Acoustoelasticity is a phenomenon that describes the alteration of acoustic characteristics in deformed elastic media.

Acoustoelasticity has been intensively studied on engineering materials like steel but has never been applied to the nearly incompressible materials like rubber or biological tissues. As a first phase of this study, acoustoelasticity is applied to a finitely deformed nearly incompressible, hyper-elastic and isotropic material with the introduction of a new strain energy function. This newly proposed function sustains dilatational waves, a phenomenon that cannot be modeled under the typical assumption of incompressibility. This new function also models dilatational wave propagation with fidelity without disturbing its ability to model other mechanical properties. The efficacy of acoustelasticity with this new function is tested by comparing analytical and experimental results. Analytical results fit well with both the measured straindependent changes of dilatational wave velocities and changes of wave reflection coefficients in a transverse direction of an axially stretched rubber plate.

Based on these results, a general inverse problem to identify applied strains and normalized material properties in an axially stretched rubber plate only from measured reflected wave signals is formulated and tested as the second phase of this study.

As a third phase, the existence and relevance of acoustoelastic effects in biological tissues are demonstrated through the measurement of changes of wave reflection coefficients from the stretched tendon. With simple mathematical model, a general inverse problem to determine strain and material properties is formulated and tested.

As final phase, a method to apply acoustoelasticity to ultrasound medical visualization is developed. This new visual and material identification technique is termed “stiffness gradient identification” or SGI. Pre-compression of target tissues with a finite size compressor is required. This compression causes a depth-dependent wave velocity field and requires a second order ordinary differential equation with variable coefficients to describe wave propagation. To solve this equation and therefore describe the wave behavior, a new approximation method termed the “modified WKB method14 is developed and tested.