## 1 Introduction
[18] explains these experimentally observed behaviors of the solitary-wave like patterns based on a Korteweg-de Vries (KdV)-type [19] solitary wave solution. The formation of solitary waves from non-solitary waves has also been reported. [PERSON] and [PERSON] [20] discuss the coalescence of longitudinal and shear waves to form shock waves in soft materials. [PERSON] [21] et al. discuss the formation of solitary waves in a carbon fiber reinforced polymer with non-solitary ultrasonic excitation. The use of the above-mentioned, stage-specific behavior of deformation waves makes the present NDT unique. Various waves are widely used in conventional NDT methods. In these methods, a linear wave is typically applied to the test object as the input and the reflected or transmitted (the output) wave is monitored. The structural or mechanical properties of the object are diagnosed through analysis of the output wave based on a certain property of the wave. Acoustic imaging [22; 23] identifies abnormality from the difference in the acoustic impedance, which alters the reflection coefficient for the input wave; hence, making a contrast in the output wave. Scanning Acoustic Microscopy [24; 25] uses the interference between the input and reflected ultrasound waves to characterize the property of the subsurface region of a specimen. X-ray diffractometry [26; 27] uses diffraction to find the lattice constant of the object material. In relatively new methods, solitary waves are also used as the input wave [28; 29; 30]. As a nonlinear wave, a solitary wave changes its wave form depending on the material's property. This feature makes it possible to detect abnormality that linear input waves are unable to detect. The present NDT algorithm is intrinsically different from these methods in the following sense. Instead of analyzing the output signal that results from a certain input wave, it analyzes the materials' self-generated deformation waves. In other words, while conventional techniques analyze the material's response to the input wave, the present method characterizes the material's response to the applied load as a wave phenomenon. Thus, the observed wave exhibits the dynamics that governs the deformation behavior for the respective stages. By knowing the dynamics for each stage and the associated features of the deformation wave, we can diagnose the current status of deformation and its future trend. Based on the stage-specific specific behaviors of the deformation wave, we have derived field theoretical criteria of deformation stages [31]. The criteria describe the spatiotemporal behavior of the displacement field in the elastic, plastic, pre-fracture, and fracture stages. In accordance with the above-mentioned form of the displacement wave, the displacement field expressed in the principal coordinates is rotation-free (because the wave is longitudinal) in the elastic stage, rotational (because the wave has transverse component due to the shear strain) in the plastic stage, localized in a small region (because the wave is a solitary wave), but dynamic in the pre-fracture stage, and localized in a small region and static (because the solitary wave becomes standing) in the fracture stage (more detailed descriptions of the characteristics of the displacement field will be discussed later in this paper). In refs. [31; 32], we demonstrated the deformation stage criteria based on these qualitative features of the displacement field. Using the optical interferometric technique known as Electronic Speckle-Pattern Interferometry (ESPI) [33; 34; 35], we continuously visualized the displacement field of metal plate specimens as the test machine applied a tensile load. With a pre-defined time interval small enough to resolve the stress-strain curve, the ESPI setup displayed the displacement field as full-field, two-dimensional optical interferometric image data.