A FULL PROBABILISTIC ANALYSIS APPROACH FOR THE MECHANICAL BEHAVIOR OF RANDOM POROUS MATERIALS BASED ON LATENT VARIABLE PROBABILITY SPACE

Uncertainty in the microstructure of random porous materials propagates to the uncertainty of macroscopic responses through fundamental physical laws. Capturing this process requires a comprehensive description of the spatial uncertainty at the microscopic level, which typically involves the introduction of a high-dimensional joint probability density function. Additionally, the uncertainty need to be coupled with nonlinear multi-scale propagation, which creates significant challenges for the uncertainty quantification of macroscopic material performance. To address this issue, this study proposes a data-physics dual-driven uncertainty analysis framework integrating variational autoencoders and probability density evolution theory, and achieves the propagation of microstructural uncertainty to homogenized stress-strain response uncertainty under uniaxial compression. Initially, a data-driven variational autoencoder (VAE) is used to map the complex, high-dimensional microstructure data into a low-dimensional latent space. In this space, the spatial uncertainty is represented by the probability distribution of the latent variables. This method effectively reduces the dimensionality of high-dimensional random variables while preserving the essential probabilistic features of the microstructure. Subsequently, sampling is performed in the probability space of the latent variables, and the samples are then decoded back into the original pixel space to reconstruct the microstructure. This enables the generation of new microstructure samples that reflect the uncertainty in the original material system. Moreover, based on a physics-driven theory of probability density evolution, deterministic sampling within the latent variable space transforms the high-dimensional uncertainty problem into a set of deterministic partial differential equations. This approach ultimately provides the complete probabilistic evolution of homogenized stress-strain curves for random porous materials. The results demonstrate that for a 64-dimensional latent probability space, merely 1000 deterministic analyses achieve comparable accuracy to 20,000 Monte Carlo simulations, confirming the method’s computational efficiency and accuracy. The proposed framework integrates the advantages of both data-driven and physics-driven approaches, offering an innovative and practical solution for the uncertainty analysis of complex material systems.