## 1 Introduction  
Structures collapse unexpectedly. Continuous application of external loads, even if their strength is considerably lower than the ultimate strength of the material, causes fractures. The current load level observed or associated deformation data is not reliable information to predict fracture. It is known that fracture is led by a defect and that defects grow in the scale level from the atomistic to macroscopic. Dislocations [1] are typical atomistic defects and their propagation is responsible for the deformation to evolve from the elastic to plastic regime. It is known that in the plastic regime the dislocations react to the stress field and lead to the generation of macroscopic defects. [PERSON] [2] formulates the dynamics of dislocation as a wave phenomenon. However, it is difficult to connect dislocation behaviors and macroscopically observable phenomena. In other words, on the one hand we know that the propagation of dislocation initiates plastic deformation. On the other hand, we cannot identify the initiation of plastic deformation as a macroscopically observable quantity, except as the yield point on the stress-strain curve. From the nondestructive testing (NDT) perspective, it is unrealistic to measure the stress-stain characteristics of test objects in the field. It is desirable to develop a methodology that allows us to diagnose the initiation of plastic deformation and the subsequent evolution of the deformation toward the final fracture. One immediate problem in such methodological development is that prevailing deformation theories are phenomenological and, thereby, stage specific. Elastic theories [3; 4; 5] describe the stress strain relationship in the elastic regime. Most plastic deformation theories [6; 7] describe plastic behavior by either mathematically modeling the constitutive relation in the plastic regime or formulating the plasticity based on the energy dissipation. Fracture [8] is treated as an independent phenomenon of deformation. This situation makes it difficult to describe the transition from one deformation regime to another. In this work, we propose that the application of a recent field theory [9] of deformation and fracture can be a solution to the problem. Being based on the physical principle known as the local symmetry of theory [10; 11; 12] (See Appendix A), this theory has a mechanism to describe deformation and fracture on the same theoretical basis. It formulates all stages of deformation and fracture based on the wave equation derived from the equation of motion that governs the dynamics of a unit volume in a deforming object. Different stages of deformation are characterized by different forms of resistive force that the unit volume exerts in response to the external load. This difference in the resistive force alters some terms of the wave equation yielding different wave solutions. Details about the wave equation and wave solutions will be discussed later in this paper. In short, the elastic stage is represented by non-decaying longitudinal waves, the early stage of plastic deformation is by decaying longitudinal and transverse waves, the developed plastic stage (the pre-fracture stage) is by travelling solitary waves, and the fracturing stage is by standing solitary waves. In all stages, these waves carry the stress energy that is caused by the external load. These forms of deformation waves in association with the corresponding deformation stages have been observed by several authors. In a tensile experiment of an aluminum alloy specimen, we [13] observed that a transverse displacement wave started to appear near the yield point and decayed towards the final fracture of the specimen. In refs. [14; 15; 16], the authors identified a solitary-wave like pattern in the displacement field of tensile loaded metal plate specimens and observed that the pattern becomes stationary when the specimen broke. Ref. [17] reports simlar observation of a solitary-wave like pattern in the displacement field for a cyclic loaded metal specimen. Ref.