A Preliminary Study on Damage Wave in Elastic-brittle Materials

Abstract

A conceptual study on damage wave propagation in elastic-brittle materials is carried out within the framework of Continuum Damage Mechanics (CDM). The extent of damage at a material point is a direct result of the evolution of microstructures and interaction with their neighbors. To account for the spatial fluctuation of damage, its gradient is proposed as an additional internal variable. The microstructural interaction can induce irreversible energy in the construction of the thermodynamic functions, through a range of dissipative mechanisms associated with microstructural changes such as nucleation, growth, and coalescence of microcracks, internal friction, irreversible phase transformation, and chemical reactions in elastic-brittle materials. Based on the theory of internal variables, a new material constitutive model involving damage evolution is presented. The governing equations for the corresponding coupled mechanism are derived and a traveling-wave solution is obtained for some limiting cases. It is shown that the evolution equation of damage is a nonlinear wave equation that has a solitary wave solution of the kink type in one-dimensional case if there is no energy dissipation with damage evolution. The speed of damage waves is determined in terms of the damping effect, the elastic energy of un-deformed material, and the dissipative energy. It is lower than the speed of elastic waves, and has a speed limit only associated with damage evolution at microscales. It is demonstrated that the theory presented here shows promise in describing damage wave propagation based upon comparisons with the available experimental results and numerical simulations.