Mechanical testing is the most common experimental technique to determine elastic stiffness of materials. In case of porous materials, especially such with very high porosity, the determination of material stiffness may be strongly biased by inelastic deformations occurring in the material samples, especially in the vicinity of the load transfer devices, such as loading platens. In contrast, ultrasonic waves propagating through a material generate very small stresses and strains (and also strain rates lying in the ‘quasistatic’ regime). Thus, they enable the direct determination of the components of elastic stiffness tensors of materials, and also of those with a very high porosity. We shortly revisit from the theoretical basis of continuum (micro)mechanics that, depending on the frequency of the employed acoustical signals, the investigated materials are characterised at different observation scales, e.g. the elasticity of the overall porous medium, or that of the solid matrix inside the material are determined. We here report the elastic properties of biomaterials and biological materials at different length scales, by using ultrasound frequencies ranging from 100 kHz to 20 MHz. We tested isotropic scaffolds for biomedical engineering, made up of porous titanium and two different bioactive glass–ceramics, and we also determined the direction‐dependent normal and shear stiffness components of the anisotropic natural composite ‘spruce wood’.

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Owing to their stimulating effects on bone cells, ceramics are identified as expressly promising materials for fabrication of tissue engineering (TE) scaffolds. To ensure the mechanical competence of TE scaffolds, it is of central importance to understand the impact of pore shape and volume on the mechanical behaviour of the scaffolds, also under complex loading states. Therefore, the theory of continuum micromechanics is used as basis for a material model predicting relationships between porosity and elastic/strength properties. The model, which mathematically expresses the mechanical behaviour of a ceramic matrix (based on a glass system of the type SiO 2 -P 2 O 5 -CaO-MgO-Na 2 O-K 2 O; called CEL2) in which interconnected pores are embedded, is carefully validated through a wealth of independent experimental data. The remarkably good agreement between porosity based model predictions for the elastic and strength properties of CEL2-based porous scaffolds and corresponding experimentally determined mechanical properties underlines the great potential of micromechanical modelling for speeding up the biomaterial and tissue engineering scaffold development process -by delivering reasonable estimates for the material behaviour, also beyond experimentally observed situations. List of symbolsA r fourth order strain concentration tensor of phase r A s fourth order strain concentration tensor of solid phase (dense CEL2 glass ceramic) A por fourth order strain concentration tensor of pores a typical cross-sectional dimension of a CEL2-based porous biomaterial sample C hom fourth order homogenised stiffness tensor C ijkl components of fourth order homogenised stiffness tensor C por fourth order stiffness tensor of pores C S fourth order stiffness tensor of solid phase (dense CEL2 glass ceramic) d characteristic length of inhomogeneity within an RVE E second order 'macroscopic' strain tensor E d deviatoric part of macroscopic strain tensor E S Young's modulus of solid phase (dense CEL2 glass ceramic) E exp experimentally determined Young's modulus of porous CEL2-based biomaterial E exp mean over all experimentally determined Young's moduli of porous CEL2-based biomaterial E hom homogenised Young's modulus of porous CEL2-based biomaterial e mean of relative error between predictions and experiments e S standard deviation of relative error between predictions and experiments e 1 unit base vector of Cartesian reference base frame f ultrasonic excitation frequency f(s)50 boundary of elastic domain of solid material phase, in space of microstresses g 1 , g 2 functions for determination of homogenised elastic constants k hom and m hom (see equation (18)) I fourth order identity tensor J volumetric part of fourth order identity tensor I Advances in Applied Ceramics 2008 VOL 107 NO 5 277K deviatoric part of fourth order identity tensor I k j DS , k jz1 DS homogenised bulk moduli of step j and jz1 in a Differential Scheme k S bulk modulus of solid phase (dense CEL2 glass ceramic) k hom homogenised bulk modulus of porous CEL2-based ...