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.

Article on a Finite Element Method for Electromechanics

12. C.M. Landis, 2002. “A New Finite Element Formulation for Electromechanical Boundary Value Problems”, International Journal for Numerical Methods in Engineering, 55, 613-628.

Articles on Ferroelectric Constitutive Behavior

41. I. Munch, M. Krauss, C.M. Landis and J.E. Huber, 2011. “Domain Engineered Ferroelectric Energy Harvesters on a Substrate”, Journal of Applied Physics 109, 104106.

34. A. Kontsos and C.M. Landis, 2010. “Phase-field Modeling of Domain Structure Energetics and Evolution in Ferroelectric Thin Films”, Journal of Applied Mechanics 77, 041014.

33. A. Kontsos and C.M. Landis, 2009. “Computational Modeling of Domain Wall Interactions with Dislocations in Ferroelectric Crystals”, International Journal of Solids and Structures, 46, 1491-1498.

28. Y. Su and C.M. Landis, 2007. “Continuum Thermodynamics of Ferroelectric Domain Evolution: Theory, Finite Element Implementation, and Application to Domain Wall Pinning”, Journal of the Mechanics and Physics of Solids, 55, 280-305.

22. C.M. Landis, 2004. “Nonlinear Constitutive Modeling of Ferroelectrics”, Current Opinion in Solid State and Materials Science, 8, 59-69.

19. C.M. Landis, J. Wang and J. Sheng, 2004. “Micro-electromechanical Determination of the Possible Remanent Strain and Polarization States in Polycrystalline Ferroelectrics and Implications for Phenomenological Constitutive Theories”, Journal of Intelligent Material Systems and Structures, 15, 513-525.

16. C.M. Landis, 2003. “On the Strain Saturation Conditions for Polycrystalline Ferroelastic Materials”, Journal of Applied Mechanics, 70, 470-478.

14. C.M. Landis, 2002. “Fully Coupled, Multi-Axial, Symmetric Constitutive Laws for Polycrystalline Ferroelectric Ceramics”, Journal of the Mechanics and Physics of Solids, 50, 127-152.

10. R.M. McMeeking and C.M. Landis, 2002. “A Phenomenological Multiaxial Constitutive Law for Switching in Polycrystalline Ferroelectric Ceramics”, International Journal of Engineering Science, 40, 1553-1577.

9. C.M. Landis and R.M. McMeeking, 2001. “A Self-Consistent Constitutive Model for Switching in Polycrystalline Barium Titanate”, Ferroelectrics, 255, 13-34.

7. C.M. Landis and R.M. McMeeking, 2000. “A Phenomenological Constitutive Law for Ferroelastic Switching and a Resulting Asymptotic Crack Tip Solution”, Journal of Intelligent Material Systems and Structures, 10, 155-163.

5. J. E. Huber, N. A. Fleck, C.M. Landis and R. M. McMeeking, 1999. "A Constitutive Model for Ferroelectric Polycrystals", Journal of the Mechanics and Physics of Solids, 47, 1663-1697.

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.

Articles on Piezoelectric and Ferroelectric Fracture

40. D. Carka and C.M. Landis, 2011. “The Analysis of Crack Tip Fields in Ferroelastic Materials”,Smart Materials and Structures 20, 094005.

38. W. Li and C.M. Landis, 2011. “Nucleation and Growth of Domains Near Crack Tips in Single Crystal Ferroelectrics”,Engineering Fracture Mechanics 78, 1505-1513.

31. W. Li, R.M. McMeeking and C.M. Landis, 2007. “On the Crack Face Boundary Conditions in Electromechanical Fracture and an Experimental Protocol for Determining Energy Release Rates”, European Journal of Mechanics A/Solids 27, 285-301.

29. J. Sheng and C.M. Landis, 2007. “Toughening due to Domain Switching in Single Crystal Ferroelastic Materials”, International Journal of Fracture, 143, 161-175.

27. J. Wang and C.M. Landis, 2006. “Effects of In-Plane Electric Fields on the Toughening Behavior of Ferroelectric Ceramics”, Journal of Mechanics of Materials and Structures, 1, 1075-1095.

26. J. Wang and C.M. Landis, 2006. “Domain Switch Toughening in Polycrystalline Ferroelectrics”, Journal of Materials Research, 21, 13-20.

23. C.M. Landis, 2004. “Energetically Consistent Boundary Conditions for Electromechanical Fracture”, International Journal of Solids and Structures, 41, 6289-6313.

21. J. Wang and C.M. Landis, 2004. “On the Fracture Toughness of Ferroelectric Ceramics with Electric Field Applied Parallel to the Crack Front”, Acta Materialia, 52, 3435-3446.

20. C.M. Landis, 2004. “On the Fracture Toughness Anisotropy of Mechanically Poled Ferroelectric Ceramics”, International Journal of Fracture, 126, 1-16.

18. C.M. Landis, 2004. “In-plane Complex Potentials for a Special Class of Materials with Degenerate Piezoelectric Properties”, International Journal of Solids and Structures, 41, 695-715.

17. C.M. Landis, 2003. “On the Fracture Toughness of Ferroelastic Materials”, Journal of the Mechanics and Physics of Solids, 51, 1347-1369.

13. C.M. Landis, 2002. “Uncoupled, Asymptotic Mode III and Mode E Crack Tip Solutions in Non-Linear Ferroelectric Materials", Engineering Fracture Mechanics, 69, 13-23.

The figure above 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.

Articles on Finite Deformation Electromechanics

30. R.M. McMeeking, C.M. Landis and S.M.A. Jimenez, 2007. “The Principle of Virtual Work for Combined Electrostatic and Mechanical Loading of Materials”, International Journal of Non-linear Mechanics, 42, 831-838.

24. R.M. McMeeking and C.M. Landis, 2005. “Electrostatic Forces and Stored Energy for Deformable Dielectric Materials”, Journal of Applied Mechanics, 72, 581-590.

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.

Articles on Rate Dependent Fracture and the Wedge Peel Test

25. T. Pardoen, T. Ferracin, C.M. Landis and F. Delannay, 2005. “Constraint Effects in Adhesive Joint Fracture”, Journal of the Mechanics and Physics of Solids, 53, 1951-1983.

15. T. Ferracin, C.M. Landis, F. Delannay and T. Pardoen, 2003. “A Systematic Study of the Plastic Wedge-Peel Test Using an Embedded Cohesive Zone Model”, International Journal of Solids and Structures, 40, 2889-2904.

8. C.M. Landis, T. Pardoen and J.W. Hutchinson, 2000. “Crack Velocity Dependent Toughness in Rate Dependent Materials”, Mechanics of Materials, 32, 663-678.

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.  More recently I have had the opportunity to work with Pradeep Sharma on flexoelectricity in thin film superlattices.

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.

Articles on the Flexoelectricity

39. N.D. Sharma, C.M. Landis and P. Sharma, 2010. “Piezoelectric Thin-Film Super-Lattices without Using Piezoelectric Materials”, Journal of Applied Physics, 108, 024304.

11. T. Dumitrica, C.M. Landis and B.I. Yakobson, 2002. “Curvature-induced Polarization in Carbon Nanoshells”, Chemical Physics Letters, 360, 182-188.

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.  Funding for the research presented on this page from ONR, ARO, and NSF grants 0238522 and 0909139 is gratefully acknowledged.

  1. Constitutive Modeling of Ferroelectrics

  2. Finite Element Method for Electromechanics

  3. Fracture of Piezoelectrics and Ferroelectrics

  4. Finite Deformation Electromechanics

  5. Ferromagnetic Shape Memory Alloys

  6. DtN Map for 2D Crack Problems and the Path-Dependence of the J-Integral

  7. Rate Dependent Fracture and the Wedge Peel Test

  8. Flexoelectricity

  9. Shear-Lag Modeling of Composites

Articles on Shear-Lag Modeling in Composites

6. C.M. Landis, I. J. Beyerlein and R. M. McMeeking, 2000. "Micromechanical Simulation of the Failure of Fiber Reinforced Composites", Journal of the Mechanics and Physics of Solids, 48, 621-648.

4. I. J. Beyerlein and C.M. Landis, 1999. "Shear-Lag Model for Failure Simulations of Unidirectional Fiber Composites Including Matrix Stiffness", Mechanics of Materials, 31, 331-350.

3. C.M. Landis and R.M. McMeeking, 1999. "Stress Concentrations in Composites with Interface Sliding, Matrix Stiffness, and Uneven Fiber Spacing Using Shear Lag Theory", International Journal of Solids and Structures, 36, 4333-4361.

2. C.M. Landis, M.A. McGlockton and R.M. McMeeking, 1999. "An Improved Shear Lag Model for Broken Fibers in Composite Materials”, Journal of Composite Materials, 33, 667-680.

1. C.M. Landis and R.M. McMeeking, 1999. "A Shear Lag Model for a Broken Fiber Embedded in a Composite with a Ductile Matrix", Composites Science and Technology, 59, 447-457.

0. C.M. Landis, 2001. "Shear Lag Modeling of Thermal Stresses in Unidirectional Composites", Proceedings of the ICF10.

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.

Ferromagnetic shape memory alloys have many of the same behaviors as ferroelectrics but with the effects of electric fields replaced by their magnetic counterparts.  Some of these materials show potential for strains 10 to 100 times larger than what is possible in ferroelectrics but with the tradeoff of a low blocking stress.  The following paper looks at this issue with a phase-field modeling framework (micromagnetics) and hypothesizes that the low blocking stress is due to a dissociation of the magnetic domain walls from the martensite twin boundaries.

Articles on Ferromagnetic Shape Memory Alloys

32. C.M. Landis, 2008. “A Continuum Thermodynamics Formulation for Micro-magneto-mechanics with Applications to Ferromagnetic Shape Memory Alloys”, Journal of the Mechanics and Physics of Solids, 56, 3059-3076.

While working on modeling switching zones in ferroelastic materials Maria Carka and I, along with Mark Mear, developed a method for applying infinite boundary conditions to small scale yielding crack problems.  The approach can also be used to create very accurate crack-tip elements.  The method is very similar to the work of Dan Givoli and co-workers on Dirichlet-to-Neumann maps.  We then stumbled upon an unexpected (to us at least) level of J-integral path-dependence in standard elastic-plastic materials.

Articles on the DtN Map for Cracks and the Path-Dependence of J

39. D. Carka, R.M. McMeeking and C.M. Landis, 2011. “A Note on the Path-Dependence of the J-Integral Near a Stationary Crack in an Elastic-Plastic Material with Finite Deformation”, submitted to the Journal of Applied Mechanics.

37. D. Carka, M.E. Mear and C.M. Landis, 2011. “The Dirichlet-to-Neumann Map for Two-Dimensional Crack Problems”, to appear in Computer Methods in Applied Mechanics and Engineering,

36. D. Carka and C.M. Landis, 2011. “On the Path-Dependence of the J-Integral in an Elastic-Plastic Material”, Journal of Applied Mechanics, 78, 011006.