Effective elastic moduli of space-filled multi-material composite lattices

Traditionally lattice materials are made of a network of beams in two and three dimensions with majority of the lattice volume being void space. Recently researchers have started exploring ways to exploit this void space for multi-physical property modulation of lattices such as global mechanical behaviour including different elastic moduli, wave propagation, vibration, impact and acoustic features. The elastic moduli are of crucial importance to ensure the structural viability of various multi-functional devices and systems where a space-filled lattice material could potentially be used. Here we develop closed-form analytical expressions for the effective elastic moduli of space-filled lattices based on an exact stiffness matrix approach coupled with the unit cell method, wherein transcendental shape functions are used to obtain exact solutions of the underlying differential equation. This can be viewed as an accurate multi-material based generalisation of the classical formulae for elastic moduli of honeycombs. Numerical results show that the effective in-plane elastic moduli can increase by orders of magnitude with a relatively lower infill stiffness (& SIM;10%). This gives an exceptional opportunity to engineer multi-material lattices with optimal specific stiffness along with characterising the mechanical properties of a multitude of lattice-like artificial and naturally occurring structural forms with space filling.