Finite Element Modeling of Fracture in Brittle Foods with Physically Consistent Parameter Calibration: A Practical Case Study on Cooled Dark Chocolate

Abstract

Fracture in food can be undesired during production and transportation but also intended during cutting, grinding or mastication. The associated peak load, the deformation at failure and the resulting fragment geometry are all product properties. This work condenses the modeling of such fracture into a physically rigorous recipe that considers the practical constraints imposed by finite element simulations where necessary and applies idealized theoretical assessments where applicable. Cooled dark chocolate serves as a reproducible model material. Two well-established modeling frameworks for Griffith-type brittle fracture are assessed at an affordable spatial discretization: a sharp-interface and a diffuse phase-field approach. The assessment covers the choice of numerical framework, its discretization and a staged identification of the model parameters. Each parameter is identified from the loading stage that governs it: elastic parameters from pre-crack tension and compression, critical energy release rate from three-point-bending peak force, and the phase-field width last. The phase-field width interferes with the structural response, crack curvature and stress fields, depending on its lower bound set by the affordable spatial resolution. Elastic slope, peak force and crack path therefore cannot be met practically by a single parameter set. The objective must be fixed for the calibration of the model parameters and reported together with the numerical parameters and the boundary value problem.