Our research is focused on field-coupled solid mechanics and fluid structure interactions of materials and adaptive structures for a variety of applications including energy, robotics, and aerospace.  Material modeling research ranges from quantum to continuum length scales and integrates uncertainty analysis techniques such as Bayesian statistics to help assess material models in light of data to explain complex material physics.  Combinations of theory, scientific computing, and experimental methods are utilized to understand materials ranging from ferroelectric ceramics, sapphire at extreme temperatures and laser exposure, and polymers that respond mechanically to electric fields and light. 

In addition to materials research, we are interested in applying materials to a variety of sensor and actuator applications.  For example, materials research applied to sapphire laser machining is under investigation to facilitate the design of high temperature pressure transducers (up to nominally 1400C) for gas turbine and structural health monitoring of space and hypersonic vehicles.  We are also working towards integrating soft electroactive elastomers into legged robotic platforms to dramatically change the stiffness (order of 100%) on time scales commensurate with the leg motion (1-10 Hz).  We are collaborating to develop embedded sensors and actuators for advanced flow control and fluid-structure models to understand structural dynamics of deformable bodies in the compressible flow regime.

Matlab Tutorials and Code

A major component of our research focuses on using probability to better understand the assumptions that go into constitutive models and structure models.  Specifically we use Bayesian statistics to analyze uncertainty in model parameters that are compared with materials experiments or adaptive structure data.  Uncertainty analysis is well known in areas such as nuclear reactor design, weather prediction, climate models, and hydrology.  Less efforts have focused on using such methods to understand material physics.  We have been applying Markov Chain Monte Carlo (MCMC) methods using the Delayed Rejection Adaptive Metropolis (DRAM) numerical algorithms (freely available here) to quantify model parameter uncertainty in models ranging from quantum informed ferroelectric continuum models, thermoacoustics of conducting membranes, and nonlinear viscoelasticity of membranes. 

Below is a description of select research projects.

Quantum-informed Nonlinear Mechanics

This research aims to integrate quantum relations into a field-coupled continuum model to predict the behavior of ferroelectric materials and other electrically insulating materials.  Density functional theory (DFT) is used to quantify energy, stress, and polarization as a function of different atomic/electronic states and lattice configurations.  Importantly, Bayesian uncertainty analysis is used to better understand approximations when homogenizing DFT calculations within a field-coupled continuum model. 
Recent results illustrate the importance of the quadrupole density in describing electrostatic stresses.  Bayesian uncertainty analysis of lead titanate DFT calculations and comparisons with a field-coupled continuum model confirmed the quadrupole density based stress.  The DFT computational data and a set of Matlab codes based on results in a recent paper is describes in the link below which contains a tutorial description of the code and source code required to replicate the results in the paper.  The links below provie a description of the code used for estimating the energy shown on the right as well as electrostrictive energy.

Bayesian DFT-continuum energy analysis

Bayesian DFT-continuum electrostriction analysis

Downloading code can be found here:
Bayesian quantum-continuum energy code
Bayesian quantum-continuum stress code

A simpler example of Bayesian calibration of a nonlinear solid can be found here.  The Matlab code that runs this example can be downloaded here.  The executable within this compressed file is main.m.

Photoresponsive Liquid Crystal Polymer Mechanics

Azobenzene is a fascinating material that undergoes photoisomerization (light induced molecular changes).  This behavior strongly depends on the wavelength and polarization of light.  When synthesized in a polymer, cooperative liquid crystal microstructure (and amorphous materials) motion induced by light leads to a macroscopic shape change of the polymer. 

We are exploring the complex photomechanical behavior of these unique materials to improve their efficiency for next generation engineering adaptive structures.  This includes a combination of unified light-matter modeling, photomechanical experiments, and time-resolved solid state nuclear magnetic resonance (NMR).  Recent modeling results have shown unified light-matter coupling that predicts homogeneous film bending, Gaussian beam structures for linear and circularly polarized light, and optical vortex induced polymer film textures.  A discontinuous Galerkin spectral element method (DGSEM) has been developed to study these materials at the microscale.  Code developed by Liang Cheng is given here along with his corresponding thesis.

Light-matter Interactions and Nonlinear Mechanics of Sapphire

A limited number of materials can withstand structural loads when exposed to ambient temperatures approaching 1400C.  Sapphire is one of these materials which provides an avenue for developing optically based pressure transducers for ultra high temperature applications.  However, standard MEMS based chemical etching methods cannot be applied to machine these materials.  Instead we are investigating laser machining methods to fabricate these sensors.

Our group is currently collaborating with Dr. Mark Sheplak's group at the University of Florida to understand light-matter interactions in sapphire and changes in thermomechanical behavior of laser machined specimens.  This includes a combination of multi-physics modeling, Bayesian statistics, and high temperature strength and fracture experiments.  Transmission electron microscopy has illustrated that dislocations form near the laser machined surface which increases the toughness.  The interactions between dislocation motion, thermal annealing, and fracture is of strong interests to quantify the underlying material reliability for pressure transducers.

Adaptive Structures for Legged Robotics

Legged robots provide unique mobility and maneuverability over wheeled robotic platforms.  Over complex terrains, legged robots provide extraordinary advantages over wheeled robots due to dynamic mobility characteristics; however, transitions from one terrain to another often requires alterations of the internal stiffness and damping of the structures contained within the robotic appendages.  To address this issue, we are integrating electroactive polymers into the legs of robots.  We have shown up to 100% stiffness change on the order of 0.1 sec (commensurate with the stride of the iSPRAWL (hexapod) robot pictured).  

The key enabling material used in this system is the dielectricelastomer VHB.  Constitutive models have been developed that incorporate finite deforming membrane electromechanics and uncertainty quantification.  Model validation of the nonlinear viscoelastic behavior can be found here.  The code and data required to run this Bayesian uncertainty analysis is found here.

Fluid-Structure Interactions and Thermoacoustics of Functional Materials

This research involves a range of fluid-structure interactions with particular interests in 1) fluid-structure interactions of compressible flow and 2) thermoacoustics of carbon materials.  The first subject is focused on coupling beams, plates, and shells with a compressible flow solver that couples the fluid and structure using the immersed boundary layer method.  This is a collaboration with Dr. Kunihiko (Sam) Taira's group. 

We are also working with Taira's group to quantify and analyze the uncertainty of thermoacoustic generation from carbon based materials such as graphene.  It has been shown experimentally that significant sound can be generated by carbon nanotube films (~100 dB).  We have used Bayesian uncertainty analysis to illustrate the key thermodynamic and heat transport parameters associated with transfer of electrical energy into high frequency acoustic energy.


Plasticity of Superconductor Composites

Research in collaboration with the Applied Superconductivity Center and David Larbalestier's group at FSU is focused on understanding the hetergeneous plasticity characteristics of niobium/tin superconducting wires for the Large Hadron Collider and beyond.  A diffusion barrier (white regions in figure) are necessary to ensure a high current density after winding the wires into the magnetic structure.  The heterogeneous deformation is currently under investigation to understand complex multiaxial loading to reduce failures from excessive plasiticity in the diffusion barrier.