Kinetics of phase transformations in the peridynamic formulation of continuum mechanics

We study the kinetics of phase transformations in solids using the peridynamic formulation of continuum mechanics. The peridynamic theory is a nonlocal formulation that does not involve spatial derivatives, and is a powerful tool to study defects such as cracks and interfaces. We apply the peridynamic formulation to the motion of phase boundaries in one dimension. We show that unlike the classical continuum theory, the peridynamic formulation does not require any extraneous constitutive laws such as the kinetic relation (the relation between the velocity of the interface and the thermodynamic driving force acting across it) or the nucleation criterion (the criterion that determines whether a new phase arises from a single phase). Instead this information is obtained from inside the theory simply by specifying the inter-particle interaction. We derive a nucleation criterion by examining nucleation as a dynamic instability. We find the induced kinetic relation by analyzing the solutions of impact and release problems, and also directly by viewing phase boundaries as traveling waves. We also study the interaction of a phase boundary with an elastic non-transforming inclusion in two dimensions. We find that phase boundaries remain essentially planar with little bowing. Further, we find a new mechanism whereby acoustic waves ahead of the phase boundary nucleate new phase boundaries at the edges of the inclusion while the original phase boundary slows down or stops. Transformation proceeds as the freshly nucleated phase boundaries propagate leaving behind some untransformed martensite around the inclusion

Active tuning of photonic device characteristics during operation by ferroelectric domain switching

Ferroelectrics have many unusual properties. Two properties that are often exploited are first, their complex, nonlinear optical response and second, their strong nonlinear coupling between electromagnetic and mechanical fields through the domain patterns or microstructure. The former has led to the use of ferroelectrics in optical devices and the latter is used in ferroelectric sensors and actuators. We show the feasibility of using these properties together in nanoscale photonic devices. The electromechanical coupling allows us to change the domain patterns or microstructure. This in turn changes the optical characteristics. Together, these could provide photonic devices with tunable properties. We present calculations for two model devices. First, in a photonic crystal consisting of a triangular lattice of air holes in barium titanate, we find the change in the band structure when the domains are switched. The change is significant compared to the frequency spread of currently available high-quality light sources and may provide a strategy for optical switching. Second, we show that periodically poled 90° domain patterns, despite their complex geometry, do not cause dispersion or have band gaps. Hence, they may provide an alternative to the antiparallel domains that are usually used in quasiphase matching and allow for tunable higher-harmonic generation

Graded ferroelectric capacitors with robust temperature characteristics

Ferroelectric thin films offer the possibility of engineering the dielectric response for tunable components in frequency-agile rf and microwave devices. However, this approach often leads to an undesired temperature sensitivity. Compositionally graded ferroelectric films have been explored as a means of redressing this sensitivity, but experimental observations vary depending on geometry and other details. In this paper, we present a continuum model to calculate the capacitive response of graded ferroelectric films with realistic electrode geometries by accurately accounting for the polarization distribution and long-range electrostatic interactions. We show that graded c-axis poled BaxSr_(1−xT)iO_3 BST parallel plate capacitors are ineffective while graded a-axis poled BST coplanar capacitors with interdigitated electrodes are extremely effective in obtaining high and temperature-stable dielectric properties

Multiscale molecular simulation of membranes

Fundamental advances in the understanding of the molecular mechanisms enable a guided strategy towards analysis, modeling, and design of nanoscale structures. An essential difficulty in molecular modeling is that relevant system sizes of interest are very large. Although molecular mechanics has developed accurate models of interactions between individual molecules, the difficulty is that it is simply infeasible to solve these models on existing – or even conceived – computers. Although accurate models of the individual interactions between the molecules are available, the engineered materials typically consist of well over a billion such molecules. However, multiscale methods are well-suited to such problems: near the region of activity, e.g., an indenter pushing through the substrate, we can use molecular resolution to understand the critical features of indenter/substrate interactions; away from the active region, we can coarse-grain to retain only the effective influence. On the other hand, existing molecular multiscale methods, such as Quasi-continuum, Bridging-scales, and Bridging-domain methods, are only suitable for crystalline materials. They rely on the Cauchy–Born rule to relate the lattice vectors to the deformation gradient tensor which is a continuum description. The main feature of crystals is the translational symmetry. However, several structures such as nanotubes, bended graphene sheets, biological structures, and animal cell membranes do not exhibit translational symmetry. In our study, a unique molecular multiscale method for noncrystalline, but highly symmetric structures, is developed. Our method is based on the Objective Structures framework. In other words our method not only exploits the translational symmetry, but also uses other symmetries such as rotational and screw symmetries. Our strategy is to approximate the energy of full atomistic system by the energy of coarse-grained particles. We incorporate the symmetries of the structure to find the neighborhood around the coarse-grained particles. We then use finite element analysis to minimize the energy

A dynamic multiscale phase-field method for cracks

The displacement discontinuity at a crack poses severe challenges to numerical solutions. Dynamic crack growth simulations using the standard continuum framework require careful treatment of appropriate jump and boundary conditions at the crack faces as well as crack kinetics to ensure unique solutions. This is difficult to implement and computationally expensive particularly when there can be multiple interacting cracks. An alternative approach that has been developed is to use phase-field methods. These introduce a phase parameter that tracks the cracked and uncracked regions of the body. A spatial regularization ensures that the phase field does not have singularities. This is coupled to standard momentum balance with the elastic stiffness going to zero in the cracked region. The evolution of the crack is then governed by the interplay between momentum balance and the evolution of the phase field. An important shortcoming of these existing phase-field methods is that the phase field evolution is typically a simple gradient flow. Therefore, the kinetics of the crack motion is restricted to fairly simple possibilities, and the dynamics of fracture is based only on the interaction with momentum balance. We present a phase-field formulation for dynamic fracture with the key feature that complex crack kinetics can be readily prescribed. We use a geometric interpretation of the gradient of the phase parameter field as a linear density (density per unit length) of crack faces. For any curve in 3D space, we write a balance for these crack faces by accounting for appropriate flux and source terms. This balance in addition introduces a crack velocity field – distinct from the material velocity – that can be constitutively prescribed as a function of crack driving force, temperature, and any other relevant fields. The net result of our approach is an evolution equation for the crack faces for which complex kinetics (e.g., stick-slip) can be easily prescribed, yet the field remains nonsingular and amenable to simple numerical methods. The balance law additionally contains a source term that enables a straightforward and transparent prescription of crack nucleation. We show that this model can simulate cracks faster than shear wave speeds by using anisotropic kinetics. We analyze energy flow around the crack tip to understand crack branching and reasons for crack speeds being limited by elastic wave speeds

A Dimensionally-Reduced Nonlinear Elasticity Model for Liquid Crystal Elastomer Strips with Transverse Curvature

Liquid Crystalline Elastomers (LCEs) are active materials that are of interest due to their programmable response to various external stimuli such as light and heat. When exposed to these stimuli, the anisotropy in the response of the material is governed by the nematic director, which is a continuum parameter that is defined as the average local orientation of the mesogens in the liquid crystal phase. This nematic director can be programmed to be heterogeneous in space, creating a vast design space that is useful for applications ranging from artificial ligaments to deployable structures to self-assembling mechanisms. Even when specialized to long and thin strips of LCEs -- the focus of this work -- the vast design space has required the use of numerical simulations to aid in experimental discovery. To mitigate the computational expense of full 3-d numerical simulations, several dimensionally-reduced rod and ribbon models have been developed for LCE strips, but these have not accounted for the possibility of initial transverse curvature, like carpenter's tape spring. Motivated by recent experiments showing that transversely-curved LCE strips display a rich variety of configurations, this work derives a dimensionally-reduced 1-d model for pre-curved LCE strips. The 1-d model is validated against full 3-d finite element calculations, and it is also shown to capture experimental observations, including tape-spring-like localizations, in activated LCE strips