ANALYTICAL AND NUMERICAL INVESTIGATIONS FOR THIN-FILM WITH CONSTRAINT UNDER UNIAXIAL TENSION

The thin-film with constraint under uniaxial tension is investigated based on the micromorphic theory and the strain gradient elasticity theory, respectively. The analytical solutions are presented for the uniaxial tension of the thin-film under different microscopic constraint boundary conditions. The presence of the boundary layer effect is predicted. By comparing the relations between these two theories, it is found that the micromorphic theory can reduce to the strain gradient elasticity theory by choosing the coupling factor as the penalty parameter. The numerical simulation results with penalty parameter agree well with those analytical solutions of the strain gradient elasticity except for the boundary layer region. It is also shown that the subroutine originally developed for the micromorphic theory can simulate the strain gradient elasticity problem due to the penalty parameter approach.