Torsion mechanical waves have the capability to characterize shear stiffness moduli of soft tissue. Under this hypothesis, a computational methodology is proposed to design and optimize a piezoelectrics-based transmitter and receiver to generate and measure the response of torsional ultrasonic waves. The procedure employed is divided into two steps: (i) a finite element method (FEM) is developed to obtain a transmitted and received waveform as well as a resonance frequency of a previous geometry validated with a semi-analytical simplified model and (ii) a probabilistic optimality criteria of the design based on inverse problem from the estimation of robust probability of detection (RPOD) to maximize the detection of the pathology defined in terms of changes of shear stiffness. This study collects different options of design in two separated models, in transmission and contact, respectively. The main contribution of this work describes a framework to establish such as forward, inverse and optimization procedures to choose a set of appropriate parameters of a transducer. This methodological framework may be generalizable for other different applications.

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Materials with fluid and matrix phases present different acoustic responses in each phase. While longitudinal waves propagate in both phases, shear waves do it only through the solid matrix. Longitudinal waves are mainly described by volumetric propagation and shear waves by deviatoric processes. In the case of nonlinear propagation cross effects occur between both components. This paper presents a new classical nonlinear model proposing a constitutive equation that separates volumetric and deviatoric effects. Four nonlinear constants of third order are defined. The formulation is compared to constitutive equations with Landau constants for weakly elasticity and both types of nonlinear constants related. Some reinterpretation of the Landau’s constants arises in terms of parallel or cross nonlinear effects between volumetric and deviatoric components.

An ultrasonic evaluation technique for damage identification of layered CFRP structures is presented. This approach relies on a model-based estimation procedure that combines experimental data and simulation of ultrasonic damage-propagation interactions. The CFPR structure, a [0/90]4s lay-up, has been tested in an immersion through transmission experiment, where a scan has been performed on a damaged specimen. Most ultrasonic techniques in industrial practice consider only a few features of the received signals, namely, time of flight, amplitude, attenuation, frequency contents, and so forth. In this case, once signals are captured, an algorithm is used to reconstruct the complete signal waveform and extract the unknown damage parameters by means of modeling procedures. A linear version of the data processing has been performed, where only Young modulus has been monitored and, in a second nonlinear version, the first order nonlinear coefficient was incorporated to test the possibility of detection of early damage. The aforementioned physical simulation models are solved by the Transfer Matrix formalism, which has been extended from linear to nonlinear harmonic generation technique. The damage parameter search strategy is based on minimizing the mismatch between the captured and simulated signals in the time domain in an automated way using Genetic Algorithms. Processing all scanned locations, a C-scan of the parameter of each layer can be reconstructed, obtaining the information describing the state of each layer and each interface. Damage can be located and quantified in terms of changes in the selected parameter with a measurable extension. In the case of the nonlinear coefficient of first order, evidence of higher sensitivity to damage than imaging the linearly estimated Young Modulus is provided.