Elastic Cherenkov effects in transversely isotropic soft materials-I: Theoretical analysis, simulations and inverse method. (November 2016)

• Record Type: Journal Article
• Authors: Li, Guo-Yang; Zheng, Yang; Liu, Yanlin; Destrade, Michel; Cao, Yanping
• Is Part Of: Journal of the mechanics and physics of solids. Volume 96(2016:Nov.)
• Page Start: 388
• Page End: 410
• Publication Date: 2016-11
• Subjects: Elastic Cherenkov effect (ECE) -- Anisotropic soft materials -- Dynamic elastography -- Supersonic shear imaging (SSI) technique -- Inverse method; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2016.05.023
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: A body force concentrated at a point and moving at a high speed can induce shear-wave Mach cones in dusty-plasma crystals or soft materials, as observed experimentally and named the elastic Cherenkov effect (ECE). The ECE in soft materials forms the basis of the supersonic shear imaging (SSI) technique, an ultrasound-based dynamic elastography method applied in clinics in recent years. Previous studies on the ECE in soft materials have focused on isotropic material models. In this paper, we investigate the existence and key features of the ECE in anisotropic soft media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non-invasive and non-destructive characterization of biological soft tissues. We also theoretically study the characteristics of the shear waves induced in a deformed hyperelastic anisotropic soft material by a source moving with high speed, considering that contact between the ultrasound probe and the soft tissue may lead to finite deformation. On the basis of our theoretical analysis and numerical simulations, we propose an inverse approach to infer both the anisotropic and hyperelastic parameters of incompressible transversely isotropic (TI) soft materials. Finally, we investigate the properties of the solutions to the inverse problem by deriving the condition numbers in analytical form and performing numerical experiments. In Part II of the paper, both ex vivo and in vivo experiments are conducted to demonstrate the applicability of the inverse method in practical use. Graphical abstract: Highlights: The elastic Cerenkov effect in transversely isotropic (TI) soft materials is addressed. Shear waves induced by a moving source in a deformed TI solid are studied. An inverse method is proposed to infer anisotropic and hyperelastic parameters. The properties of the solution to the inverse method is investigated.