A phase-field model is developed for predicting the polarization switching and domain structure evolution under an applied electric field in ferroelectric polycrystals. The model takes into account realistic grain structures as well as various energetic contributions, including elastic energy, electrostatic energy, and domain wall energy. A hysteresis loop – average polarization as a function o...

Abstract. In this paper we consider the hyperbolic-elliptic system of two conservation laws that describes the dynamics of an elastic material governed by a non-monotone strain-stress function. Following Abeyaratne and Knowles, we propose a notion of admissible weak solution for this system in the class of functions with bounded variation. The formulation includes an entropy inequality, a kinet...

This work develops a framework for SIMP-based topology optimization of a metallic panel structure subjected to design-dependent aerodynamic, inertial, elastic, and thermal loads. Multi-physics eigenvalue-based design metrics such as thermal buckling and dynamic flutter are derived, along with their adjoint-based design derivatives. Locating the flutter point (Hopf-bifurcation) in a precise and ...

A systematic investigation is presented of grain boundaries and grain boundary networks in two dimensional flexible membranes with crystalline order. An isolated grain boundary undergoes a buckling transition at a critical value of the elastic constants, but, contrary to previous findings, the shape of the buckled membrane is shown to be asymptotically flat. This is in general not true in the c...

We developed a phase-field model to study the stress-driven grain boundary migration in elastically inhomogeneous polycrystalline materials with arbitrary elastic inhomogeneity and anisotropy. The dependence of elastic stiffness tensor on grain orientation is taken into account, and the elastic equilibrium equation is solved using the Fourier spectral iterative-perturbation method. We studied t...

We propose a method for generating well-shaped curved unstructured meshes using a nonlinear elasticity analogy. The geometry of the domain to be meshed is represented as an elastic solid. The undeformed geometry is the initial mesh of linear triangular or tetrahedral elements. The external loading results from prescribing a boundary displacement to be that of the curved geometry, and the final ...

Diffusionless phase transitions are at the core of the multifunctionality of (magnetic) shape memory alloys, ferroelectrics and multiferroics. Giant strain effects under external fields are obtained in low symmetric modulated martensitic phases. We outline the origin of modulated phases, their connection with tetragonal martensite and consequences for their functional properties by analysing th...

We theoretically study the topography of a biphasic surfactant monolayer in the vicinity of domain boundaries. The differing elastic properties of the two phases generally lead to a nonflat topography of "mesas," where domains of one phase are elevated with respect to the other phase. The mesas are steep but low, having heights of up to 10 nm. As the monolayer is laterally compressed, the mesas...

We propose a method that automatically tracks and segments living cells in phase-contrast image sequences, especially for cells that deform and interact with each other or clutter. We formulate the problem as a many-to-one elastic partial matching problem between closed curves. We introduce Double Cyclic Dynamic Time Warping for the scenario where a collision event yields a single boundary that...