Gaussian process emulation for rapid in-plane mechanical homogenization of periodic masonry

Numerical homogenization strategies can provide average mechanical responses, either in stress or coupled-stress quantities, which include many phenomenological features. Nonetheless, a direct application of numerical homogenization in sensitivity analysis in which uncertainty is propagated becomes impractical, as hundreds or thousands of simulations are conventionally required. In this study, a reliable and rapid predictive surrogate model is developed aiming to characterize the homogenized response of masonry. The case of English-bond arrangement is addressed, and the following steps are considered: (1) creation of a synthetic database through numerical homogenization based on a Finite-Element method, generated by randomization of model parameters; (2) training of a nonlinear Gaussian process; and (3) approximation of homogenized stress-strain curves for a masonry wall and for both linear and nonlinear ranges. The performance of the proposed technique is evaluated using training-validation-test in terms of computational accuracy. Results indicate that computational time is lessened 1200% while relative errors remain below 5-10%.