The main aim of this contribution is to apply the relative entropy apparatus in the homogenization of the fibrous and particulate composites [1] with truncated uncertainties. Homogenization, i.e., calculation of the effective material tensors, is proposed for the composites having constituents with material properties defined using the truncated Gaussian distributions. The generalized iterative stochastic perturbation technique is implemented for this purpose and validated using a Monte Carlo simulation; an additional semi-analytical probabilistic technique is also applicable. Both techniques are based on the Least-Squares Method and machine-learning response functions that link effective characteristics to the corresponding elasticity-tensor components of the original composite constituents. A numerical solution to the homogenization problem is obtained here by applying the Probabilistic Finite Element Method, implemented in a hybrid manner using the systems ABAQUS and MAPLE 2025. Truncation effect in Bhattacharyya distances for the effective tensor is analyzed in addition to the same relative entropy computed for the non-truncated Gaussian uncertainty sources, and also the Kullback-Leibler distance [2]. Three types of composites are analyzed in this work, namely fiber-reinforced structure (CFRP), carbon black polymer-based particulate composite, and a similar structure, where the polymer matrix contains rubber particles. Their effective elastic and thermal characteristics will be discussed. Computations of the relative entropies will be supported by the determination of the first four probabilistic characteristics of the effective material tensor. All probabilistic functions of the homogenized composites will be presented in addition to the input uncertainty level of the composite constituents' elastic characteristics. Additional study on the non-local homogenization procedure and cellular solids will complete this contribution. References [1] M. Kamiński, Probabilistic entropy and relative entropy for the effective characteristics of the fiber-reinforced composites with stochastic interface defects. Comput. Meth. Appl. Mech. Engrg. 432A, 2024, 117308, https://doi.org/10.1016/j.cma.2024.117308. [2] F. Zhang, Y. Liu, C. Chen et al., Fault diagnosis of rotating machinery based on kernel density estimation and Kullback-Leibler divergence. J. Mech. Sci. Technol. 28, 2014, 4441–4454, https://doi.org/10.1007/s12206-014-1012-7.