Direct ink write (DIW) is a nascent additive manufacturing technique that is capable of rapidly fabricating arbitrary complex three-dimensional ceramic objects. DIW involves a sintering step that greatly influences many of the salient features of the printed object, such as internal porosity and grain microstructures. Herein, we present a mesoscopic modeling framework to examine solid-state sintering in DIW processes. The proposed modeling framework accounts for interface (i.e., free surfaces and grain boundaries) thermodynamics and captures various mass transport mechanisms. With the aid of several statistical (e.g., n-point statistics and chord length distributions) and topological (e.g., curvature) metrics, the role of particle size/distribution, equilibrium dihedral angles, and interfacial anisotropy in the microstructural evolution in filament-based DIW is explored and quantified. In broad terms, our modeling approach provides future avenues to explore the microstructural evolution and interfacial phenomena in DIW processes.