Stretching the Printability Metric in Direct‐Ink Writing with Highly Extensible Yield‐Stress Fluids

ABSTRACT Direct‐ink writing leverages the rheological complexity of yield‐stress fluids to construct complex geometries, particularly those with large gaps. However, extensional rheology is often overlooked when studying how ink properties relate to printability. Here, we test our hypothesis that extensional properties correlate with drawability, a key indicator of printability that signifies speed robustness, resolution, and gap‐spanning performance. We formulated cementitious suspensions using hydroxyapatite particles, tuning them for yield stress and extensibility – two crucial properties for printability – then test‐printed them. Adding the modifier hydroxypropyl methylcellulose can enhance extensibility, but this may lead to the opposite effect at high particle loadings, presenting a challenge in materials design. To achieve a wide range of yield stress and extensibility, we modulate particle interactions, allowing for rigorous testing of our hypothesis. This approach created inks with high extensibility and high yield stress – generally considered mutually exclusive properties. Correlation analysis reveals that extensional failure strain (strain‐to‐break) is a reliable indicator of drawability rather than yield stress. Combining our findings with previous studies on buildability establishes a direct rheology‐manufacturing relationship (shear yield stress to buildability and extensional strain‐to‐break to drawability), providing a comprehensive framework for designing high‐performance inks that are self‐supporting, capable of high‐speed printing, and allow gap‐spanning features.