Nowadays, subjects such as grain& grain boundary, crystalline settling of material, their slipperiness, alteration of the shapes of crystals as a result of loading, grain growth and the effects of boundary in reinforcement of materials has increased the importance of microstructural studies. In RRVI institute, this research topics can be summarized topically as follows:

1. Dual Phase Steels
2. Multiscale Modeling
3. Phase Field
4. Very High Cycle Fatigue

In the field of mechanics, rapid progress in the past two centuries has occurred, due in large measure to the ability of investigators to represent physical laws in terms of rather simple equations. In many cases the governing equations were not so simple; therefore, certain assumptions, more or less consistent with the physical situation, were employed to reduce the equations to types more easily soluble. Thus, the process of linearization has become an intrinsic part of the rational analysis of physical problems. An analysis based on linearized equations, then, may be thought of as an analysis of a corresponding but idealized problem.

Structures are subjected to loading that is mostly time dependent in a weak or strong fashion. Response histories under weakly time-dependent loading may be calculated by using the quasi-static analysis procedure.

For moderately or strongly time dependent loading, calculation of response quantities requires a full dynamic analysis procedure as it is presented in the previous chapter assuming that the structure is deterministic and the loading history is fully determined or known,i.e., it obeys a specific rule or a definite function of time such as constant, linear, non-linear, harmonic, etc.