In conventional casting, metal cools once. Grains nucleate, grow, and freeze in a single thermal cycle. In additive manufacturing, each new layer reheats the layers below. The thermal history is a sawtooth — melt, solidify, reheat, partially remelt, resolidify — repeated hundreds of times. Grains that formed in layer 1 are thermally reworked by layers 2, 3, and beyond. The microstructure at the end depends not on one cooling curve but on the entire build history.
A mesoscopic grain-envelope model (arXiv:2603.06627) uses a phase-field front-propagation method to simulate grain growth under these conditions. Each grain is represented not as a discrete polygon but as a diffuse envelope — a continuous field that transitions smoothly across the grain boundary. The envelope advances according to a microscopic-solvability kinetic law that determines growth rate from local undercooling and crystallographic orientation.
The thermal model couples a modified heat-conduction equation with moving heat sources and latent heat release. Multi-pass, multi-layer build-up is captured: the laser or electron beam deposits material, heats the substrate, moves on. The grain boundaries respond to the evolving thermal field, growing, retreating, and reorienting as each layer is added.
The structural insight: in additive manufacturing, the microstructure is a cumulative record of process history. A grain's final morphology and orientation encode information about every thermal cycle it experienced. This makes the grain structure simultaneously a material property and a manufacturing signature — reading the microstructure tells you how the part was built.