Sharif Digital Repository

In many problems, the traditional elasticity cannot predict phenomenon such as nano-scale defects, surface effects, and stress concentration correctly. For example, analysis near the crack tip, dislocation and inhomogeneity shows inconsistent results because in this case values of stress go to infinity. Therefore for solving these kinds of problems, higher order continuum theories were introduced. The appearance of additional constants in the equations of motion can represent the atomic nature of materials. Furthermore, they can be utilized for determining properties of materials vibration with high frequency, granular materials, and polymers.First strain gradient theory introduced by... 

To account for certain essential features of material such as micro-structure effects and dispersive behaviour and optical branches in dispersion curves, a fundamental departure from classical elasticity to generalized continuum theories is required. Among the generalized continuum mechanics, micromorphic elasticity is capable of capturing these physical phenomena completely. In the mathematical framework of micromorphic elasticity, in addition to the traditional elastic moduli tensors, some additional tensors are introduced in the pertinent governing equations of motion. A precise evaluation of the numerical values of the aforementioned elastic moduli tensors in the realm of the...