This work presents a global surrogate modelling of mechanical systems with elasto-plastic material behaviour based on support vector regression (SVR). In general, the main challenge in surrogate modelling is to construct an approximation model with the ability to capture the non-smooth behaviour of the system under interest. This paper investigates the ability of the SVR to deal with discontinuous and high non-smooth outputs. Two different kernel functions, namely the Gaussian and Matèrn 5/2 kernel functions, are examined and compared through one-dimensional, purely phenomenological elasto-plastic case. Thereafter, an essential part of this paper is addressed towards the application of the SVR for the two-dimensional elasto-plastic case preceded by a finite element method. In this study, the SVR computational cost is reduced by using anisotropic training grid where the number of points are only increased in the direction of the most important input parameters. Finally, the SVR accuracy is improved by smoothing the response surface based on the linear regression. The SVR is constructed using an in-house MATLAB code, while Abaqus is used as a finite element solver.

This contribution deals with the uncertainty quantification for applied nonlinear structural engineering problems, including high stochastic dimensions. A finite element problem with different material models is investigated. The efficiency, accuracy and convergence of sparse PCE are studied numerically and compared with Monte-Carlo Simulation (MCS) for non-linear structural analysis including elasto-plastic and damage models. In both models, the Young's modulus is considered as random fields discretised by Karhunen Loeve Expansion (KLE). In the provided studies, sparse PCE converges fast and is highly efficient for linear elastic and elasto-plastic material models. However, sparse PCE loses its effectiveness and exhibits lower accuracy for the damage material model.