A NEW REPRESENTATION FOR THE STRAIN-ENERGY OF ANISOTROPIC ELASTIC-MATERIALS WITH APPLICATION TO DAMAGE EVOLUTION IN BRITTLE MATERIALS

In this paper, we develop a new representation of the strain energy of an elastic material using twenty-one scalar measures of strain. These measures are associated with material line elements which are directe d along the six axes of symmetry of a regular icosahedron, and they in clude: six measures of axial strain and fifteen measures of the angula r strain. When the strain energy is a quadratic function of strain, th is representation yields twenty-one elastic moduli which naturally sep arate into only two physically different types. This is in contrast to the five physical types of moduli associated with the common rectangu lar Cartesian representation of the stiffness tenser. By formulating e volution equations for the elastic moduli, we describe general changes in the elastic state of a brittle material. Due to the physical natur e of these moduli, we anticipate that the evolution equations will hav e simplifying features when expressed in terms of the new representati on of the strain energy presented here. In general, these evolution eq uations are restricted by sufficient conditions which ensure that the change in the elastic state is a dissipative process in the sense that the second law of thermodynamics is satisfied. It is shown that not a ll changes of the elastic state can be interpreted as damage evolution , even if they are dissipative and cause reductions of the magnitudes of the twenty-one moduli. To ensure damage evolution, we propose an ad ditional restriction on the strain energy. Furthermore, a simple modif ication of the strain energy is introduced to model the effect of crac k closure. Specific equations for damage evolution which satisfy all n ecessary restrictions are presented. These equations characterize dama ge evolution in a material that exhibits a transition from an isotropi c to an anisotropic elastic state. Examples are considered which show physically reasonable brittle material response.