Acta Mech 214, 31–48 (2010) DOI 10.1007/s00707-010-0310-0 S. Kapuria · P. Kumari · J. K. Nath Efficient modeling of smart piezoelectric composite laminates: a review Received: 15 October 2009 / Revised: 9 November 2009 / Published online: 22 April 2010 © Springer-Verlag 2010 Abstract Current research issues in the development of efficient analysis models and their efficient numerical implementation for smart piezoelectric laminated structures are discussed in this paper. The improved zigzag theories with a layerwise quadratic variation of electric potential have emerged as the best compromise between accuracy and cost for hybrid composite, sandwich and FGM beams and plates. The concept of associating surface potentials to electric nodes and internal potentials to physical nodes is very effective in modeling the equipotential electroded surfaces. Unified formulations for shear and extension mode actuation, and modeling of piezoelectric composite actuators and sensors are discussed. Future challenge lies in developing efficient theories capable of predicting the interlaminar transverse shear stresses in hybrid laminates directly from the constitutive equations. 1 Introduction The design of structures involved in the advanced technology including the next generation of aerospace vehi- cles, automobiles, robotics, medical instruments and sports products is undergoing a sea change in order to make them ultra-reliable with a near-zero incidence of failure and to fulfill stringent performance require- ments under a challenging environment. This has led to the concept of multifunctional structures wherein multiple properties of materials are exploited in such a way that besides its major designated functionality, the same structural component can accomplish at least one more task, such as the active vibration control, health monitoring etc. of the host structure. Composite and sandwich laminates integrated with embedded or surface- mounted piezoelectric sensors and actuators (hereafter called hybrid laminates) to introduce self-sensing and actuation capabilities, form a very important part of this new generation of smart structures. The piezoelectricity, which is an electromechanical phenomenon that couples mechanical and electric fields, was first discovered in quartz by Pierre and Jacques Curie in 1880 [18]. The research on the use of piezoelectric materials as distributed sensors and actuators for smart structural system was initiated [34] about a hundred years later with the advent of polymeric piezoelectric materials [4]. Beginning with the pioneering book of Tiersten [149] on piezoelectric plate vibration, several books [43, 109, 115, 127, 155, 156] have appeared on the mechanics of piezoelectric and smart plates and shells. For large scale structural control applications such as in aerospace structures, monolithic piezoelectric actuators and sensors suffer from certain shortcomings with regard to tailorable anisotropic actuation, i.e. directional actuation, robustness against damage during use and handling, ability to cover the entire structure for distributed actuation and sensing, and conformability to curved structural members such as shells and tubes. Recent developments of the piezoelectric fiber reinforced S. Kapuria (B ) · P. Kumari · J. K. Nath Department of Applied Mechanics, IIT Delhi, Hauz Khas, New Delhi, India E-mail: kapuria@am.iitd.ac.in Tel.: +91-11-26591218 Fax: +91-11-26581119