Two-scale computational approach using strain gradient theory at microlevel

Realistic description of heterogeneous material behavior demands more accurate modeling at macroscopic and microscopic scales. In this frame, the multiscale techniques employing homogenization scheme offer several solutions. Most recently developed two-scale scheme employing second-order homogenization requires the nonlocal theory at the macrolevel, while the classical local continuum theory is kept at the microlevel. In this paper, a new second-order computational homogenization scheme is proposed employing the higher-order theory at both macro- and microlevel. Discretization is performed by means of the C-1 finite element developed using the strain gradient theory. The new gradient boundary conditions employed on representative volume element (RVE) are derived. The relation between the internal length scale parameter and the RVE size has been found. The new procedure is tested on a benchmark example, where the results have been compared to the solutions obtained by the usual second-order homogenization using the local concept on the RVE.