On the Role of Interface Energies in the Description of Material Behavior

Abstract

At the level of constitutive equations relating macroscopic stress and strain measures, real materials exhibit a variety of behaviors. In the years, there was a tendency to focus on some prominent properties of material response and to study them individually; the result was the development of independent, sometimes unrelated, branches of Continuum Mechanics, such as Fracture Mechanics, Damage Mechanics, and many theories sharing the name of Plasticity.

Some hope for recovering a unified view is provided by a simple model, based on the assumption that the total energy of a body is the sum of two parts, a bulk part representing the elastic strain energy and a surface part associated with defects occurring both at the macroscopic and at the microscopic level. In the model, defects are represented by discontinuities in the displacement field. Such discontinuities may be large or small, concentrated at a single surface or distributed over surface-like regions diffused throughout the body. The first case is typical of fracture, and the second of plastic deformation.

At the present stage, the model is restricted to the one-dimensional case. Two or three dimensional generalizations are far from trivial, due to mathematical difficulties. Within this limit, fracture was studied in [1], plasticity in [4], and damage and other forms of progressive failure were considered in [3], [5]. A first comprehensive account was given in [2]. The present communication can be viewed as an updated review of the state of the research; mainly, it is based on the contents of a paper in progress [6], in which emphasis is given to the mathematical structure of the model. The complete text of the communication is reported in [7].