Phase Field Models for Thin Elastic Structures with Topological Constraint

Retrieving Topological Information for Phase Field Models

The phase field approach has become a popular tool in modeling interface motion, microstructure evolution, and more recently the shape transformation of vesicle membranes under elastic bending energy. While it is advantageous to employ phase field models in numerical simulations to automatically handle topological changes to the microstructures or the configurations of vesicle membranes, detect...

Phase-field crystals with elastic interactions.

We report on a novel extension of the recently introduced phase-field crystal (PFC) method [Elder, Phys. Rev. Lett. 88, 245701 (2002)10.1103/PhysRevLett.88.245701], which incorporates elastic interactions as well as crystal plasticity and diffusive dynamics. In our model, elastic interactions are mediated through wave modes that propagate on time scales many orders of magnitude slower than atom...

Invertibility and noninvertibility in thin elastic structures

The nonlinear elastic energy of a thin film of thickness h is given by a functional E. Friesecke, James and Müller derived the Γ-limits, as h → 0, of the functionals hE for α ≥ 3. In this article we study the invertibility properties of almost minimizers of these functionals, and more generally of sequences with equiintegrable energy density. We show that they are invertible almost everywhere a...

Innovative Elastic Thin-Film Solar Cell Structures

Thermoelastic Relaxation in Elastic Structures, with Applications to Thin Plates

A new result enables direct calculation of thermoelastic damping in vibrating elastic solids. The mechanism for energy loss is thermal diffusion caused by inhomogeneous deformation, flexure in thin plates. The general result is combined with the Kirchhoff assumption to obtain a new equation for the flexural vibration of thin plates incorporating thermoelastic loss as a damping term. The thermal...