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Research Overview

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Prof. Cai’s research lies at the intersection of materials science, solid mechanics and high-performance computing.  The main goal is to predict the properties of materials through the evolution of their microstructures.  An example is the prediction of the stress-strain curves of metals during plastic deformation through large-scale simulation of dislocations, which are line defects inside the crystal.  Understanding the synthesis and deformation mechanisms of nano-scale objects (such as nanowires) through atomistic and continuum modeling is another major area of interest.  We aim to push the capability of materials modeling through the use of advanced numerical algorithms and machine learning techniques, and taking advantage of new novel computational architectures (such as GPUs).  The group is also starting experimental and computational research on metal additive manufacturing (3D printing).

Phase field model of growth kinking of germanium nanowire Dislocation dynamics simulation of single crystal copper during plastic deformation Coarsening of grain structure of a polycrystal at high temperature

 

 

Prof. Darve’s research lies at the intersection of applied mathematics and computational engineering with a focus on fast algorithms to solve complex engineering problems. One of the core areas is solving large-scale sparse linear systems, which requires novel numerical schemes, mathematics, and the design of parallel algorithms. This is key to many areas including solid mechanics, fluid mechanics, and material science. More recently, novel methods have emerged that promise to revolutionize the way scientific computing is done. They include machine learning (deep neural networks, hierarchical Gaussian processes, random forests) and statistical scientific computing. These new ideas promise to open radically new ways of expressing and solving engineering problems, going beyond what current partial differential equations models are capable of.


 

 

Prof. Farhat and his Research Group (FRG) develop mathematical models, advanced computational algorithms, and high-performance software for the design and analysis of complex systems in aerospace, marine, mechanical, and naval engineering. They contribute major advances to Simulation-Based Engineering Science. Current engineering foci in research are on the nonlinear aeroelasticity and flight dynamics of Micro Aerial Vehicles (MAVs) with flexible flapping wings and N+3 aircraft with High Aspect Ratio (HAR) wings, layout optimization and additive manufacturing of wing structures, supersonic inflatable aerodynamic decelerators for Mars landing, and underwater acoustics. Current theoretical and computational emphases in research are on high-performance, multi-scale modeling for the high-fidelity analysis of multi-physics problems, high-order embedded boundary methods, uncertainty quantification, and efficient model-order reduction for time-critical applications such as design and active control.


 

 

Prof. Gu’s research is on experimental mechanics of nanoscale solids. Her group combines solid mechanics, materials science and chemistry to make nanostructures and architected composites, and develops experimental techniques to detect nanoscale loads, displacements and structural changes. One major area of research in the group is in-situ electron microscope mechanical testing of metallic nanocrystals, in order to learn about the influence of defects, interfaces and free surfaces on strength, ductility and failure in metals. Our research findings can be applied to areas such as lightweight structural materials for fuel-efficient vehicles, nanoscale 3D printing, and strong and tough metallic alloys. 

Tension test on a notched platinum nanopillar (~100 nm) inside of a scanning electron microscope Ultra strong and lightweight Cu meso-lattice made with two-photon lithography Self-assembled monolayer of polymer-grafted Au nanocrystals with tunable mechanical properties

 

 

Prof. Lew’s research group works on the design and mathematical analysis of numerical methods to simulate solids and fluids, and in the modeling of selected processes is solids. Current areas of focus are: (a) Methods and models to simulate crack propagation, with a focus on hydraulic fracturing, (b) Creation of meshing tools for problems with evolving domains, advancing in particular the applicability of the method of Universal Meshes that we introduced, and (c) Creation of methods, models, and experiments to analyze and tailor the microstructure of 3D printed metallic parts.

The meshes for the elephant standing in two different positions were obtained by deforming the same Universal Mesh Simulation of a propagating hydraulic fracture in 3D

 

Prof. Pinsky works in the theory and practice of computational mechanics with a particular interest in multiphysics problems in biomechanics. His work uses the close coupling of techniques for molecular, statistical and continuum mechanics with biology, chemistry and clinical science. Areas of current interest include soft tissue mechanics and the mechanics of human vision (ocular mechanics). Topics in tissue mechanics include multiphasic (solid-fluid-ionic) modeling based on thermodynamics, statistical mechanics and computational methods.  Topics in the mechanics of vision include the mechanics of transparency, which investigates the mechanisms by which corneal tissue self-organizes at the molecular scale using collagen-proteoglycan-ion interactions to provide mechanical resilience and almost perfect transparency; modeling metabolic and swelling processes in soft tissues; imaging applied to microscale organization of soft tissues for clinical applications aimed at improving vision and investigating the mechanical behavior of diseased tissues. 

Model for the electro-mechanics of collagen-proteoglycan interaction Finite element model results predicting post-surgical swelling in the human cornea