Glass is a versatile material that is used industrially for a wide variety of purposes. Its physical properties such as thermal and chemical resistance, electrical insulation and hardness distinguish glass from transparent plastics. These properties are particularly important in the field of optics. In the production of high-performance lenses in the field of optical lasers, the requirements for precision and flexibility in shaping are constantly increasing. To meet these requirements, additive manufacturing processes are becoming increasingly important. Despite the large number of manufacturing processes, high temperatures are usually required to bring the starting material into the desired shape. The temperature and its gradients significantly influence the material properties of glass during the phase transformation. The local fusion of material at the interface between the particles taking place at high temperatures is a multiphysics process in nature. The mathematical model of multi-field problems is challenging due to thermodynamics-dictated principles. In order to fulfill the thermodynamic consistency, an extension of the Hamilton principle is employed to drive the governing differential equations. The evolution equations and corresponding driving forces formulated within this framework are thermo-mechanically coupled. A hybrid strategy based on both finite elements and mesh free finite differences methods is utilized to numerically implement the mathematical model. This procedure is called the Neigbhored Element Method (NEM). The numerical code is implemented in the ANSYS software environment. The aim is to simulate the phase transformation of glass during additive manufacturing processes. The influence of different temperature gradients and different process parameters should be taken into account. Such numerical tool provides insights into controlling the design parameters of 3D printed parts such as unwanted distortions, residual stresses and desired mechanical stiffness.