Dynamics and Homogenization of Periodic Metamaterials

Objectives
Periodic metamaterials can be realized in the form of lattices of beams deformable both axially and flexurally. These architected materials can exhibit uncommon mechanical properties for both static and dynamic applications, such as auxetic behaviour and elastic wave manipulation and control. The course aims to provide the fundamentals of the mechanics of periodic metamaterials. The student will learn (i) the most effective methods to analyze their static and dynamic behaviors; and (ii) the static and dynamic homogenization techniques to describe their macroscopic behavior.

Topics
Dynamics of periodic beam lattices: unit cell, direct and reciprocal bases, governing equations, Bloch theorem, quasi-periodic conditions, dispersion relation, dynamic anisotropy, dispersion surfaces and waveforms
Homogenization of periodic beam lattices: static homogenization, dynamic homogenization, lattice acoustic tensor
Prestressed beam lattices: macro and micro instabilities, strain localization and shear bands in the lattice and the equivalent continuum, structured interfaces for wave channeling and manipulation

Required Skills
Course of “Foundations of Mechanics and Acoustics”

Course Modality and Verification of Learning
The classes will be given in hybrid (i.e., onsite and online) format. The teaching activity includes theoretical lessons, applications and exercises.
The exam consists of a written test with multiple-choice questions on the topics of the course.