First- and Second-Order Phase Transformation Modeling Based on the Hamilton Principle: A Coupled Thermo-Mechanical Approach for Glass Additive Manufacturing
This study addresses the complex microstructural evolution and residual stress challenges in glass additive manufacturing induced by extreme thermal histories. The authors propose a unified variational framework based on the extended Hamilton’s principle, which for the first time couples thermo-mechanical and phase transformation processes to simultaneously capture both the first-order melting and second-order glass transition under large deformations. A kinetic freezing mechanism is incorporated to model glass formation. The framework integrates a temperature-dependent viscosity constitutive law, the single-slice neighborhood element method (NEM), and a three-dimensional finite element implementation in ANSYS. The approach successfully reproduces time–temperature–transformation (TTT) behavior across varying cooling rates and accurately predicts residual stresses and macroscopic warpage during laser-based deposition, establishing a high-fidelity multiphysics simulation foundation for glass additive manufacturing.