Topological derivatives of leading-and second-order homogenized coefficients in bi-periodic media

Rémi Cornaggia (1) , Bojan B Guzina (2) , Marc Bonnet (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Civil Engineering [Minneapolis]
3 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

We derive the topological derivatives of the homogenized coefficients associated to a periodic material, with respect of the small size of a penetrable inhomogeneity introduced in the unit cell that defines such material. In the context of an-tiplane elasticity, this work extends existing results to (i) time-harmonic wave equation and (ii) second-order homogenized coefficients, whose contribution reflects the dispersive behavior of the material.

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des solides [physics.class-ph]

Rémi Cornaggia, Bojan B Guzina, Marc Bonnet. Topological derivatives of leading-and second-order homogenized coefficients in bi-periodic media. WAVES 2017 - 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation, May 2017, Minneapolis, United States. ⟨hal-02065548⟩