Backward Mach cone of shear waves induced by a moving force in soft anisotropic materials

Abstract

When a point force travels in a solid with a speed greater than the velocity of the elastic wave induced, the interfering elastic wave fronts will form a Mach cone. This phenomenon is called the elastic Cherenkov effect (ECE). In this study, the ECE in soft matter was investigated with emphasis on backward Mach cone formation. Phase diagrams were proposed based on the theoretical analysis to elucidate key features of the ECE in a wide material parameter space, including the critical conditions for the onset of backward Mach cones and the cone angles. Subsequently, finite element models were developed to validate the theoretical solutions. Our results show that backward Mach cones can be formed in some typical soft tissues under the described conditions, which is important for the use of the ECE in characterizing the mechanical properties of these soft tissues in vivo. Our method and results also illustrate that backward Mach cones can be generated in soft phononic crystals with periodic microstructures, indicating that they are promising material systems for studying the ECE in soft matter.