Phase-field models represent cracks as a smooth, continuous damage field. My work focused on developing computationally efficient algorithms for large-scale fracture simulations — introducing adaptive mesh refinement guided by an energy based error indicator, and automatic time-stepping to capture rapid crack propagation accurately. The framework is implemented in FEniCS with MPI parallelism and applied to brittle, cohesive, and thermo-mechanical fracture problems.

Functionally graded materials have spatially varying properties — for example, transitioning from ceramic to metal across a component — making them ideal for high-temperature and structural applications, but challenging to model for fracture. I extended the phase-field cohesive zone framework to FGMs, where material parameters vary continuously as a function of spatial coordinates. The adaptive implementation captures complex crack paths and mixed-mode failure with adaptive meshing, offering a robust tool for fracture design in graded structures.

Topology optimization finds the optimal distribution of material within a design domain to maximize structural performance under given constraints. My work scaled this to large 3D problems using FEniCS and MPI-based parallel computing. The resulting geometries are fabricated using 3D printing, bridging computational design with physical manufacturing.

Auxetic materials exhibit a negative Poisson's ratio — they expand laterally when stretched — a counter-intuitive behaviour that leads to enhanced indentation resistance, energy absorption, and acoustic damping. Using topology optimization, I designed microstructures using FGMs that achieve auxetic responses through tailored geometry rather than intrinsic material properties and the designs were validated through 3D-printed physical samples.

Evolutionary Deep Neural Networks (EDNN) are a mesh-free, physics-informed approach that evolves the solution of PDEs in time by training a neural network to satisfy the governing equations and boundary conditions. My current research at Johns Hopkins applies EDNN to coupled physics problems in solid mechanics — working toward efficient solvers that generalise across geometries and loading conditions without requiring labeled simulation data.