Mineral–collagen interactions in elasticity of bone ultrastructure – a continuum micromechanics approach

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Multiscale modeling of elastic properties of cortical bone (2010, methodology): “In another parametric study, we selected a much higher value for collagen elastic modulus, 11.9 GPa as proposed by Cusack and Miller [63] and used by Hellmich et al. [ 38 ] and Fritsch et al. [14,40], and repeated all the modeling steps using both the Mori–Tanaka and the self-consistent methods with”
Spherical and acicular representation of hydrates in a micromechanical model for cement paste: prediction of early-age elasticity and strength (2009, background): “In (21), P scs sph denotes the Hill tensor related to the Eshelby-Laws problem where a single spherical inclusion of stiffness C p is embedded in a (fictitious) infinite matrix of elastic stiffness C hom ; for evaluation aspects concerning P scs sph see Appendix A.1 or [ 34 ,52,53].”
The effect of the nanogranular nature of shale on their poroelastic behavior (2007, methodology): “Within the framework of microporomechanics, the Hill concentration tensor (or P-tensor) characterizes the interaction between the different phases, and it is expressed as [ 40 ]:”