First- and Second-Order Phase Transformation Modeling Based on the Hamilton Principle: A Coupled Thermo-Mechanical Approach for Glass Additive Manufacturing

Abstract

Additive manufacturing of glass inherently involves complex thermal histories characterized by extreme heating and rapid cooling rates. These extreme conditions directly govern the final microstructure and mechanical integrity of the printed material. This work presents a comprehensive multi-physics material model derived from the extended Hamilton principle, establishing a unified variational framework for coupled thermal, mechanical, and phase transformation processes at finite strains. The formulation integrates a rigorous thermodynamic description of first-order melting and second-order glass transitions with a kinematic split accounting for thermal expansion, phase specific density changes, and viscoelastic deformation. A temperature dependent viscosity model is employed to capture the kinetic freezing of the microstructure inherent to vitrification. The numerical implementation utilizes a monolithic Neighbored Element Method (NEM) for the solution of the heat equation, ensuring computational efficiency and stability. Numerical investigations at the material point level validate the models ability to reproduce Time-Temperature-Transformation (TTT) behavior under varying cooling rates. Furthermore, three dimensional Finite Element simulations in ANSYS of a laser-based deposition process demonstrate the accumulation of residual stresses and macroscopic warpage resulting from the interplay between phase transformation kinetics and viscous relaxation.