Geometrical frustration in nonlinear mechanics of screw dislocation.

The existence of stress singularities and reliance on linear approximations pose significant challenges in comprehending the stress field generation mechanism around dislocations. This study employs differential geometry and calculus of variations to mathematically model and numerically analyse screw dislocations. The kinematics of the dislocation are expressed by the diffeomorphism of the Riemann-Cartan manifold, which includes both the Riemannian metric and affine connection.

Emergence of colour symmetry in free-vibration acoustic resonance of a nonlinear hyperelastic material.

We investigated free-vibration acoustic resonance (FVAR) of two-dimensional St Venant-Kirchhoff-type hyperelastic materials and revealed the existence and structure of colour symmetry embedded therein. The hyperelastic material is isotropic and frame indifferent and includes geometrical nonlinearity in its constitutive equation. The FVAR state is formulated using the principle of stationary action with a subsidiary condition.