A Computational Strategy for Code- and Mesh-Agnostic Nonlinear Global–Local Analysis

Abstract

Global, coarse mesh and local, refined mesh modeling strategy is a common solution approach for domains spanning many orders in length scale. In this article, a nonintrusive computational strategy for iterative solution to the nonlinear behavior in the subdomains is proposed. To estimate the residual force on the interface connecting the subdomains with nonmatching discretizations, variational principles with an intermediate framework are proposed to assure satisfaction of virtual work principle in the subdomains and to assure displacement/traction compatibility at the interface. To map nodal force from one subdomain to the other, both global Lagrange multiplier (GLM) and local Lagrange multiplier (LLM) methods are discussed. Quasi-Newton iterative updates are used to correct displacements on the interface connecting the different subdomains until equilibrium is reached. A symmetric rank 1 update as well as the Broyden–Fletcher–Goldfarb–Shanno (BFGS) update are considered for accelerating the solution convergence. The developed method is suitable for the modular construction of submodels with nonmatching discretizations and even allows coupling between subdomains analyzed using different (commercial or custom) codes. The iterative global–local coupling strategy is validated on several examples, including an L-shaped domain with local nonlinearity and a rectangular plate with a propagating crack. Another example illustrating the coupling of domains independently analyzed using commercial finite element codes ANSYS and ABAQUS is next demonstrated. Finally, the method is demonstrated to analyze semiconductor chip assemblies where plastic ratcheting of the interconnect line causes passivation coating fracture.