Porosity-Dependent Elasticity and Strength of Ceramic Bone Biomaterials: Micromechanics-based Assessment of Power Functions

Andreas Fritsch, Christian Hellmich, and Philippe Young


Ceramic bone biomaterials, Continuum micromechanics, Power law, Structureproperty relations


Porosity is a key factor in bone bio material design – it should be large enough as to allow for vascularization, but if it becomes too large, important mechanical properties such as stiffness and strength get too much compromised.Hence, porosity-mechanical properties are of key interest, and such relationships have been investigated experimentally,relating the data from mass or imaging tests to data from mechanical and acoustical tests. Since such experimental campaigns may become very expensive and time-consuming,mathematical models have been more and more introduced to the field. Recently, self-consistent continuum micro mechanics formulations have turned out as expressedly efficient and reliable tools to predict ceramic biomaterials’ stiffness and strength, as function of the biomaterial-specific porosity, and of the ‘universal’ properties of the individual crystals: their stiffness, strength, and shape. We here examine to which extent such structure property relationships can be represented by dimensionless power functions, as to provide an efficient interface to commercial software for large-scale simulation of heterogeneous structures in biomedical engineering, such as bone organ-implant compounds.

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