ELASTIC AND FRACTURE PROPERTIES OF THE 2-DIMENSIONAL TRIANGULAR AND SQUARE LATTICES

Lattice models are finding increasing use in modeling the elastic and fracture behaviour of inhomogeneous or multi-phase systems. The elastic and failure properties of a rotationally invariant formulation of the bond-bending model on the two-dimensional triangular (with first-neighbour couplings) and on a novel version of the square lattice (involving first- and second-neighbour couplings) are examined. Expressions for the elastic constants of the bond-bending model on the above mentioned lattices are given in terms of the two- and three-body force constants. The tensile failure surface of the bond-bending model on the triangular and square lattices is calculated, and displays some degree of anisotropy in both cases. The central-force model (with a zero bond-bending constant) on the triangular lattice shows the highest degree of anisotropy, namely 50%. The presence of the bond-bending coupling constant improves the degree of isotropy of the tensile failure surface for both the triangular and square lattices. It is therefore concluded that the role of the bond-bending coupling constant is to provide for a more uniform energy distribution among the bonds, so that preferential bond cleavage does not occur upon the application of stress. The square lattice with both first-and second-neighbour interactions offers a clear advantage over the triangular lattice without being significantly more demanding computationally: for the same value of the bond-bending constant, the degree of anisotropy of the tensile failure surface is decreased by a factor of two, as compared to the triangular lattice.