A continuum model for phase transformations in the glass production based on Hamilton principle

Glass is an extensively used material in numerous branches such as automotive and aerospace industries as well as residential construction. The conventional production methods of glass are either subtractive or molding-based. However, for geometrically complex structures, additive manufacturing techniques are inevitable. Additive manufacturing of glass is a relatively new field especially when it comes to mathematical modeling and numerical simulation. A continuum-based mathematical model based on extended Hamilton’s principle is developed in this paper for phase transformation during the manufacturing process. The application of the model can be in the simulation of laser powder bed fusion (L-PBF) method. Since the focus is on modeling the phase change, mechanical deformation is excluded from the energy formulation. Three distinct phases, namely crystalline powder, liquid (molten), and amorphous solid, is considered, and the transformation of these phases is thermally driven. Whether a molten material turns into either crystalline or amorphous solid depends on the cooling rate. The proposed model is naturally capable of switching between these two paths in an energetic framework. To find an optimal setting for the manufacturing process in glass industry, numerical tools are remarkable alternatives to trial-and-error procedures which are time-consuming and expensive. The mathematical model is implemented using AceGen in the framework of finite element method leading to an in-house user element that can be invoked by many FE solver.