## 5 Discussion  
The multiscale characterisation and analysis of the cortical bone tissue shown in this paper included several steps of analyses at different spatial scales, namely, microscopic and macroscopic scales. The micromechanical analyses performed in the microstructure of the cortical bone tissue initially took place through a homogenisation analysis. This procedure allowed to estimate both the micromechanical properties of the mineral bone material of the matrix, as well as the homogenised apparent properties of the bone tissue. Specifically, using the information of the performed mechanical tests (Table 1), we could fit the properties of the mineral bone matrix by means of the homogenisation problem (Equation (14)), and then, the overall macroscopic or apparent behaviour (Equation (15)). Several interesting conclusions can be drawn from this analysis, as we shall reveal next. Assuming an orthotropic mechanical behaviour of the bone mineral matrix, the microstructural arrangement of the cortical pores yields to an approximately orthotropic mechanical behaviour at the apparent level as well, along the longitudinal and transversal directions. This can be concluded from Equation (15) where it is seen that the components 1-3 and 2-3 of the matrix are one order of magnitude lower than the others. With a broad consensus, an orthotropic behaviour of the cortical bone is considered in the literature [4; 58; 59; 60]. Assuming an orthotropic apparent behaviour for the bone tissue, the following values are estimated, using homogenisation, in the longitudinal and transversal directions: \(\mathrm{E_{L}}\) = 16.32 GPa, \(\mathrm{E_{T}}\) = 19.31 GPa, \(\mathrm{\upsilon_{LT}}\) = 0.373 and \(\mathrm{\upsilon_{TL}}\) = 0.442. These values are within the range of values measured in the literature for cortical bone tissue. For example, values in the range of 15-22 GPa are reported for the elasticity modulus of equine cortical bone [61; 62; 63; 64]. On the other hand, for human bone tissue, values in the range of 10-25 GPa are found for the elasticity modulus, and 0.3-0.6 for the Poisson's ratio [4]. In the microstructural approach mineral bone is considered a homogeneous material without distinguishing among hydroxyapatite or collagen. A multiscale analysis may be recursively established  
Figure 9: Stress field [MPa]. (**a**) Transversal component: macroscopic results, (**b**) transversal component: multiscale results, (**c**) transversal component: microscopic results. (**d**) Longitudinal component: macroscopic results, (**e**) longitudinal component: multiscale results, (**f**) longitudinal component: microscopic results. at the microstructural level to accurately obtain the micromechanical interaction and overall behaviour of mineral bone [11; 65; 66]. Results referring to the multiscale approach were obtained using the fitted properties of the mineral bone matrix at the microscopic domain in the localisation problem. These results show a smooth variation along the microstructure of the displacement field (see Figure 7). Therefore, as a first approach, the displacement field may be estimated through its macroscopic modelling. However, both the strain field and--most importantly--the stress field show peak magnification of 3\(\times\) versus their macroscopic and homogenised (mean) values (see Figure 9). This is an extra and important added value given by the multiscale approach. It is currently accepted that the mechanical stimulus which orchestrates many bone processes and diseases, such as osteoporosis, remodelling or consolidation, is local and microstructural [27; 33; 34; 35; 36; 67; 68; 69; 70]. In this context, a multiscale approach is critical to link mechanical loading of the bone organ with internal and microstructural evolution of the bone tissue. Finally, as highlighted in the introduction, the low porosity level of the cortical bone makes this tissue not very attractive from a multiscale point of view, assuming a priori a similar mechanical behaviour to the mineral bone tissue matrix.