Table 1.

Compilation of material parameters from experimental and numerical studies in the literature

Material parameter	Microstructure	Abbreviations	Experimental studies	Numerical studies
Young’s modulus (GPa)	Matrix	E mat	13.8–15.3a; 10.8b	14.122v,w,x,y; 14z; 14.6aa,ab,ac; 14.6–15.4ad; 25.8ae; 10af; 4ag; 18.5–27.1ah
	Osteon	E ost	(0.63–0.76) * Ematc; 0.91 * Ematd; ~ 0.85 * Emate; 7.4–18.5f	9.13v,x,z; 9z; 13.5aa,ab; 13.5–14.3ad; 12.85w; 22.5ae; 4.4ag; 16.6–25.1ah; 13.3ac
	Cement line	E cl	Ecl > Ematg,h; Ecl < Emati; 0.7 * Ematj	6.85v,x; 7z; 10.12aa,ab; 0.75 * Eostad; 9.64w; 3.3ag; 0.09ac,ai
Poisson’s ratio	Matrix	ν mat		0.153v,w,x; 0.3aa,ab,ae,ag; 0.15z,af; 0.24–0.33ah
	Osteon	ν ost		0.17v,w,x,z; 0.33aa,ab; 0.3ae,ag; 0.24–0.33ah
	Cement line	ν cl		0.49v,w,x,y,z; 0.41aa,ab; 0.3ag
Critical damage initiation strain (MAXPE criterion)	Matrix	${\epsilon }_{\text{max},\text{mat}}^0$	~ 0.01k; 0.005l,m; 0.011n	0.004v,x,y,aa,ab,ad; 0.0065w; ${\left({\sigma }_{\text{mat}}^0=0.55\ast {\sigma }_{\text{ost}}^0\right)}^{\text{ac}}$
	Osteon	${\epsilon }_{\text{max},\text{ost}}^0$		0.004v,x,y,aa,ab,ad; 0.0065w;
	Cement line	${\epsilon }_{\text{max},\text{cl}}^0$		0.004v,x,y,aa,ab,ad; 0.0065w; ${\left({\sigma }_{\text{cl}}^0=0.06\ast {\sigma }_{\text{ost}}^0\right)}^{\text{ac}}$
Critical interface strain (QUADE criterion)	Cement line	${\epsilon }_{n,\text{cl}}^0$		${\left({\sigma }_{n,\text{cl}}^0={\sigma }_{n,\text{mat}}^0\right)}^{\text{ae}}$
	Cement line	${\epsilon }_{s,\text{cl}}^0$	${\left({\tau }_{s,\text{cl}}^0\sim 0.1\ast {\tau }_{s,\text{mat}}^0\right)}^o;$ ${\left({\tau }_{s,\text{cl}}^0\lesssim {\tau }_{s,\text{ost}}^0\right)}^p$	${\left({\tau }_{s,\text{cl}}^0=0.12\ast {\tau }_{s,\text{mat}}^0\right)}^{\text{ae}}$
Strain energy release rate (kJ/m2)	Matrix	G mat	(~ 0.6–0.8)q; (~ 0.05T–0.2L)r; (~ 0.05–0.2K)s; (0.05–0.13K)k; ~ 0.2t	0.238v,w,x,z,ac,af; 0.09K,aa; 0.132ab; 0.05K,ae; 1.16ah
	Osteon	G ost	(Gost > Gmat)u	0.86v,w,x,z,ac; 0.11K,aa; 0.120ab; 0.05K,ae
	Cement line	G cl		0.146v,w,x,z; 0.05K,aa; 0.084ab; 0.05K,ae 0.1629ac,ag

The mean value is given in case mean ± SD was reported in the cited article. Where no quantitative data were available, relative measures were reported. Values for damage initiation were considered in experimental data reporting stress intensity or fracture energy (strain energy release rate). The stiffness for the matrix was measured under wet conditions. Symbols used in the table: ~ approximate value interpreted from figures; ^KG calculated from a reported stress intensity factor K, where G = K²/E, assuming E = 20 GPa (Koester et al. 2008); ^Ttransverse osteons (crack parallel to osteons); ^Llongitudinal osteons (crack perpendicular to osteons)

^aFaingold et al. (2014); ^bNyman et al. (2006); ^cRho et al. (1999); ^dRho et al. (2002); ^eMullins et al. (2009); ^fHengsberger et al. (2002); ^gSkedros et al. (2005); ^hMilovanovic et al. (2018); ⁱBurr et al. (1988); ^jMontalbano and Feng (2011); ^kChan et al. (2009); ^lGargac et al. (2014); ^mGustafsson et al. (2018b); ⁿSun et al. (2010); ^oDong et al. (2005); ^pBigley et al. (2006); ^qNorman et al. (1995); ^rZimmermann et al. (2009); ^sKoester et al. (2008); ^tNalla et al. (2005); ^uMullins et al. (2009); ^vAbdel-Wahab et al. (2012); ^wLi et al. (2013); ^xVergani et al. (2014); ^yBudyn and Hoc (2007); ^zBaptista et al. (2016); ^aaIdkaidek and Jasiuk (2017); ^abWang et al. (2017); ^acIdkaidek and Jasiuk (2017); ^adBudyn et al. (2008); ^aeDemirtas et al. (2016); ^afRodriguez-Florez et al. (2017); ^agGiner et al. (2017); ^ahMischinski and Ural (2011); ^aiNobakhti et al. (2014)