A second-order reduced homogenization for nonlinear structures with periodic configurations in cylindrical coordinates

A high-efficiency second-order reduced homogenization (SORH) method is established for the inelastic problem of periodic heterogeneous structures in cylindrical coordinate. The composite structures investigated in this paper are periodical in radial, axial and circumferential directions. The new second-order linear/nonlinear local solutions at microscale are given by introducing various multiscale auxiliary functions. And, the nonlinear high-order homogenization solutions are obtained at macroscale using a modified asymptotic expansion method. The significant novelties of the work are (i) an effective reduced model on the basis of transformation field analysis given to solve the nonlinear multiscale problems in cylindrical coordinates with less computational amount and (ii) a new second-order nonlinear multiscale algorithm established using asymptotic expansion technique for simulating the heterogeneous cylindrical structure. Finally, by three typical numerical examples including nonlinear elastic and elasto-plastic periodic problems, the validity and accuracy of the proposed algorithms are verified.