Geometric charges and nonlinear elasticity of two-dimensional elastic metamaterials

Elastic interactions between two-dimensional geometric defects.

In this paper, we introduce a methodology applicable to a wide range of localized two-dimensional sources of stress. This methodology is based on a geometric formulation of elasticity. Localized sources of stress are viewed as singular defects-point charges of the curvature associated with a reference metric. The stress field in the presence of defects can be solved using a scalar stress functi...

Two Dimensional Adsorbed Charges

Axial and Torsional Free Vibrations of Elastic Nano-Beams by Stress-Driven Two-Phase Elasticity

Size-dependent longitudinal and torsional vibrations of nano-beams are examined by two-phase mixture integral elasticity. A new and efficient elastodynamic model is conceived by convexly combining the local phase with strain- and stress-driven purely nonlocal phases. The proposed stress-driven nonlocal integral mixture leads to well-posed structural problems for any value of the scale parameter...

Acoustic and elastic metamaterials

We will review some of the recent advances in the field of acoustic and elastic metamaterials. These research fields became hot topics in last few years with an increasing number of papers that grows almost exponentially. The interest on these artificial structures arouses because of their potential application in designing novel devices for sound and vibration control. Their applications cover...

Two-dimensional elastic turbulence.

We report numerical evidence of elastic turbulence phenomenology in a two-dimensional periodic Kolmogorov flow. By direct numerical simulations of the Oldroyd-B viscoelastic model at very small Reynolds numbers, we find that above the elastic instability threshold the flow develops an elastic turbulent regime. We observe that both the turbulent drag and the Lyapunov exponent increase with the W...