A data-driven analysis on bridging techniques for heterogeneous materials and structures

Abstract

A bridging technique based on Lagrange multipliers, namely the Arlequin method, is widely used for coupling multi-scale models. However, the definition of the following key parameters is still unclear: the energy partition functions, the characteristic length of the coupling operator and the size of the coupling zone. This work aims to investigate the influences of these factors on the coupling accuracy by conducting global sensitivity analysis on different multi-scale models. To this end, a data-driven model that approximates the input/output behavior of the numerical model is built by using the Sparse Polynomial Chaos Expansion (SPCE) methodology. Then, Sobol’ indices that quantify the sensitivity of the input factors are calculated analytically from the data-driven model with a negligible additional computational cost. Interaction effects among different parameters are also captured. Using this approach, several benchmark tests, including a coarse-fine bar model, a particle-continuum model and a 2D-1D sandwich model, are considered to explore the optimal settings of the coupling factors, which hopefully help for the multi-scale analysis of heterogeneous materials and structures.