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.

在现代工程应用中，将软材料和硬材料连接起来是一个具有挑战性的问题。为了缓解具有机械性能不匹配的材料之间的界面处的应力集中，在新一代工程复合材料的设计中，功能梯度过渡相的使用变得越来越普遍。但是，由于计算量大，当前旨在模仿此类复杂系统的机械行为的宏观模型通常无法纳入微结构细节在整个相间的影响。在本文中，我们建议用零厚度的界面代替薄但有限的功能梯度相间。这是通过在表面弹性框架内开发的原始模型来实现的，这说明了实际相间的弹性和惯性行为。通过将计算的反射系数与使用不同基准模型获得的反射系数进行比较，可以在弹性波传播的背景下评估建议的等效模型的性能。数值结果表明，我们的动态表面弹性模型在较宽的频率范围内提供了参考相间模型的精确近似。我们证明了这种建模方法在腱到骨间期的梯度组织系统的表征中的应用，该过程完成了在亚毫米宽的区域内将软组织合并为硬组织的艰巨任务。通过将计算出的反射系数与使用不同基准模型获得的反射系数进行比较。数值结果表明，我们的动态表面弹性模型在较宽的频率范围内提供了参考相间模型的精确近似。我们证明了这种建模方法在腱到骨间期的梯度组织系统的表征中的应用，该过程完成了在亚毫米宽的区域内将软组织合并为硬组织的艰巨任务。通过将计算出的反射系数与使用不同基线模型获得的反射系数进行比较。数值结果表明，我们的动态表面弹性模型在较宽的频率范围内提供了参考相间模型的精确近似。我们证明了这种建模方法在腱到骨间期的梯度组织系统的表征中的应用，该过程完成了在亚毫米宽的区域内将软组织合并为硬组织的艰巨任务。