ON THE REDUCTION OF CONSTANTS IN PLANAR COSSERAT ELASTICITY WITH EIGENSTRAINS AND EIGENCURVATURES Iwona Jasiuk The George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia, USA Martin Ostoja-Starzewski Department of Mechanical Engineering McGill University Montre ´al Que´bec, Canada We study the reduced parameter dependence in linear plane Cosserat elasticity with eigenstrains and eigencurvatures. The focus is on singly connected inhomogeneous materials. We find conditions on the eigenstrains and eigencurvatures for the planar stress field to be invariant under a shift in area Cosserat compliances. The analysis can be extended to multiply connected inhomogeneous or multiphase materials. The special case is linear planar uncoupled micropolar thermoelasticity where eigenstrains represent the product of thermal expansion and temperature change. Keywords Cosserat planar elasticity, eigencurvatures, eigenstrains, stress invariance In this article we study a reduced parameter dependence in linear plane Cosserat (micropolar) elasticity with eigenstrains and eigencurvatures. The related problem of planar Cosserat elasticity with neither eigenstrains nor curvatures was studied in [1], whereas the problem of classical elasticity with eigenstrains was just recently considered in [2]. These two studies were generalizations of the seminal work of Cherkaev, Lurie, and Milton [3], who showed that the stress field in two-dimensional Communicated by Jo´zef Ignaczak on May 30, 2003. Presented at the Symposium dedicated to Richard B. Hetnarski at the Fifth International Congress on Thermal Stresses, Thermal Stresses 2003, Blacksburg, Virginia, June 8–11, 2003. I. Jasiuk gratefully acknowledges the support of the National Science Foundation through the grant CMS-0085137. The work of M. Ostoja-Starzewski was made possible by support from the NSERC and the Canada Research Chairs Program. Address correspondence to Martin Ostoja-Starzewski, Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montre´ al, Que´ bec H3A 2K6, Canada. E-mail: martin.ostoja@mcgill.ca Journal of Thermal Stresses, 26: 1221–1228, 2003 Copyright # Taylor & Francis Inc. ISSN: 0149-5739 print/1521-074X online DOI: 10.1080/01495730390232156 1221