Abstract: Lattice structure with piezoelectric behavior characterized in that the lattice structure (1) comprises a periodic succession of unitary cells (10), wherein each unitary cell (10) is made of a dielectric material, is bending or torsion dominated and comprises nanometric structural connectors (11) connected to each other through nodes (12) defining a non-centrosymmetric shape having a topological constraint that induces torsion or bending of said structural connectors (11); and wherein the unitary cells (10) are connected to each other at least in series defining a continuous electric potential accumulation path with two opposed ends (2, 3), the unitary cells (10) being arranged within the lattice structure (1) in a non-centrosymmetric disposition accumulating and conducting without cancellation the electric gradient generated on each unitary cell (10) through the lattice structure (1) to said two opposed ends (2, 3).