  In continuum mechanics, the non-centrosymmetric micropolar theory is usually
used to capture the chirality inherent in materials. However when reduced to a
two dimensional (2D) isotropic problem, the resulting model becomes non-chiral.
Therefore, influence of the chiral effect cannot be properly characterized by
existing theories for 2D chiral solids. To circumvent this difficulty, based on
reinterpretation of isotropic tensors in a 2D case, we propose a continuum
theory to model the chiral effect for 2D isotropic chiral solids. A single
material parameter related to chirality is introduced to characterize the
coupling between the bulk deformation and the internal rotation which is a
fundamental feature of 2D chiral solids. Coherently, the proposed continuum
theory is also derived for a triangular chiral lattice from a homogenization
procedure, from which the effective material constants of the lattice are
analytically determined. The unique behavior in the chiral lattice is
demonstrated through the analyses of a static tension problem and a plane wave
propagation problem. The results, which cannot be predicted by the non-chiral
model, are validated by the exact solution of the discrete model.
