The influence of volumetric shrinkage on the metal solidification process under localized energy deposition

Accurate simulation of metal melting and solidification under localized energy deposition is crucial for the advancement of beam-based manufacturing technologies. This study presents an extended multi-physics model that addresses a critical limitation of prior approaches by incorporating volumetric changes from phase transitions and thermal expansion, in addition to capillary and thermocapillary effects. Validation against the benchmark problems—including a one-dimensional Stefan problem, two-dimensional solidification with free surface, and axisymmetric laser melting—demonstrates the high fidelity of the proposed model in describing melt-pool dynamics and free-surface evolution. The numerical implementation features a novel mass-correction algorithm that reduces the mass conservation error by several orders of magnitude, while a smoothed mushy-zone formulation in the enthalpy method mitigates the discretization artifacts in solid–liquid interface tracking. The results indicate that volumetric shrinkage plays an important role in surface topography formation during solidification.