Variational eigenstrain multiscale finite element method

Abstract

A new subgrid (subscale) finite element method is proposed, which is termed as the variational eigenstrain multiscale method. It combines the essential ideas of Hughes' variational multiscale formulation [Comput. Methods Appl. Mech. Engrg. 127 (1995) 387] with Eshelby's inclusion theory [Proc. R. Soc. Lond. A 252 (1957) 561] and Mura's equivalent eigenstrain principle [Micromechanics of Defects in Solids, Martinus Nijhoff Publisher, 1987] to homogenize numerical error due to finite element discretization. By synthesizing variational multiscale method with the equivalent eigenstrain principle, we have developed a new finite element formulation that can automatically homogenize its own discretization errors so that it may attain better accuracy in a coarse scale finite element computation than that of the original coarse scale finite element computation. The paper provides the theoretical foundation of the method as well as two numerical examples that illustrate and validate the proposed method.