Constitutive equation of damaged material as multiphase continuum

For on-line non-destructive detection data interpretation, the elastic parameters variations of constitutive equation of material are the main information to evaluate what happened or happening within the materials. The effectiveness of inverse problem solving process is determined by the constitutive equations used. For solid medium, when cracking or liquefying happened, the damaged portion of material is a multiphase medium. Unlike the multiphase medium in general sense, for non-destructive detection, the damaged material is viewed as solid-liquid-gas mixture. When liquid phase or gas phase are found at some where, the damaged portion is determined. For this reasoning process, the measured parameters are compared with the initial idea parameters. So, the physical soundness of the used constitutive equations is the key factor. Based on rational mechanics, using the intrinsic geometrical field representation of motion, this research formulates the constitutive equations for the damaged medium as a multiphase medium. It shows that, the combination of passive wave detection and active wave detection can be uniquely interpreted by fatigue model or cracking model. However, for actual case, when the fatigue and the cracking contribution is in-distinguishable, the inverse problem has no unique answer. These results may help to position the damage place and evaluate the damage level more reliably through the use of unique constitutive formulation.