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Hard, biological materials are generally hierarchically structured from the nano-to the macroscale in a somewhat self-similar manner consisting of mineral units surrounded by a soft protein shell. Considerable efforts are underway to mimic such materials because of their structurally optimized mechanical functionality of being hard and stiff as well as damagetolerant. However, it is unclear how different hierarchical levels interact to achieve this performance. In this study, we consider dental enamel as a representative, biological hierarchical structure and determine its flexural strength and elastic modulus at three levels of hierarchy using focused ion beam (FIB) prepared cantilevers of micrometre size. The results are compared and analysed using a theoretical model proposed by Jäger and Fratzl and developed by Gao and co-workers. Both properties decrease with increasing hierarchical dimension along with a switch in mechanical behaviour from linear-elastic to elastic-inelastic. We found Gao's model matched the results very well.

This study investigates bone-tooth association under compression to identify strain amplified sites within the bone-periodontal ligament (PDL)-tooth fibrous joint. Our results indicate that the biomechanical response of the joint is due to a combinatorial response of constitutive properties of organic, inorganic, and fluid components. Second maxillary molars within intact maxillae (N=8) of 5-month-old rats were loaded with a μ-XCT-compatible in situ loading device at various permutations of displacement rates (0.2, 0.5, 1.0, 1.5, 2.0 mm/min) and peak reactionary load responses (5, 10, 15, 20 N). Results indicated a nonlinear biomechanical response of the joint, in which the observed reactionary load rates were directly proportional to displacement rates (velocities). No significant differences in peak reactionary load rates at a displacement rate of 0.2 mm/min were observed. However, for displacement rates greater than 0.2 mm/min, an increasing trend in reactionary rate was observed for every peak reactionary load with significant increases at 2.0 mm/min. Regardless of displacement rates, two distinct behaviors were identified with stiffness (S) and reactionary load rate (LR) values at a peak load of 5 N (S5 N=290–523 N/mm) being significantly lower than those at 10 N (LR5 N=1–10 N/s) and higher (S10N–20 N=380–684 N/mm; LR10N–20 N=1–19 N/s). Digital image correlation revealed the possibility of a screw-like motion of the tooth into the PDL-space, i.e., predominant vertical displacement of 35 μm at 5 N, followed by a slight increase to 40 μm at 10 N and 50 μm at 20 N of the tooth and potential tooth rotation at loads above 10 N. Narrowed and widened PDL spaces as a result of tooth displacement indicated areas of increased apparent strain within the complex. We propose that such highly strained regions are “hot spots” that can potentiate local tissue adaptation under physiological loading and adverse tissue adaptation under pathological loading conditions.

High‐toughness, high‐strength ceramics, such as self‐reinforced Si3N4, derive their superior mechanical properties from microstructures that promote very steeply rising R curves. Furthermore, accurately evaluating the R curve at the earliest stages of crack growth is necessary for correctly understanding, and predicting, the mechanical behavior. Compliance‐ and optical‐based methods for evaluating the crack length, and R curve, at the early stages of crack extension from machined notches are discussed. The earliest stages of crack growth are missed during measurements of the crack length by optical observations due to the nonuniform extension of the crack front during initial crack extension. The most accurate method of evaluating the crack length over all amounts of crack extension is from compliance measurements analyzed by solving a system of equations that incorporates both the effects of the notch and the changes in compliance with the development of bridging tractions. Such a method is computationally expensive, but for materials with steeply rising R curves, simply applying the linear‐elastic compliance evaluation, which only accounts for the notch, but not the bridging tractions, gives a result within about 1%. At longer crack extensions, such an approximation method will incur significant errors; however, at this stage, optical measurements can provide accurate assessments of crack length and enable an accurate assessment of the R curve.

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In this study, an in vivo ligature-induced periodontitis rat model was used to investigate temporal changes to the solid and fluid phases of the joint by correlating shifts in joint biomechanics to adaptive changes in soft and hard tissue morphology, and functional space. After 6 and 12 weeks of ligation, coronal regions showed a significant decrease in alveolar crest height, increased expression of TNF-α, and degradation of attachment fibers as indicated by decreased collagen birefringence. Cyclical compression to peak loads of 5-15N at speeds of 0.2-2.0N/mm followed by load relaxation tests showed decreased stiffness and load rate values, load relaxation, and load recoverability, of ligated joints. Shifts in joint stiffness and reactionary load rate increased with time while shifts in joint relaxation and recoverability decreased between control and ligated groups, complementing measurements of increased tooth displacement as evaluated through digital image correlation. Shifts in functional space between control and ligated joints were significantly increased at the interradicular (Δ10-25μm) and distal coronal (Δ20-45μm) regions. Histology revealed time-dependent increases in nuclei elongation within PDL cells and collagen fiber alignment, uncrimping, and directionality, in 12-week ligated joints compared to random orientation in 6-week ligated joints and to controls. We propose that altered strains from tooth hypermobility could cause varying degrees of solid-to-fluid compaction, alter dampening characteristics of the joint, and potentiate increased adaptation at the risk of joint failure.

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