Estimation of the effective elastic constants of bone scaffolds fabricated by direct ink writing

Direct ink writing is a popular method for fabrication of scaffolds, yet its widespread usage in clinical practice requires guarantee of compatibility of a scaffold with bone tissues. Mechanical compatibility is mandatory to prevent stress shielding and is expressed using the difference between effective elastic constants (EECs) of a scaffold and tissue. In this paper, the solution for EECs of a calcium phosphate scaffold is derived for any combination of input parameters, inclusive of the contact radius at the joints, a feature arising mainly from the Theological properties of the ink. The model was validated by the comparison with data from the literature and those obtained from tests on produced scaffolds and monoliths. The contact radius significantly influences the elastic response and local stresses in the structure. The inverse solution can be used for estimation of bulk properties and is also helpful for the quality assessment of fabrication process.