Concurrent multi-scale analysis of elastic composites by a multi-level computational model Original Research Article

In this paper, an adaptive multi-level computational model is developed to comprehensively address issues of discretization and physically based modeling error in structures consisting of heterogeneous micro-structures. The model consists of three essential levels, (i) a purely macroscopic domain (level-0) with homogenized material parameters; (ii) a macro–micro domain (level-1) with the micro-domain represented by the periodic repetition of a representative volume element (RVE) and (iii) purely microscopic domain (level-2) where the RVE ceases to exist and extended micro-structural regions need to be modeled. All micro-structural computations of arbitrary heterogeneous domains are conducted using the adaptive Voronoi cell finite element model. An intermediate layer is used between the macroscopic and microscopic regions for smooth transition. The level-1 domain is utilized to estimate criteria for switching from macroscopic to microscopic calculations. Physically based error indicators are developed for transition from macroscopic to microscopic domain. Statistical functions are used to assess the extent of the RVE domains for non-uniform micro-structures. For the macroscopic domains, h- and hp-adaptations are executed using conventional error indicators based on the energy norm. The numerical simulations are compared with results from pure micro-mechanics and other multi-level models in the literature. The model is also tested for a realistic problem with macroscopic stress risers.