Table 2.

Iteration scheme for deriving the macroscopic loading of the biomaterial inducing quasi-brittle failure in the most unfavorably stressed hydroxyapatite needle

Iteration steps
1.	Choice of initial value for ${\mathrm{\Sigma }}_{\text{congl},11}$.
2.	Computation of macroscopic stress tensor according to Eq. (5).
3.	Downscaling of macroscopic stress tensor to the level of hydroxyapatite needles as function of the needle orientation, ${\mathit{\sigma }}_{\text{HA}}^{\text{polyHA}}(\mathit{\vartheta },\mathit{\phi })$, $\mathit{\vartheta }=0\dots \mathit{\pi }$, $\mathit{\phi }=0\dots 2\mathit{\pi }$, by means of Eqs. (2–13).
4.	Calculation of the corresponding normal and shear stress component experienced by single hydroxyapatite needles, for any needle orientation, $\mathit{\vartheta }=0\dots \mathit{\pi }$, $\mathit{\phi }=0\dots 2\mathit{\pi }$, and for any tangential plane, $\mathit{\psi }=0\dots 2\mathit{\pi }$, by means of Eqs. (14–18).
5.	Evaluation of the failure criterion given by Eqs. (19) and (20), respectively:
	–If ${\mathfrak{f}}_{\text{HA}}({\mathbf{\Sigma }}_{\text{congl}})<0$, then $|{\mathrm{\Sigma }}_{\text{congl},11}|$ is increased; return to step 2.
	–If ${\mathfrak{f}}_{\text{HA}}({\mathbf{\Sigma }}_{\text{congl}})=0$, then the load iteration is completed, and the current magnitude for ${\mathrm{\Sigma }}_{\text{congl},11}$ induces failure of the material.
	–If ${\mathfrak{f}}_{\text{HA}}({\mathbf{\Sigma }}_{\text{congl}})>0$, then $|{\mathrm{\Sigma }}_{\text{congl},11}|$ is decreased; return to step 2.