Anisotropic meta-models for computationally expensive simulations in nonlinear mechanics

Nonintrusive methods are now established in the engineering community as a pragmatic approach for the uncertainty quantification (UQ) and global sensitivity analysis (GSA) of complex models. However, especially for computationally expensive models, both types of analyses can only be completed by employing surrogates that replace the original models and are considerably less expensive. This work studies the construction of accurate and predictive meta-models for their use in both UQ and GSA, and their application to complex problems in nonlinear mechanics. In particular, meta-models based on radial functions are examined and enhanced with anisotropic metrics for improved predictiveness and cost effectiveness. Three numerical examples illustrate the performance of the proposed methodology.