Mechanics of stretchy elastomer lattices

The recent advances in soft matter and advanced manufacturing have enabled the design and fabrication of elastomer lattices for versatile engineering applications. Compared with conventional engineering structures, elastomer lattices exhibit ultra-high reversible stretchability, while maintaining relatively low density. Mechanistic understanding of the mechanics of elastomer lattices is of great importance for their structural design and optimization. However, the existing studies in this field are limited to empirical models or finite element methods, while the theoretical modeling remains largely unexplored. This work reports a class of theoretical models for the mechanics of elastomer lattices over finite deformation. The potential energy function is constructed as a superposition of the stretching and bending modes, which are associated with the elongation and rotation of lattice beams, respectively. The stress-stretch behavior is determined with the aid of the principle of stationary potential energy. The model is then extended to explain the mechanics of hierarchical elastomer lattices by introducing the principal stretches in each hierarchical order as generalized coordinates. A set of holonomic constraint equations are written to define the kinematic compatibility and uniaxial stress state for hierarchical lattices, which are numerically solved via a nonlinear optimization algorithm. Results from the proposed theoretical models agree well with finite-element simulations and experiments. Case studies are performed for various material constitutive models, volume fractions, lattice architectures, and deformation modes, demonstrating the generality and robustness of the proposed theoretical models.