A geometric formulation of linear elasticity based on discrete exterior calculus

A direct formulation of linear elasticity cell complexes based on discrete exterior calculus is presented. The primary unknowns are displacements, represented by a primal vector-valued 0 -cochain. Displacement differences and internal forces 1 -cochain dual 2 -cochain, respectively. macroscopic constitutive relation enforced at -cells with the help musical isomorphisms mapping cochains to smooth fields vice versa. balance momentum established -cells. governing equations solved as Poisson’s equation non-local non-diagonal material Hodge star. Numerical simulations several classical problems analytic solutions presented validate formulation. Excellent agreement known obtained. provides method calculate relations between displacement for any lattice structure, when structure required follow prescribed elastic behaviour. This also first critical step in developing formulations dissipative processes complexes. • Formulation using (DEC). Derivation new sharp isomorphism. star elasticity. validation standard mechanical solutions.