The continuous limit for a metamaterial composed of several unit cells which
are unstable under traction is developed within the realm of elastodynamics.
The resulting variational structure is crucially supplemented by a unilateral
constraint, which turns the otherwise linear problem into a complementarity
problem. Indeed, the absence of the unilateral constraint significantly alters
the response of the system, notably missing the fundamental equilibrium state.
We show that proper dealing with the unilaterally constrained Lagrangian leads
to the reproduction at the macro-level of all the features exhibited by the mi-
crostructure. The Hamiltonian of the system is also discussed and plays a fun-
damental role in addressing the non-smooth transition between the equilibrium
states.
| Subject : | : | oral |
| Topics | : | 7-4 - Mechanics and physics of structures |
| PDF version | : |  PDF version |
