3D modeling for acoustic waves and vibrations in solid structures with frictional cracks

Abstract

We present a numerical modeling tool for engineering applications related to materials and systems having internal frictional contacts in their structure. The technique is based on a semi-analytical method for simulating contact mechanical problems, called the Method of Memory Diagrams (MMD) [1,3], which is able to calculate hysteretic frictional contact responses. The MMD is applicable when an axisymmetric contact system is excited by an arbitrarily changing shift in 3D [2] and can be extended to the contact of globally plane surfaces with isotropic roughness. The method uses some assumptions and does not provide the full functionality of purely numerical contact modeling, but is much more efficient computationally. This quantitative gain in performance makes the MMD applicable to the case of acoustic or random excitation signals containing a large number of oscillations.The integration of the MMD contact model in a finite element environment [4] (COMSOL) allows to simulate acoustic wave propagation and vibration in structures or materials containing hidden frictional interfaces (cracks, delaminations, loose joints, etc). We discuss proof-of-concept results in a simple 3D geometry containing to a surface-breaking crack insonified by an oblique compression wave simultaneously exciting normal and tangential interactions.