A novel phase?field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable

Metamaterials response is generally modeled by generalized continuum based theories. Their inherent substructure leads to a necessity for higher-order theories, and especially in damage mechanics, such generalization difficult acquire. We exploit the action formalism order obtain governing equations mechanics metamaterials. Additionally, using auxilliary variables, variational formulation endowed with first rate of variable that missing standard approaches. The presented variables directly weak form. implement finite element method approach open-source computing platform called FEniCS solve this deformation numerically. simulations are demonstrated simple geometries mixed mode (I II) as well III.