dependent length scale in the finite weakest link model, which captures the transition from localized to diffused damage with an increasing strain rate. The model’s predictions of the scaling behavior of the mean dynamic tensile strength and its standard deviation are in good agreement with the results of stochastic discrete element simulations of dynamic uniaxial tension of aluminum nitride specimens. The resulting probability distributions of the size and rate-dependent macroscopic tensile strength can be used as the input probability distributions in stochastic finite element simulations and help mitigate the mesh sensitivity of the output probability distributions of structural strength.


Mr. Krishanu Sen, Graduate Student, University of Minnesota (Elliott group)
Numerical study of instabilities for a growing aneurysm, based on the mechanics of tissue growth and remodeling
Abstract: Saccular intracranial aneurysms are a relatively common phenomenon in humans. Indeed, as much as 4% of the population develops such aneurysms in their lifetime. Most aneurysms are benign, but some will grow and rupture. When rupture does occur there is a high mortality rate.  Unfortunately, it is currently not possible to accurately predict which aneurysms are likely to rupture. Therefore, there is a need to develop improved modeling and simulation methodologies that are capable of identifying, in the early stages of aneurysm development, the characteristic signatures of aneurysms that will eventually rupture. In this work, we aim to model the mechanics of aneurysms as a tissue growth and remodeling process. Accordingly, we adopt a continuum kinematic-growth formulation for the tissue that postulates a multiplicative decomposition of the continuum deformation gradient into separate growth and elastic-deformation parts.  This is similar to many continuum models of plastic deformation.  Further, a separation of time-scales assumption is adopted such that elastic deformations may be treated as quasi-static relative to the time scale on which tissue growth evolves.  In this talk, we will first briefly review previous work on mixture theory growth models, and then we will describe the development of a custom finite element code (based on the deal.ii library) for simulating the dynamics of tissue growth in a symmetric hollow sphere subjected to controlled internal inflation.  Considering different mechanical loading rates, we aim to study the effect of tissue growth on the overall mechanical response of the sphere.  Some preliminarily results will be presented and discussed.


Dr. Subrahmanyam Pattamatta, Postdoctoral Fellow, University of Minnesota (Tadmor group and Elliott group)
Simulation of nanostructure loading at arbitrary rates: Equilibrium Maps, Time-dependent Kintetic Monte Carlo, and Superbasin Acceleration
Abstract: Due to the extreme nonconvexity of the interatomic potential energy landscape the response of nanostructures to applied loading is inherently stochastic. This complexity is addressed head-on by the construction, using a branch-following and bifurcation approach, of an "Equilibrium Map" (EM) of the nanostructure. The EM describes all of the stable and unstable states of the structure and the transitions between them at each value of applied loading. A kinetic Monte Carlo (KMC) procedure with superbasin acceleration, adapted for time-dependent rate tables, is used to simulate the response of the nanostructure at arbitrary loading rates based on its EM. The method is applied to the uniaxial compression of a nanoslab of nickel modeled using a classical interatomic potential. The set of possible equilibrium solutions for this simple problem is surprisingly complex thereby demonstrating the need for such an approach.


Dr. Youxing Chen, Postdoctoral Fellow, University of Minnesota (Mara group (CEMS))
Mechanical Manipulation of Magnesium: A study into the influence of interfaces on mechanical performance
Abstract: Magnesium (Mg) alloys, one of the most promising lightweight structural materials for automobile and aerospace applications, suffers from low strength and limited ductility at room temperature, due to a lack of available slip systems in hexagonal close-packed (hcp) structures. Improving strength without a concomitant loss of ductility is a hurdle to widespread application of Mg based materials. Rather than grain refinement or alloying with rare earth elements, our approach is to improve the strength and deformability of Mg alloys through stabilization of the bcc phase of Mg in metal laminates. Since bcc Mg can be stabilized when located between bcc Nb when the individual layer thickness is below 5 nm, the ductility is improved as bcc Mg has additional active room temperature slip systems over hcp Mg. In-situ TEM mechanical testing is a useful tool for real-time observation of deformation mechanisms at nanometer scales. Our results directly validate the hypothesis that bcc Mg can accommodate large plastic deformation and further reveal that in bcc/bcc Mg/Nb, a reversible bcc-hcp phase transformation occurs during loading and unloading. The fundamental understanding of deformation mechanisms of bcc Mg in Mg/Nb laminates are investigated utilizing a combination of experiments and modeling.

19-Oct-2018 — Special time: Friday, 9am-12pm Akerman Hall 225, 2:30-4:30pm Tate Hall 105

Special all-day event in honor of Prof. Kaushik Bhattacharya, California Institute of Technology, who is being awarded the University of Minnesota Outstanding Achievement Award. The event includes lectures by students and postdocs in the morning and presentations by President Eric Kaler, Prof. Richard James and Prof. Kaushik Bhattacharya in the afternoon. A full program is available here.


Mr. Shivam Sharma, Graduate Student, Aerospace Engineering and Mechanics, University of Minnesota
Element-wise electromagnetic modulation of Phononic Metamaterials
Abstract: Reciprocity or time reversal symmetry is a fundamental principle in wave propagation phenomena, which states that waves can symmetrically travel from one point to another in reversal manner. This is applicable in electromagnetic waves, optics, acoustic and mechanical waves. However, a growing area of interest is concerned with the breaking of the reciprocity principle for unidirectional elastic wave propagation, which can lead to the realization of acoustic systems analogous to electronic devices such as diodes. We have designed an acoustic diode and tested it experimentally. Geometric nonlinearities controlled by electromagnets are utilized at the unit cell level. Geometric nonlinearities allow the unit cell to change shape significantly while electromagnets allow dynamic tuning of the unit cell. This tuning allows for periodically modulating elastic properties of the structure in space and time. This spatiotemporal modulation of elastic modulus breaks mechanical reciprocity and induces one-way transmission of the waves, thus, enabling the structure to behave like an acoustic diode, which is analogous to an electronic diode.


Mr. Tarun Gangwar, Graduate Student, Department of Civil, Environmental and Geo-Engineering, University of Minnesota (Schillinger group)
Imaging informed multiscale modeling of plant stems
Abstract: Plant materials exhibit a wide range of highly anisotropic mechanical behavior due to a hierarchy of micro-heterogeneous structures at different length scales. A rational understanding of mechanical behavior of plant materials will open the door for the biomechanical tailoring of plants for the specific bioengineering applications. we present a micromechanics approach that derives a hierarchical microstructure driven model of macroscopic stiffness and strength properties of anisotropic culm materials. As model input, it requires mechanical properties of the base constituents such as cellulose and lignin as well as morphology and volume fractions of all heterogeneous components at each hierarchical level. The latter can be retrieved from imaging data at different length scales, obtained from scanning electron microscopy, transmission electron microscopy and computed tomography (CT). Validating the predictions of macroscopic stiffness moduli and ultimate strength for bamboo material with measurements recently reported by Dixon and Gibson (J. Royal Soc. Interface, 2014), we demonstrate that the micromechanics model provides excellent accuracy without any further phenomenological calibration. In the next step, we plan to upscale the effect of microstructure instabilities on macroscopic material behavior. The goal of the work is to simulate the lodging behavior of oats to identify the significant traits in their genome to enable breeding of lodging resistant oats. Hence, in addition to the material model, an accurate and robust characterization of geometry from imaging datasets is an essential step. For the same, we developed a generic two-stage variational image segmentation model consisting of a flux augmented Chan-Vese energy functional for coarsely resolving local geometric features and phase field fractures inspired model to automatically eliminate the fine connections between the objects. We demonstrated the capability of our model in the context of bone segmentation. Our model is able to segment clinical CT datasets for femur and vertebra bones taken at the Academic Health Center of the University of Minnesota robustly and accurately.


Prof. Jorge Viñals, School of Physics and Astronomy, University of Minnesota
A nanoscale model of plastic defect motion
Abstract: A consistent, small scale model of plastic motion in a crystalline solid is discussed which is based on a phase field description. By allowing for independent mass motion given by the phase field, and lattice distortion, the solid can remain in mechanical equilibrium on the timescale of plastic motion. Singular (incompatible) strains are determined by the phase field, to which regular distortions are added to satisfy mechanical equilibrium. A numerical implementation of the model is presented, and used to study a benchmark problem: the motion of an edge dislocation dipole in a two dimensional hexagonal lattice.


Mr. Ariel Ibarra Pino, Graduate Student, University of Minnesota (Elliott group)
Post-bifurcation of an infinite Euler-Bernoulli beam on a nonlinear elastic foundation
Abstract: Periodic architectured metamaterials are man-made heterogenous materials designed to have special properties, e.g. auxetic and fluid-like behavior. Currently, there is an interest in exploiting instabilities of such materials for certain applications (for example, buckling is used for energy trapping). It is believed that local parameters (within the periodic cell) control the onset of instabilities as well as the behavior of the material deep into the post-bifurcated regime.

The creation of a "unit cell design theory" for architecture materials will require developing an understanding of the relationships between local cell parameters, the onset of instability, and the post-bifucation behavior. In order to uncover such relationships and to accelerate the development of a unit cell theory, we revisit the classical problem of buckling of an axially loaded beam on an elastic foundation. We employ a set of analytical and numerical tools leading to bifurcation diagrams to explore the postbuckled regime of the system. Details of our computed bifurcation diagram are presented.  A systematic study of a previously unreported equilibrium solution branch and its associated bifurcation point is discussed.


Dr. Jingfu Liu, Research Engineer, Sentient Science
Multiscale modeling of metal additive manufacturing: Challenges and Opportunities
Abstract: Additive manufacturing (a.k.a. 3D printing) is revolutionizing the manufacturing industry due to the significant advantages and capabilities, including rapid prototyping, fabrication of complex geometries, reduction of product development cycles, and high utilization of material. As metal AM becomes increasingly popular, a major barrier remains to rapidly qualify additive components that will meet functional requirement dictated by original design intent. Current methods to qualify AM parts heavily rely on experimental testing, which is very expensive and time consuming. The most obvious and promising approach to obtain rapid part qualification is through extensive use of computational modeling. This seminar will discuss the updated status of advanced modeling techniques at different scales in AM process. Also, current challenges and potential opportunities will be discussed to qualify AM components through a comprehensive simulation tool.

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


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.


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.


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.


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.


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.


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.


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.


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).


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.


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.


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


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.


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.


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.


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.


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.


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


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.


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: 2019-01-18 at 10:28:02 -- this is in International Standard Date and Time Notation