Research
QR kinematics and its applications : Theory and experiments
In recent years, a novel upper-triangular (QR) decomposition has been proposed to describe the kinematics of a finite deformation. This decomposition has several advantages especially with the ease of computation and experiments. The objective of our research group is to implement this novel method to solve problems in finite deformation elasticity, plasticity and viscoelasticity. This technique has already been proved to be useful in delineating an experimental method to measure physically relevant quantities such as, plastic component of the stretch tensor. We are looking to set up these experiments in order to utilize the full potential of this novel method.
Fiber reinforced laminated composites have gained much momentum in structural and aerospace applications due to their low weight to strength ratio. In our lab, we develop theoretical and numerical models to understand different properties and phenomena in composite materials. Progressive damage in laminated composites is of particular interest. Currently, an experimental lab for composite materials is under development where these materials will be tested for the verification of the developed models.
Mechanics of fiber reinforced laminated composites
Strain-gradient theories and multiscale mechanics
In most theories of classical structural mechanics, it is tacitly assumed that the material properties are independent of the size of the structure. This assumption, however, is not valid for certain material properties due to the underlying microstructures and their changes during a deformation process. For example, the inhomogeneous distribution of dislocations leads to a size-dependent plasticity. Our group investigates these size effects of structural materials. Since understanding the underlying microstructure is key to study the size effects, we are also interested in multiscale analysis. We use both analytical as well as computational tools in our study.
In many real-life problems, a mechanical deformation is often coupled with chemical reactions. Two types of situations can be envisaged for these problems: (i) a mechanical deformation can expedite a chemical reaction and, (ii) a chemical reaction affects the material strength resulting in mostly irreversible deformation processes. Chemical degradation of material strength falls under the latter category. These problems are particularly challenging because the governing physical laws such as, laws of thermodynamics, conservation of mass, conservation of momentum are highly coupled. We are working on developing a continuum mechanics framework that takes chemical reactions and the induced deformation proceeses into account.