Adjoint Design Sensitivity Analysis of Fracture Mechanics Using Molecular-Continuum Multiscale Approach

We have developed a multiscale design sensitivity analysis method for transient dynamics using a bridging scale method by a projection operator for scale decomposition. Employing a mass-weighted projection operator, we can fully decouple the equations of motion into fine and coarse scales using the orthogonal property of complimentary projector to the mass matrix. Thus, independent solvers in response analyses can be utilized for the fine scale analysis of molecular dynamic (MD) and the coarse scale analysis of finite element analysis. To reduce the size of problems and to improve the computational efficiency, a generalized Langevin equation is used for a localized MD analysis. Through demonstrative numerical examples, it turns out that the derived sensitivity analysis method is accurate and efficient compared with finite difference sensitivity.Copyright © 2011 by ASME