While the quest for understanding and even mimicking biological tissue has propelled, over the last decades, more and more experimental activities at the micro and nanoscales, the appropriate evaluation and interpretation of respective test results has remained a formidable challenge. As a contribution to tackling this challenge, we here describe a new method for identifying, from nanoindentation, the elasticity of the undamaged extracellular bone matrix. The underlying premise is that the tested bovine bone sample is either initially damaged (i.e. exhibits micro-cracks a priori) or that such micro-cracks are actually induced by the nanoindentation process itself, or both. Then, (very many) indentations may relate to either an intact material phase (which is located sufficiently far away from micro-cracks), or to differently strongly damaged material phases. Corresponding elastic phase properties are identified from the statistical evaluation of the measured indentation moduli, through representation of their histogram as a weighted sum of Gaussian distribution functions. The resulting undamaged elastic modulus of bovine femoral extracellular bone matrix amounts to 31 GPa, a value agreeing strikingly well both with direct quasi-static modulus tests performed on SEM-FIB-produced micro-pillars (Luczynski et al., 2015), and with the predictions of a widely validated micromechanics model (Morin and Hellmich, 2014). Further confidence is gained through observing typical indentation imprints under Scanning Electron Microscopy (SEM), which actually confirms the existence of the two types of micro-cracks as described above.

Mechanical property measurement protocols have their origins in metallurgy as well as in mechanical and civil engineering—metals being the first materials used on a broad industrial scale. Recent decades have evidenced growing interest in applying these protocols to biological materials or materials mimicking or replacing biological tissue. However, the mechanical properties of biological materials have been found to be highly variable and seemingly hard to capture by traditional protocols. A slow, emerging thought is that perhaps the mechanical theories underlying the testing protocols emanating from the metals field might not be fully applicable to the highly complex, hierarchically organized biological materials and might need further development. The articles in this issue highlight different and complementary, yet also interdependent, approaches to the challenge of extending theoretical and applied mechanics to the level needed for satisfying and reliably capturing the properties of biological materials. This issue also encompasses corresponding, far-reaching consequences for measurement techniques and evaluation protocols aimed at the determination of mechanical protocols.

From the biological/chemical perspective, interface concepts related to the cell surface/synthetic biomaterial interface and the extracellular matrix/biomolecule interface have wide applications in medical and biological technologies. Interfaces also play a significant role in determining structural integrity and mechanical creep and strength properties of biomaterials. Structural arrangement of interfaces combined with interfacial interactions between organic and inorganic phases significantly affects the mechanical properties of biological materials, allowing for a unique combination of seemingly inconsistent properties, such as fracture strength and tensile strength being both high—as opposed to traditional engineering materials, which have high fracture strength linked to low tensile strength and vice versa. While there has been a tremendous amount of work focused on the effects of structural arrangements on biomaterial properties, both experimental and computational studies of the strength, deformation, and viscosity of the interface itself are limited to just a few systems. Even in such studies, the actual interface stress is rarely analyzed, and correlated to the overall material strength or creep properties. This article provides a focused overview of such studies in hard biological materials, followed by a new vision of how the results of interfacial molecular studies could be consistently linked to multiscale, micromechanics-based perceptions of hierarchical biological materials.

Driving the field of micro computed tomography toward more quantitative, rather than qualitative, approaches, we here present a new evaluation method, which uses the unique linear relationship between gray values and x-ray attenuation coefficients, together with the energy-dependence of the latter, to identify (i) the average x-ray energy used in the CT device, (ii) the x-ray attenuation coefficients, and (iii), via the x-ray attenuation average rule, the intravoxel composition, i.e., the microporosity, which, amongst others, governs the voxel-specific mechanical properties, such as stiffness and strength. The method is realized for six 3D tricalcium phosphate scaffolds, seeded with pre-osteoblastic cells and differentiated for 3, 6, and 8 weeks, respectively. The corresponding voxel-specific microporosities turn out to increase during the culturing period (resulting in reduced elastic properties, as determined from micromechanical considerations), while the overall macroporosity remains constant. The new methods are expected to further foster the development of a rationally based and computer-aided design of biomaterials and tissue engineering scaffolds.

Biomimetics deals with the application of nature-made ‘design solutions’ to the realm of engineering. In the quest to understand mechanical implications of structural hierarchies found in biological materials, multiscale mechanics may hold the key to understand ‘building plans’ inherent to entire material classes, here bone and bone replacement materials. Analyzing a multitude of biophysical hierarchical and biomechanical experiments through homogenization theories for upscaling stiffness and strength properties, reveals the following design principles: The elementary component ‘collagen’ induces, right at the nanolevel, the mechanical anisotropy of bone materials, which is amplified by fibrillar collagen-based structures at the 100 nm-scale, and by pores in the micrometer-to-millimeter regime. Hydroxyapatite minerals are poorly organized, and provide stiffness and strength in a quasi-brittle manner. Water layers between hydroxyapatite crystals govern the inelastic behavior of the nano-composite, unless the ‘collagen reinforcement’ breaks. Bone replacement materials should mimic these ‘microstructural mechanics’-features as closely as possible.

Computer Tomographic (CT) image data have become a standard basis for structural analyses of bony organs. In this context, regression functions between stiffness components and Hounsfields units (HU) from Computer Tomography, related to X-ray attenuation coefficients, are widely used for the definition of the (actually inhomogeneous and anisotropic) material behavior inside the organ. Herein, we suggest to derive the functional dependence of the fully orthotropic stiffness tensors on the Hounsfield units from the physical information contained in the X-ray attenuation coefficients: (i) Based on voxel average rules for the X-ray attenuation coefficients, we assign to each voxel the volume fraction occupied by water (marrow) and that occupied by solid bone matrix. (ii) By means of a continuum micromechanics representation for bone, which is based on voxel-invariant (species and whole bone-specific) stiffness properties of solid bone matrix and of water, we convert the aforementioned volume fractions into voxel-specific orthotropic stiffness tensor components. The micromechanics model, in combination with the average rule for X-ray attenuation coefficients, predicts a quasi-linear relationship between axial Young's modulus and HU, and highly nonlinear relationships for both circumferential and radial Young's moduli as well as for the shear moduli in all principal material directions. Corresponding whole-organ Finite Element analyses of a partially dentulous human mandible characterized by atrophy of the alveolar ridge show that volumetric strain concentrations/peaks within the organ are decreased when considering material anisotropy, and increased when considering material inhomogeneity.

Hydroxyapatite biomaterials production has been a major field in biomaterials science and biomechanical engineering. As concerns prediction of their stiffness and strength, we propose to go beyond statistical correlations with porosity or empirical structure-property relationships, as to resolve the material-immanent microstructures governing the overall mechanical behavior. The macroscopic mechanical properties are estimated from the microstructures of the materials and their composition, in a homogenization process based on continuum micromechanics. Thereby, biomaterials are envisioned as porous polycrystals consisting of hydroxyapatite needles and spherical pores. Validation of respective micromechanical models relies on two independent experimental sets: Biomaterial-specific macroscopic (homogenized) stiffness and uniaxial (tensile and compressive) strength predicted from biomaterial-specific porosities, on the basis of biomaterial-independent (‘universal') elastic and strength properties of hydroxyapatite, are compared to corresponding biomaterial-specific experimentally determined (acoustic and mechanical) stiffness and strength values. The good agreement between model predictions and the corresponding experiments underlines the potential of micromechanical modeling in improving biomaterial design, through optimization of key parameters such as porosities or geometries of microstructures, in order to reach desired values for biomaterial stiffness or strength.

Bone materials are characterized by an astonishing variability and diversity. Still, because of ‘architectural constraints’, their fundamental hierarchical organization or basic building plans remain largely unchanged during biological evolution. These building plans govern the mechanical interaction of the elementary components of bone (hydroxyapatite, collagen, water; with directly measurable tissue-independent elastic properties), which are here quantified through a multiscale homogenization scheme delivering effective elastic properties of bone materials: At a scale of 10 nm, long cylindrical collagen molecules, attached to each other at their ends by ∼1.5 nm long crosslinks and hosting intermolecular water inbetween, form a contiguous matrix called wet collagen. At a scale of several hundred nanometers, wet collagen and mineral crystal agglomerations interpenetrate each other, forming the mineralized fibril. At a scale of 5 microns, the solid bone matrix is represented as collagen fibril inclusions embedded in a foam of largely disordered (extrafibrillar) mineral crystals. Remarkably, needle and sphere type representations of disordered minerals deliver quasi-identical mechanical behavior of such extrafibrillar porous polycrystals. At a scale above the ultrastructure lacunae are embedded in extracellular bone matrix, forming the extravascular bone material. Model estimates predicted from tissue-specific composition data agree remarkably well with corresponding stiffness experiments across cortical and trabecular materials, which opens new possibilities in the exploitation of computer tomographic data for nano-to-macro mechanics of bone organs, especially in combination with currently investigated extensions towards damage and failure.

Wood exhibits a highly diversified microstructure. It appears as a solid-type composite material at a length scale of some micrometers, while it resembles an assembly of plate-like elements arranged in a honeycomb fashion at the length scale of some hundreds of micrometers. These structural features of wood result in different load carrying mechanisms at different observation scales and at different loading conditions. In this paper, we elucidate the main load carrying mechanisms by means of a micromechanical model for wood across different species, based on tissue-independent stiffness properties of cellulose, lignin, and water. The model comprises three homogenization steps, two based on continuum micromechanics and one on the unit cell method. The latter represents plate-like bending and shear of the cell walls, due to transverse shear loading and axial straining in the tangential direction Accurate representation of these deformation modes results in accurate (orthotropic) stiffness estimates, which deviate, on average, by less than 10 % from corresponding experimental results, across a variety of softwood species.

Based on ‘universal’ mechanical building blocks inherent to all different bones, this paper shows the integration of two classically separated fields of bone biomechanics, namely bone micromechanics[1] on the one hand, and bone poromechanics[2] on the other. Indeed, despite the complex hierarchical organization of bone, it was recently possible to identify such elementary components at the micro and nanolevel of the material for the explanation of the diversity of macroscopic (poro-)elastic properties of different bones. The mechanical properties (i.e. elasticity) of these elementary components are (within limits of experimental scatter) the same for all bones; they are ‘universal’, i.e. independent of tissue type, species, and anatomical location. The mechanical interaction between these elementary components (mechanical morphology) and the dosages of these components in different tissues determine the macroscopic material properties.

Continuum micromechanics has turned out as well-suited theoretical tool to derive tissue-dependent elastic properties at different length scales from upscaling the elasticity of ‘universal’ building blocks from the nanometer scale. Once respective micromechanics models are developed and validated, poro-micromechanics allows for the quantification of poroelastic properties such as the Biot and Skempton coefficients, as functions of the volume fractions of mineral, collagen, and the micropore space (Haversian and Volkmann canals, and the inter-trabecular space). Skempton coefficients, related to undrained conditions, allow for quantification of the marrow pressure rise due to impact loading, as can be shown by model predictions of non-destructive impact experiments. Moreover, the aforementioned poroelastic properties enter the governing equations for wave propagation in anisotropic porous media. They allow for the prediction of undrained, fast and slow waves, as is verified by comparison of model results with experimental findings.