A machine learning approach to finite element modeling of sintering deformation using densification data

Abstract

This paper presents a recent development in the densification-based finite element method (DFEM) of sintering deformation, in which a machine learning model replaces the volumetric component of classical constitutive laws. Accurate constitutive laws are traditionally considered essential for finite element (FE) modeling; however, this study shows that sintering deformation is largely insensitive to parameter variations provided volumetric deformation is captured. Classical models often fail to reproduce densification behavior accurately, motivating the use of artificial neural networks (ANNs). Dilatometer data from multiple thermal profiles were analyzed to determine the activation energy (Q) using the master sintering curve. Additional parameters (Cs1, n, and ζ) were adjusted to fit experimental densification curves. Although FE simulations using these parameter sets produced consistent deformation results, they lacked sufficient accuracy in reproducing the experimental behavior. To address this, ANNs were trained in two steps: first on theoretical data to capture fundamental sintering behavior, and then on experimental data for refinement. Using temperature, integral temperature, and relative density as inputs, the ANN predicted densification rate with high accuracy. The ANN was successfully embedded into ABAQUS via a creep subroutine, providing a robust, scalable, and accurate framework for simulating sintering deformation.