Research topics span:
  • Simulations of Lamb wave propagation in two- and three-dimensional domains
  • Nonlinear wave propagation by internal material defects
  • Mechanical reliability analysis of electrical circuits under shock and thermal cycling conditions
  • Numerical studies on thin-film blisterings in nano-scale
  • Failure analysis of structures under extreme events such as impact and blast
  • Method of Finite Spheres
  • Peridynamics
  • Earthquake analysis of nuclear power plants

Method of Finite Spheres (meshless method): For several decades, the development of the finite element method has been pursued and the method is now quite efficient for the analysis of complex structures and, indeed, many quite general multi-physics problems. However, the finite element method requires an expensive mesh generation and, in some cases, notably in nonlinear analysis, mesh regenerations may be necessary. On the other hand, meshless techniques eliminate the mesh generation procedure in the analysis, but are confronting difficulties in numerical integration; namely, the integrands are not polynomial functions. Also, the essential boundary conditions are not as easily imposed as in the traditional finite element method. To overcome these difficulties, some research focused on coupling finite element methods and meshless techniques, with the premise to utilize the mutual advantages. The basic idea is that finite elements are employed for the domain which is easily meshed and would not need re-meshing in a geometrically nonlinear analysis, and the meshless discretizations are used for the domain which is difficult to mesh and may need re-meshing in nonlinear analysis. However, a major difficulty lies in enforcing compatibility in the displacements as assumed for the meshless domain and the finite element domain: that is, to ensure the continuity of the displacements and possibly displacement derivatives between the domains. Although some methods for coupling were proposed, full displacement compatibility in the coupled domain seems not ensured. We propose a new displacement-based scheme to couple finite elements and finite spheres.

Progressive Collapse (2004-2006): After WTC collapse in 2001, the building collapse mechanism has been investigated intensively. The objective of this project is to develop a fast running algorithm that will enable the detection of buildings' susceptibility to progressive collapse due to extreme loadings.

Thin Film Blistering:  SEM imageThe delamination mechanism of proton implanted single crystal ferroelectric BaTiO3 thin film layer from its bulk BaTiO3 substrate has been investigated. The blisters nucleate and evolution during isochronal annealing. The single crystal thin film layer splits as the hydrogen gas diffuses and internal pressure increases. Delamination mechanism from pressurized hydrogen in the implantation-induced damage zone makes coarsening of the cavities. Blister nucleation and evolution relation criterion have been derived considering diffusion of gas molecules and a simplified de-bonding criterion is proposed in terms of dimensionless parameters based on the force equilibrium condition. Three dimensional numerical simulation of two-bubble evolution and delamination of thin film is performed using a finite element method.

Lamb Wave Phased Array: Analytical studies for the Lamb wave  propagation have been performed for many decades based on the continuum and plate theories, and the development of numerical techniques such as finite element analysis (FEA) enabled the calculation in the sophisticated geometries. Both methodologies have been widely used for the validation of experimental results. However, most of the numerical calculations have been performed by simplifying the numerical model to two dimensional models. A weak formulation of the dielectric-mechanical coupled system is derived, and a fast running algorithm for large scale simulations is implemented.

Discretized Nonlocal Mechanics (Peridynamics): DamageThe development of physics-based numerical methodologies which can quantitatively predict the performance and durability of blast resistance materials/structures is essential to estimate the safety of the structures which may be made of different kinds of materials by exploiting the best attributes of the hybrid materials. However, the wide range of the temporal and spatial domains for the analysis makes it difficult to use a unified approach to analyze materials and to design structures effectively. For example, traditional continuum theories require that deformation fields have smoothness although this is not the case when a localization or crack occurs. Mathematically, localizations and cracks cause the loss of the well-posedness of strong form equations, and the mathematical framework developed in continuum mechanics has not been appropriate in explaining the discontinuities in the spatial domain. Various kinds of meshless methods have been developed to get around this difficulty numerically. However, they still require a special relation that governs the initiation of cracks as well as their growth velocity and direction.