Strain-gradient homogenization: A bridge between the asymptotic expansion and quadratic boundary condition methods.

• A homogenization approach is provided to compute the strain gradient elasticity coefficients. • We modify the method based on quadratic boundary conditions to eliminate the persistence of strain gradient elasticity effects for a homogeneous solid. • The principle of the approach consists to establish a bridge with the method based on asymptotic series expansion. • The case of a composite with fibers is considered as an illustration in order to show the improvement of the corrected method. In this paper we deal with the determination of the strain gradient elasticity coefficients of composite material in the framework of the homogenization methods. Particularly we aim to eliminate the persistence of the strain gradient effects when the method based on quadratic boundary conditions is considered. Such type of boundary conditions is often used to determine the macroscopic strain gradient elastic coefficients but leads to contradictory results, particularly when a RVE is made up of a homogeneous material. The resulting macroscopic equivalent material exhibits strain gradient effects while it should be expected of Cauchy type. The present contribution is to provides new relationship to correct the approach based on the quadratic boundary condition. To this purpose, we start from the asymptotic homogenization approach, we establish a connection with the method based on quadratic boundary conditions and we highlight the correction required to eliminate the persistence of the strain gradient effects. An application to a composite with fibers is provided to illustrate the method. [ABSTRACT FROM AUTHOR]