The asymptotic behavior of an elastic thin film penalized by a van der Wals type interfacial energy is investigated when both its thickness and the magnitude of the additional energy vanish in the limit. Keeping track of both mid-plane and out of plane deformations (through the introduction of the Cosserat vector), the resulting behavior strongly depends upon the ratio between thickness and int...

The dynamical evolution of the Hajicek 1-form is derived in Einstein-Cartan (EC) theory. We find that like Einstein theory gravity, equation related to a projected part tensor (${\stackrel{^}{G}}_{ab}$) on generic null surface $\mathcal{H}$, particularly ${\stackrel{^}{G}}_{ab}{l}^{a}{{q}^{b}}_{c}$, where ${l}^{a}$ and ${{q}^{a}}_{c}$ are outgoing generators $\mathcal{H}$ induced metric transve...

A theory of discrete Cosserat rods is formulated in the language of discrete Lagrangian mechanics. By exploiting Kirchhoff’s kinetic analogy, the potential energy density of a rod is a function on the tangent bundle of the configuration manifold and thus formally corresponds to the Lagrangian function of a dynamical system. The equilibrium equations are derived from a variational principle usin...

In this article, we derive the balance of linear and angular momentum equations for geometrically exact Cosserat rods from a two dimensional Lagrangian field approach in space and time. As we use a full quaternion description for the rotatory part of the balance equations, they constitute a system of nonlinear hyperbolic partial differential algebraic equations. We prove their equivalence to th...