Universal Nonlinear Elastic Wave Behavior in Materials, and the Implications to Nanoscale Material Mechanics and Damage Diagnostics

摘要

The concept of universality class is the centerpiece of the modern theory of critical phenomena. The basic premise of this work is that the concept can be applied to the description of the nonlinear elastic behavior of a broad class of materials. As we do not have the defining characteristic for a universality class as yet (Hamiltonian, order parameter, etc.), this premise entails extrapolating the concept of such a class from unique signatures observed in the material nonlinear elastic behavior. The signature(s) must be extracted from experiment. Among the benefit of establishing a universal description are the vast simplification in describing materials to be elastically the same over a huge number of length scales. Further, we will have the ability to use membership in the universality class for nondestructive testing (we believe that membership in the universality class is conferred on many materials only as a consequence of damage).