Quantum Finite Element Method framework for hybrid quantum-classical NISQ computers, leveraging the variational quantum linear solver algorithm.

Generator functions are developed for explicit quantum circuits, allowing for use of heterogeneous material properties and element lengths in FEM discretization of the 1-d steady state heat equation.

Link to paper: Q-FEM-FEAD 

The Variational Multiscale Enrichment method is extended to model the wave propagation and impact response in hyperelastic materials at large deformations.

A time integration scheme for VME is developed, showing excellent agreement with direct numerical simulations for heterogeneous materials.

Model order reduction by replacing the fine-scale problem with an LSTM-based surrogate to achieve computational efficiency

Link to preprint: VME_Finite_Def_JAM, Multilayered_Fractals_Quasistatic 

Quantitative prediction of drastically different size effects in micropillars with different orientations, in accord with experimental observations, and without making any ad-hoc modifications to boundary conditions or theory.

Prediction of the formation of a kink band in layer-parallel compression of nano metallic laminates numerically, in qualitative accord with experimental observations, and studying underlying mechanisms for the formation of kink bands.

Modified and utilized massively parallel group codes in C++ (Deal ii), leveraging a dislocation mechanics-based plasticity approach

Link to papers: SizeEffectsActaMat, NMLKinkbandCrystals 

Developed a PDE-based framework to model a propagating rupture/crack front in a straight fault layer under external loads, using an ansatz of field dislocation mechanics theory.

Developed a MPI-based C++ code using PETSc to model crack propagation coupled with elastodynamics, using mixed FEM and FVM based approach (central upwind scheme), achieving 30\% reduction in runtime

Static fault friction laws, short-slip, self-healing, and the supershear behavior in cracks (under impact loading) are numerically demonstrated without putting in by hand any such discontinuous 'on-off' criterion/feature in our model.

Link to paper: FrictionSupershearJMPS 

Formulation of dual variational principles for solving the highly nonlinear PDEs of inverse design problems in the actuation of soft membranes based on a prescribed principal stretch formulation. 

Computational implementation of the dual formulation with object-oriented code design in C++.

Examples of interesting design shapes, such as a hemisphere and a hat shape, are computationally demonstrated, with solutions having reasonable quality factors.

Developed a computational approach to estimate various elastic stiffnesses of one-dimensional continua and nanostructures (incorporating the effects of surface residual stresses and surface energy) modeled as special Cosserat rods.

A cross-sectional nonlinear warping problem is solved using Lagrangian FEM formulation for various material models like Saint-Venant isotropic/orthotropic model, Neo-Hookean model, and Mooney-Rivlin model.

Link to papers: CMAMEbulkrods, CMAMEsurfaceeffects