**General Interest**

We are interested in understanding and manipulating dynamic systems through theoretical, computational, and data-driven tools. A major focus is on understanding the propagation of waves in complex micro-structured solids and liquids and on creating materials which can be used to control their temporal and spatial characteristics. We are also interested in other dynamic systems related to solid structures such soft robots and aeroelastic flutter. One of our recent efforts is to explore the application of modern deep learning tools to problems in mechanics and physics.

*We are not married to a specific area of research*. Students in our group are encouraged to develop a broad set of skills and work on several different problems. These problems span the spectrum of theoretical, computational, data-driven, and experimental problems in the area of mechanics broadly defined.

**Theoretical Mechanics**

Our group has done work in the area of homogenization theory as it applies to the dynamics of composites. Coherent dynamic homogenization principles are essential for metamaterials and we have contributed to the development of field averaging based elastodynamic homogenized constitutive parameters. These parameters are invariant under coordinate transformations and homogenization itself. They display the unusual characteristics required from metamaterials (negative density, stiffness etc.) and are important candidates for realizing transformation elastodynamic devices such as cloaks and concentrators.

Our group is involved in the development of modeling principles which will govern the dynamics of a new class of soft robots called the boundary constrained swarm robot. The robot will have the capability of changing shape, performing a range of maneuvers, and applying a large amount of force. The techniques needed for modeling such a robot will include principles from large deformation nonlinear elastodynamics, multi-body rigid dynamics, variational methods, optimization techniques, and inverse problem solutions.

**Computational Mechanics**

We have developed a complete suite of algorithms for phononic bandstructure computations. These algorithms are based on fast variational solutions to the elastodynamic eigenvalue problem which are further accelerated through GPU computations over a cluster of distributed NVIDIA GPUs. We can calculate and sort thousands of phononic eigensurfaces for arbitrarily complex 3-D unit cells and extract not only bandgap locations but also properties which are essential to thermal calculations. These include density of states, phase and group velocities over very large frequency domains (calculations by Yan Lu at IIT.)

In collaboration with Prof. James Guest from John’s Hopkins we have implemented topology optimization routines for the optimization of 3-D phononic crystals. Below is an example result of topology optimization implemented for maximizing the bandgap in 3-D FCC phononic crystals made of Tungsten-Carbide and Epoxy phases (calculations by Yan Lu at IIT, Yang Yang at JHU) – the first ever topology optimization study for 3-D phononic crystals

**Data-driven Modeling**

We have recently shown how to apply convolutional neural networks (CNN) to problems in mechanics. The specific model problem we were concerned with was the prediction of eigenvalues of a phononic crystal. We were able to show that CNNs can vastly overpower traditional NN architectures such as MLPs (deep or shallow) in prediction accuracy and generalization capability. Furthermore, they can be trained with a fraction of the data required by MLPs. This study is the first application of modern DL architectures to any problem in the broad area of mechanics.

Exploiting spatial-temporal characteristics of the data has proven to provide the desired improved data efficiency in engineering applications. Traditional Deep Learning tools such as Convolutional Neural Networks, Long-Short Term Memory Networks and Autoencoders are able to provide these characteristics.

**Dynamics**

More generally we have interest in the analysis and control of dynamic systems, seeing wave mechanics as a specific area within the more general area of dynamics. Dynamics is further seen merely as the solution space of multi-parameter partial differential equations which connects it to deep mathematical fields. Some ongoing considerations include the analysis, experiment, and control of flow induced flutter instabilities in flying wing aircrafts.