General selection of lattice shape in ductile-reinforced brittle structures for increased stiffness

Abstract

Ductile reinforcements are used in brittle structures to increase the overall stiffness and strength. However, the optimum lattice shape geometry according to which the ductile reinforcements must be laid down, has not been generally established. In this work, a ductile isotropic lattice structure is constructed from a unit cell and the brittle matrix is “filled” in the empty spaces thereafter. In homogeneous stress conditions, the brittle part will experience the same applied remote stress as is felt by the ductile lattice. The statistical theory of brittle failure is invoked to bring home the point that the unit cell area of the lattice is arbitrary (for a given total area) and hence the lattice shape geometry does not influence the probability of survival of the structure. Therefore, a suitable geometry shape (triangle or square) maybe chosen to further enhance the overall stiffness at a given probability of survival. It has been concluded that an (equilateral) triangular lattice is better suited compared to a square lattice if the ductile reinforcement lattice bars have the same stiffness. The technique and conclusion is generally true for any choice of brittle and ductile materials. Also, the conclusion holds true for both compressive and tensile loading.