Wave propagation across a functionally graded interphase between soft and hard solids: Insight from a dynamic surface elasticity model

Abstract

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.

Numerical investigation of the dynamic behavior of a Ti/TiB functionally graded material using Split Hopkinson Pressure Bar test

“…Nevertheless, modern investigations of the high-rate behavior of FGMs have started with the works of a few authors. 38,39…”

“…Nevertheless, modern investigations of the high-rate behavior of FGMs have started with the works of a few authors. 38,39 Indeed, Tasdemirci et al 40 simulated multilayer materials under high strain rate compression using Split Hopkinson Pressure Bar (SHPB) apparatus The authors proposed a technique to understand wave propagation effects. Finally, Kidane and Shukla 41 carried out an experimental investigation to discuss FGMs' thermo-mechanical constitutive behavior under dynamic loading.…”

Parameter identification of a second-gradient model for the description of pantographic structures in dynamic regime

“…These unusual mechanical behaviors at the macro-scale are due to the interactions of the underlying microstructure of the metamaterial. For example, we may mention the so-called locally resonant acoustic metamaterials [8], or the lattice fiber materials [9] as well as inclusions' effect due to their moduli mismatch [10]. The role of material symmetry considering static and dynamic properties of materials is discussed in [11].…”