A simplified (and exaggerated) schematic of the crystal structure of barium titanate is illustrated above.  This material, as well as other ferroelectrics, demonstrates a wealth of interesting physical behaviors including temperature, stress and electric field induced phase transitions, pyroelectricity, piezoelectricity, and domain switching.  Our research includes the development of constitutive models for these coupled and in most cases nonlinear phenomena.  We have developed phase-field models for domain wall evolution, single crystal continuum-transformation constitutive laws, and polycrystalline self-consistent and phenomenological constitutive models.

In some cases the development of the constitutive model is an ultimate goal.  However, we are also interested in using the constitutive models to make predictions of the electromechanical fields within specific device architectures and around material defects like crack and electrode tips.  Due to the nonlinear nature of the constitutive laws for ferroelectrics, we need to use numerical techniques to solve for these fields.

The figures above are of a 180 degree domain wall pinned by an array of charged line defects.  An electric field is applied and the critical field required for the domain wall to break through the array is computed.

With our constitutive models and numerical methods in hand, we have investigated how electrical and mechanical fields influence domain switching near steadily growing crack tips.  Our formulation allows us to determine the relative amounts of energy “sucked up” by domain switching and flowing into the crack tip.  Our other interests in the fracture area has focused on the electromechanical boundary conditions on the crack faces.  We have proposed a set of “energetically consistent” boundary conditions that ensure agreement between the crack tip energy release rate and the “global” energy release rate in conservative materials.

The figure below shows a calculation of the domain switching zone near a steadily growing crack tip in a ferroelastic material.  We are interested in the level of toughening that can be attributed to the dissipation due to domain switching.

All of the work displayed above assumes small deformations and a linear kinematics description of the material deformation.  This simplification allows us to neglect the electrical forces on the material and the associated Maxwell stresses that are induced by long-range electrical interactions.  Bob McMeeking and I have revisited the rather old and established field on the continuum mechanics of deformable dielectrics.  We have disposed of what we believe is a non-physical decomposition of the electric field into applied and “lattice” components.  While we identify the Maxwell stress, which certainly does exist, we recognize that separating this stress contribution from the Cauchy stress in the material is not possible since the thermodynamic constitutive relations can only relate their sum to the material free energy.

With Thomas Pardoen, John Hutchinson and others I have also worked on the problem of rate dependent fracture with applications to polymers and adhesives.  In our work we have treated the bulk material as a standard viscoplastic material and we investigate the fracture behavior of the material using a rate dependent cohesive zone.  Professor Pardoen and I have also looked at using different cohesive zone approximations to model the wedge peel test on two metal plates bonded by an adhesive layer.

During my time at Rice University I had the opportunity to interact with Boris Yakobson and Traian Dumitrica.  Among many other contributions to the modeling of the physical behavior of carbon nanotubes, they computed the polarization that was induced by the curvature of a graphene sheet.  Prior to completing their computation I told them that this property would be independent of the chirality of the tube and in fact this is what they found.  Unfortunately, at the time of writing the paper I had not heard of the term “flexoelectric” and so did not refer to this property as such.

Last, but not least, during my graduate studies I was also interested in modeling the strength of composites.  We developed a simplified micromechanics framework to investigate the stress distributions in fibers in composites with arbitrarily located fiber breaks.  This class of models is commonly referred to as “shear-lag” models.  We used these models to investigate fiber stresses and simulate composite strength under a wide range of geometrical and interface conditions.

This page contains the following topics.  Please scroll down or click on the links below to find them.  The numbering of the articles corresponds to the numbering on my CV.

Our research interests are in the mechanics and physics of smart materials.  Our recent work has focussed on the behavior of ferroelectric ceramics.  These materials are of technological interest due to the exceptionally strong coupling between their mechanical and electrical responses.  These materials are useful in sensors, actuators and memory devices.