29 Nonlinear Shear Elasticity

Jean‐Luc Gennisson1 and Sara Aristizabal2

1 Imagerie par Résonance Magnétique Médicale et Multi‐Modalités, Université Paris‐Saclay, Orsay, France

2 Well Living Lab, Rochester, MN, USA

29.1 Introduction

The characterization of mechanical properties of soft matter is of interest for medical applications. For example, shear elasticity is a pertinent indicator for a diagnosis of tissue degradation. Linear and nonlinear elastic moduli of soft materials can be obtained (i) by dynamic experiments imaging low‐frequency shear wave propagation or (ii) by acoustoelastic measurements of speed variations under static strains. The first part goes through solving an inverse problem in the linear case or fitting experimental and theoretical results in the nonlinear one. The second part describes the measurement of linear shear wave in a material under uniaxial stress. Quantifying shear nonlinearity may be important for medical applications. For example, it could be used to tell malignancies apart from benign tumors. In this chapter, nonlinearity is defined from the expression of the strain energy density at higher orders and specifically expressed in the case of soft media [1]. Three different methods to assess third‐order shear coefficients are presented (Sections 29.2, 29.3, and 29.4). Finally, an estimation of the fourth‐order parameter is presented (Section 29.5).

29.2 Shocked Plane Shear Waves

Although the nonlinear behavior of transverse ...

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