Conservation integrals in couple stress elasticity

Noether's theorem on invariant variational principles is applied in the cas e of infinitesimal couple stress elasticity, thereby extending the analysis of Knowles and Sternberg (1972. On a class of conservation laws in lineari zed and finite elastostatics. Arch. Ration. Mech. Anal. 44, 187-211) beyond the range of classical elasticity. Two conserved integral quantities are d educed which generalize the J-integral and L-integral in the notation of Bu diansky and Rice (1973: Budiansky, B. and Rice, J. R. (1973) Conservation l aws and energy-release rates. J. Appl. Mech. 40, 201-203). An expression fo r an M-integral is also obtained, but it is demonstrated that there is no c orresponding conservation law for this integral. Relationships of the deriv ed path integrals to other similar quantities for couple stress elasticity which have appeared in the literature are discussed. (C) 2000 Elsevier Scie nce Ltd. All rights reserved.