Sensitivity Analysis for Coupled Atomistic and Continuum Simulations Using Bridging Scale Decomposition

Abstract

This paper presents sensitivity analysis methods for coupled atomistic and continuum problems. Many bridging methods, which couple atomistic simulations to continuum simulations, have been proposed. They offers the ability to examine atomistic-scale dynamics in great detail, and yet keep the computation affordable by only using molecular dynamics (MD) in localized regions and a continuum simulation method everywhere else. Among the many excellent methods developed, the bridging scale decomposition is, in our opinion, the most advanced and is inherently geared for dynamic problems. We are investigating the impact of design changes at the macrolevel; including material, sizing, and shape, to the responses at the atomistic level. This paper focuses on sensitivity analysis for one-dimensional (1D) problems, where responses of atomistic motion to the changes in design variables are formulated analytically. These formulations are then implemented numerically in Matlab. Accuracy of the sensitivity coefficients are verified using overall finite difference method. The major contributions of this paper are: first, it demonstrates the feasibility of the sensitivity analysis for the bridging scale; second, the paper proposes a method that overcomes the issue of discontinuity in shape design due to the discrete nature of the MD simulations; and third, the paper provides a basis for future extension to 2D and 3D problems that support structural design.

Keywords:

• Bridging scale
• Design sensitivity analysis
• Langevin equation

Notes

k = 1, Δk = 0.001%.

m = 1, Δm = 0.001%.

A _a  = 1, ΔA _a  = 0.001%.

A _b  = 1, ΔA _b  = 0.001%.

ℓ _c  = 120h, Δℓ _c  = 0.01%.

ℓ _c  = 120h, Δℓ _c  = 10%.

^#Communicated by G. Hulbert.