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 a 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 rheological properties of the ink. The model was validated by comparison with data from the literature and those obtained from tests on produced scaffolds and monoliths. The contact radius significantly influences elastic response, especially for small overlap between the printed layers. The inverse solution can be used for estimation of bulk properties but is also helpful for quality assessment of the fabrication process.

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Principles and advantages of a new concept based on the ab initio aided strain gradient elasticity theory are shown in comparison with the classical Barenblatt cohesive model. The method is applied to the theoretical prediction of the critical energy release rate and the crack tip opening displacement at the crack instability in nanopanels made of germanium and molybdenum crystals. The necessary length scale parameter l1 is determined for germanium and molybdenum by the best gradient elasticity fits of ab initio computed screw dislocation displacements and phonon dispersions. Values of ab initio computed critical energy release rates and crack opening profiles revealed that the length l1 is related to inflexion points of profiles. A novel ab initio method in combination with continuum mechanics was successfully tested to replace molecular statics dependent of availability of interatomic potentials. The asymptotic strain gradient elasticity solution for displacement components near the crack tip in materials with cubic lattice was also derived.