Nakshatrala's general research interest includes mathematical formulation and analysis, and development of computational techniques for problems in structural, solid, and fluid mechanics. His current research interests include degradation/healing of man-made and natural materials, and heterogeneous porous media (both flow and structural aspects).

Nakshatrala's application areas include degradation/healing of civil and aerospace structures and materials, geosciences (contaminant transport, carbon-dioxide sequestration, enhanced oil recovery) and bio-mechanics. The research goal is to develop relevant mechanics, numerical techniques, and mathematical tools to model and study various (steady state and transient) multiscale phenomena. Specific research topics of interest include:

Geomechanics

• Flow and transport in deformable porous media
• Constitutive modeling of geomaterials
• Fracturable porous media

Computational Mechanics

• Multiscale and stabilized finite elements
• Coupled problems, structure-structure interaction, fluid-structure interaction
• Numerical homogenization and upscaling techniques
• Numerical optimization and sensitivity analysis
• Applications and numerical techniques for differential-algebraic equations (DAEs)

Continuum Physics

• Modeling degradation / healing of materials and structures
• Nonlinear continuum mechanics
• Thermomechanical constitutive modeling & Implicit constitutive modeling
• Theory of interacting continua

Applied Mathematics and High Performance Computing

• Partial Differential Equations (More of a spectator)
• Maximum Principles
• Applied Optimization
• Parallel Computing