Probabilistic Upscaling of Material Failure Using Random Field Models – A Preliminary Investigation

Complexity of failure is reflected from sensitivity of strength to small defects and wide scatter of macroscopic behaviors. In engineering practices, spatial information of materials at fine scales can only be partially measurable. Random field (RF) models are important to address the uncertainty in spatial distribution. To transform a RF of micro-cracks into failure probability at full structural-scale crossing a number of length scales, the operator representing physics laws need be implemented in a multiscale framework, and to be realized in a stochastic setting. Multiscale stochastic modeling of materials is emerging as a new methodology at this research frontier, which provides a new multiscale thinking by upscaling fine-scale RFs. In this study, a preliminary framework of probabilistic upscaling is presented for bottom-up hierarchical modeling of failure propagation across micro-meso-macro scales. In the micro-to-meso process, the strength of stochastic representative volume element (SRVE) is probabilistically assessed by using a lattice model. A mixed Weibull-Gaussian distribution is proposed to characterize the statistical strength of SRVE, which can be used as input for the subsequent meso-to-macro upscaling process using smeared crack finite element analysis.