The interphase joining tendon to bone plays the crucial role of integrating soft to hard tissues, by effectively transferring stresses across two tissues displaying a mismatch in mechanical properties of nearly two orders of magnitude. The outstanding mechanical properties of this interphase are attributed to its complex hierarchical structure, especially by means of competing gradients in mineral content and collagen fibers organization at different length scales. The goal of this study is to develop a multiscale model to describe how the tendon-to-bone insertion derives its overall mechanical behavior. To this end, the effective anisotropic stiffness tensor of the interphase is predicted by modeling its elastic response at different scales, spanning from the nanostructural to the mesostructural levels, using continuum micromechanics methods. The results obtained at a lower scale serve as inputs for the modeling at a higher scale. The obtained predictions are in good agreement with stochastic finite element simulations and experimental trends reported in literature. Such model has implication for the design of bioinspired bi-materials that display the functionally graded properties of the tendon-to-bone insertion.

Functional grading is a distinctive feature adopted by nature to improve the transition between tissues that present a strong mismatch in mechanical properties, a relevant example being the tendon-to-bone attachment. Recent progress in multi-material additive manufacturing now allows for the design and fabrication of bioinspired functionally graded soft-to-hard composites. Nevertheless, this emerging technology depends on several design variables, including both material and mechanistic ingredients, that are likely to affect the mechanical performance of such composites. In this paper, a model-based approach is developed to describe the interaction of ultrasound waves with homogeneous and heterogeneous additively manufactured samples, which respectively display a variation either of the material ingredients (e.g., ratio of the elementary constituents) or of their spatial arrangement (e.g., functional gradients, damage). Measurements are performed using longitudinal bulk waves, which are launched and detected using a linear transducer array. First, model is calibrated by exploiting the signals measured on the homogeneous samples, which allow identifying relationships between the model parameters and the material composition. Second, the model is validated by comparing the signals measured on the heterogeneous samples with those predicted numerically. Overall, the reported results pave the way for characterizing and optimizing multi-material systems that display complex bioinspired features.

Joining soft to hard materials is a challenging problem in modern engineering applications.In order to alleviate stress concentrations at the interface between materials with such a mismatch in mechanical properties, the use of functionally graded interphases is becoming more widespread in the design of the new generation of engineered composite materials.However, current macroscale models that aim at mimicking the mechanical behavior of such complex systems generally fail in incorporating the impact of microstructural details across the interphase because of computational burden. In this paper we propose to replace the thin, but yet finite, functionally graded interphase by a zero-thickness interface. This is achieved by means of an original model developed in the framework of surface elasticity, which accounts for both the elastic and inertial behavior of the actual interphase. The performance of the proposed equivalent model is evaluated in the context of elastic wave propagation, by comparing the calculated reflection coefficient to that obtained using different baseline models. Numerical results show that our dynamic surface elasticity model provides an accurate approximation of the reference interphase model over a broad frequency range. We demonstrate application of this modeling approach for the characterization of the graded tissue system at the tendon-to-bone interphase, which fulfills the challenging task of integrating soft to hard tissues over a submillimeter-wide region.

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