Associate
Professor

Mechanical
Engineering and Materials Science

MEMS,
MS 321

Rice
University, P.O. Box 1892

Houston,
TX 77251-1892

phone:
(713) 348-3609

fax:
(713) 348-5423

office:
224 Mechanical Engineering Building

**Research Interests**

*Deformation, Polarization and Fracture of
Ferroelectric Ceramics*

Ferroelectric ceramics are becoming widely
employed materials for actuators and sensors. As such, prediction of device
performance and reliability are important technological problems. Due to both
linear and non-linear coupling of the mechanical and electrical fields,
adequate non-linear ferroelectric constitutive laws have yet to be developed.
New phenomenological constitutive laws for ferroelectric/ferroelastic switching
need to be developed and compared to experimental observations.

The development of self consistent models for
describing the non-linear switching behavior of ferroelectrics serves as a
useful guide to proposing new phenomenological laws. Concepts and models for
the description and evolution of the switching surface in stress and electric
field space, the associated increments of remanent strain and polarization and
the effects of transforming linear properties must still be understood, tested,
and included in a phenomenological constitutive law. Once acceptable
constitutive laws are developed there exists an abundance of boundary value
problems to be solved, including predicting the performance of actuators or
sensors and determining the fields and poling patterns near crack tips and
metal electrodes. Furthermore, the toughness of ferroelectric ceramics under
the added influence of applied electric field needs to be investigated further.

The current state of theory for fracture of
materials in the presence of electric fields is unsatisfactory. Aside from the
lack of a constitutive law for ferroelectric switching which would be required
for determining the fields around a crack tip, even the linear piezoelectric
theory is incomplete. Recently a theory has been proposed which splits the
total energy release rate into an electrical and mechanical part, and the
mechanical part has been used to fit experimental measurements of fracture
loads in the presence of electric fields. The question is, where does the
electrical energy go? In order to attain a complete energetic picture of
electromechanical fracture the boundary value problem must be posed in a more
consistent fashion with the appropriate (non-zero) traction and electric
displacement boundary conditions on the crack faces. Once this is accomplished,
a cohesive zone model which relates tractions and surface charges to potential
and displacement jumps across the crack surfaces will be useful in accounting
for the energetics of the fracture process. Furthermore, once a constitutive
law is formulated, the toughness of ferroelectric materials can also be
examined with the "transformation toughening" mechanism of domain
switching using the steady state crack growth model described in the next
section.

*Embedded Process Zone Models for Fracture
of Rate Dependant Materials*

Epoxies (usually with reinforcing rubber
particles) are being considered as an alternative to spot welding for joining
sheet metal in the auto industry. Understanding the mechanisms that control the
toughness of these materials is an important engineering problem. Epoxy
adhesives exhibit both increases and decreases in fracture toughness with
increases in crack velocity depending on the material system and mechanism of
failure ahead of the crack tip, e.g. void growth or crazing. The model being
used to investigate the toughness of these material systems employs a steady
state formulation with a cohesive fracture surface. The bulk material is able
to deform plastically and a cohesive surface on the crack plane controls crack
propagation. Both the bulk material and the cohesive zone constitutive laws can
be rate dependent. The steady state toughness of the material is then computed
as a function of both the bulk and cohesive zone properties. Improvement of the
cohesive zone models will come from micromechanics models for the processes
occurring ahead of the crack tip. For polymers and epoxies modeling of crazing
and void growth are useful.

Also, metals loaded at high strain rates also
exhibit a crack velocity dependent toughness. For this material inertia can
become an important factor which can be easily treated in the steady state
formulation. When the metal fails by a ductile mechanism it is possible to use
a rate dependent Gurson model for the cohesive surface. Along these lines it is
not necessary to limit the cohesive zone to a one dimensional constitutive law,
instead one can utilize the full multiaxial predictive capabilities of the
Gurson model. This will allow the model to account for the actual triaxial
stress states that will occur ahead of the crack tip.

**Journal Publications**

"Continuum thermodyanmics of ferroelectric domain evolution: Theory, finite element implementation and application to domain wall pinning ", with Yu Su, *Journal of the Mechanics and Physics of Solids*, **55**, pp. 280-305, (2007).

"Effects of in-plane electric fields on the toughening behavior of ferroelectric ceramics ", with J. Wang, *Journal of Mechanics of Materials and Structures*, preprint, (2007).

"Domain switch toughening in polycrystalline ferroelectrics ", with J. Wang, *Journal of Materials Research*,
**21**, pp. 13-20, (2006).

"Constraint Effects in Adhesive Joint Fracture ", with T. Pardoen, T. Ferracin and F. Delannay, *Journal of the Mechanics and Physics of Solids*, **53**, pp. 1951-1983, (2005).

"Electrostatic Forces and Stored Energy for Deformable Dielectric Materials
", with R.M. McMeeking, *Journal of Applied Mechanics
*, **72**, pp. 581-590, (2005).

"Energetically
Consistent Boundary Conditions for Electromechanical Fracture", *International
Journal of Solids and Structures*, **41**, pp. 6291-6315, (2004).

"Micro-electromechanical
Determination of the Possible Remanent Strain and Polarization States in
Polycrystalline Ferroelectrics and the Implications for Phenomenological Constitutive
Theories ", with J. Wang and J. Sheng, *Journal of Intelligent
Materials Systems and Structures*, **15**, pp. 513-525, (2004).

"Non-linear
Constitutive Modeling of Ferroelectrics ", *Current Opinion in Solid
State and Materials Science*, **8**, pp. 59-69, (2004).

"On the
Fracture Toughness of Ferroelectric Ceramics with Electric Field Applied
Parallel to the Crack Front ", with Jianxin Wang, *Acta Materialia*, **52**, pp.
3435-3446, (2004).

"On the Fracture
Toughness Anisotropy of Mechanically Poled Ferroelectric Ceramics ", *International
Journal of Fracture*, **126**, pp. 1-16, (2004).

"In-Plane
Complex Potentials for a Special Class of Materials with Degenerate
Piezoelectric Properties ", *International Journal of Solids and
Structures*, **41**, pp. 695-715, (2004).

"On the Strain
Saturation Conditions for Polycrystalline Ferroelastic Materials ", *Journal
of Applied Mechanics*, **70**, pp. 470-478, (2003).

"On the Fracture
Toughness of Ferroelastic Materials ", *Journal of the Mechanics and
Physics of Solids*, **51/8**, pp. 1347-1369, (2003).

"On the
determination of the cohesive zone properties of an adhesive layer from the
analysis of the wedge-peel test",with T. Ferracin, F. Delannay and T.
Pardoen, *International Journal of Solids and Structures*, **40**, pp.
2889-2904, (2003).

"Fully Coupled,
Multi-Axial, Symmetric Constitutive Laws for Polycrystalline Ferroelectric
Ceramics", *Journal of the Mechanics and Physics of Solids*, **50/1**,
pp. 127-152, (2002).

"Uncoupled,
Asymptotic Mode III and Mode E Crack Tip Solutions in Non-Linear Ferroelectric
Materials", *Engineering Fracture Mechanics*, **69/1**,
pp. 13-23, (2002).

"A New Finite
Element Formulation for Electromechanical Boundary Value Problems", *International
Journal for Numerical Methods in Engineering*, **55**, pp. 613-628 (2002).

"A
Phenomenological Multi-axial Constitutive Law for Switching in Polycrystalline
Ferroelectric Ceramics", with R.M. McMeeking, *International Journal
of Engineering Science, ***40**, pp. 1553-1577 (2002).

"Curvature-induced
Polarization in Carbon Nanoshells", with T. Dumitrica and B.I.
Yakobson, *Chemical Physics Letters*,
**360**, pp. 182-188 (2002).

"Crack Velocity
Dependent Toughness in Rate Dependent Materials", with T. Pardoen and
J. W. Hutchinson, *Mechanics of Materials*, **32**, pp. 663-678, (2000).

"Micromechanical
Simulation of the Failure of Fiber Reinforced Composites", with I. J.
Beyerlein and R. M. McMeeking, *Journal of the Mechanics and Physics of
Solids*, **48/3**, pp. 621-648, (2000).

"A
Phenomenological Constitutive Law for Ferroelastic Switching and a Resulting
Asymptotic Crack Tip Solution", with R. M. McMeeking, *Journal of
Intelligent Material Systems and Structures*, **10**, pp. 155-163, (1999).

"A Constitutive
Model for Ferroelectric Polycrystals", with J. E. Huber, N. A. Fleck
and R. M. McMeeking, *Journal of the Mechanics and Physics of Solids*, **47/8**,
pp. 1663-97, (1999).

"A Shear-Lag Model
for Failure Simulations of Unidirectional Fiber Composites Including Matrix
Stiffness", with I. J. Beyerlein, *Mechanics of Materials*, **31/5**,
pp.331-350, (1999).

"Stress
Concentrations in Composites with Interface Sliding, Matrix Stiffness, and
Uneven Fiber Spacing Using Shear Lag Theory", with R.M. McMeeking, *International
Journal of Solids and Structures*, **36/28**, pp. 4333-4361, (1999).

"An Improved
Shear Lag Model for Broken Fibers in Composite Materials", with M.A.
McGlockton and R.M. McMeeking, *Journal of Composite Materials*, **33/7**, pp.
667-680, (1999).

"A Shear Lag Model
for a Broken Fiber Embedded in a Composite with a Ductile Matrix",
with R.M. McMeeking, *Composites Science and Technology*,** 59/3**,
pp. 447-457, (1999).

"A Self-Consistent
Constitutive Model for Switching in Polycrystalline Barium Titanate",
with R. M. McMeeking, *Ferroelectrics*,
**255**, pp. 13-34, (2001).

**Conference Proceedings**

"Modeling Fracture
in Ferroelastic Ceramics", *Fracture Mechanics of Ceramics 14 and 15*, edited by K.H. White et al. (2003).

"Micro-Electromechanically
Informed Phenomenological Constitutive Models for Ferroelectrics",
with J. Wang and J. Sheng, *Proceedings of the SPIE*, **5053**,
(2003).

"A New Finite
Element Formulation for Electromechanics", *Proceedings of the SPIE*, **4699**,
pp. 31-39, (2002).

"Asymptotic
Mode III and Mode E Crack Tip Solutions in Ferroelectric Materials", *Proceedings
of the ICF10*, (2001).

"Shear Lag
Modelling of Thermal Stresses in Unidirectional Composites", *Proceedings
of the ICF10*, (2001).

"Crack
Velocity Dependent Toughness in Rate Dependent Materials", *Proceedings
of the ICF10*, (2001).

"Predictive
Fracture Model for Steady-State Failure of Adhesively-Bonded Joints with
Extensive Plastic Yielding", with T. Ferracin, J.Y. Sener, F. Delannay
and T. Pardoen, *Proceedings of the ICF10*, (2001).

"Symmetric
Constitutive Laws for Ploycrystalline Ferroelectric Ceramics", *Proceedings
of the SPIE*, **4333**, pp. 271-278, (2001).

"Modeling of
Fracture in Ferroelectric Ceramics", with R. M. McMeeking, *Proceedings
of the SPIE*, **3992**, pp. 176-184, (2000).

"A Self
Consistent Model for Switching in Polycrystalline Ferroelectrics: Electrical
Polarization Only", with R. M. McMeeking, *Proceedings of the SPIE*, **3667**,
pp. 172-180, (1999).

"Annihilation Radii for Dislocations
Intercepting a Free Surface with Application to Heteroepitaxial Thin Film
Growth", with M. Chang, S. K. Mathis and G. E. Beltz, in III-V and IV-IV
Materials and Processing Challenges for Highly Integrated Microelectronics and
Optoelectronics (edited by S. A. Ringel, E. A. Fitzgerald, I. Adesida, and D.
C. Houghton), *Materials Research Society Symposium Proceedings*,** 535**,
pp. 9-14 (1999).

"A Network Model for the Plastic
Compaction of Monodispersed Spherical Powder", with G. Deutschmann and R.
M. McMeeking, Proceedings of the AIChE PTF Topical Conference on Advanced
Technologies for Particle Processing, Miami Beach, Florida, November 15-20,
(1998).