Predictive multiscale theory for design of heterogeneous materials

Abstract

A general multiscale theory for modeling heterogeneous materials is derived via a nested domain based virtual power decomposition. Three variations on the theory are proposed; a concurrent approach, a simplified hierarchical approach and a statistical power equivalence approach. Deformation at each scale of analysis is solved either (a) by direct numerical simulation (DNS) of the microstructure or (b) by higher order homogenization of the microstructure. If the latter approach is chosen, a set of multiscale homogenized constitutive relations must be derived. This is demonstrated using a computational cell modeling technique for a four scale metal alloy. In each variation of the theory, a transfer of information occurs between the scales giving a coupled formulation. The concurrent approach achieves a more comprehensive coupling than the hierarchical approach, making it more accurate for dynamic fast time scale simulations. The power equivalence approach is strongly coupled and is useful for performing larger scale simulations as the expensive multiple scale DNS boundary value problems are replaced with statistical higher order continua. Furthermore, these continua may be solved on a single spatial discretisation using an extended finite element framework, making the theory applicable within existing high performance computing codes.

Multi-length scale micromorphic process zone model

“…The study of the fracture of those materials has been an active field of research for decades and many aspects of its underlying mechanisms have been addressed in the literature [2,6,7,9,10,12,[17][18][19][20][21]27,30]. In particular, those studies identified the mechanism of ductile fracture as nucleation, growth and coalescence of voids around inclusions.…”

Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes

“…how information is transferred among scales? Among the recent works, we can mention the method of Guidault et al [28] based on the LATIN method and domain decomposition concepts, the multi-grid method proposed in [29], the method of Cloirec et al [30] based on Lagrange multipliers, the multi-scale projection method of Belytschko and coworkers [31,32], the concurrent multi-scale approach of Liu and coworkers [33][34][35], the hp FEM method of Krause et al [36,37], the concurrent multi-level method of Gosh et al [38,39] based on the Voronoi Cell FEM; the multi-resolution approach proposed by Tsukanov and Shapiro [40] based on distance fields. The proposed GFEM gl is also related to the refined global-local FEM proposed by Mao and Sun [41] and based on linear combinations of global and local approximations.…”

Multi-scale solid oxide fuel cell materials modeling

“…This evolution often cannot be explained in a single length scale. To handle problems ranging over several length scales, multi-scale modeling methods have been developed and applied in the analysis and design of materials [60,61], such as high toughness alloys, cemented carbides [28,62,68,69,72,73,105,108], porous materials [26], polymer/clay composites [86], and irradiated materials [112]. Multi-scale modeling methods may offer a solution for predicting material aging and long term reliability of fuel cells.…”

“…A multi-scale approach has emerged as a promising tool to solve material design problems involving several length scales [60][61][62]. In an effort to develop a modeling tool to predict performance and material degradation of fuel cell components, use of a multi-scale framework is proposed in this paper.…”