A neural network-aided Bayesian identification framework for multiscale modeling of nanocomposites

Abstract

This work proposes a Bayesian framework for determining the mechanical properties of carbon based nanocomposites. In particular, Bayesian parameter inference is applied to learn the parameters that characterize the CNT/polymer interface in the microscale. These parameters are associated with great uncertainties and their characterization is a difficult task, since microscale measurements are costly and hard to obtain. To overcome this, the present study introduces a computational framework for updating the prior beliefs on the values of these parameters, by using measurements on large-scale structures comprised of the composite. In terms of modeling, the CNT/polymer interface is formulated with the cohesive zone model and a bilinear bond-slip constitutive law. Typically, predicting the response of such systems requires multiscale analysis approaches, such as the FE2 method, employed in this work. Despite its accuracy, FE2 is associated with immense computational demands for large-scale problems and, therefore, its application to the Bayesian setting, which requires multiple model evaluations, is prohibitive. To alleviate this cost, a surrogate modeling technique is developed which utilizes artificial neural networks, trained to predict the nonlinear stress–strain relationship of representative volume elements of the microstructure. The data set over which the neural network is trained, is obtained by analyzing a limited number of different RVE configurations using a detailed finite element analysis. The elaborated methodology is first validated through a numerical example from 2D elasticity, which demonstrated its high accuracy and its significant cost reduction capabilities. It is then applied to a more challenging large-scale problem from 3D elasticity. Even though this paper focuses on the characterization of the mechanical properties of composite materials, the proposed numerical procedure is generic and can be straightforwardly applied to other physically analogous phenomena related to nano-composite modeling, such as parameter identification in heat transfer or electrical conduction.