A novel second-order reduced homogenization approach for nonlinear thermo-mechanical problems of axisymmetric structures with periodic micro-configurations

Abstract

A novel second-order reduced homogenization (SORH) approach is introduced for analyzing dynamic thermo-mechanical coupling problems in axisymmetric inelastic structures with periodic micro-configuration. The axisymmetric heterogeneous structures are periodically distributed in radial and axial directions and homogeneous distribution in circumferential directions. Firstly, the nonlinear coupled thermo-mechanical model is proposed, and the high-order nonlinear local problems, effective material parameters and the nonlinear homogenization equations are derived successively by the multiscale asymptotic expansion. Further, in order to reduce the large computational amount evaluated by the classical multiscale homogenization approach, the reduced-order nonlinear multiscale models and the corresponding finite-element algorithms are established in detail. The key features of the proposed approach are that an efficient reduced-model form based on transformation field analysis (TFA) to analyze nonlinear local cell problems is proposed and a nonlinear thermo-mechanical problem which considers the mutual coupling for the temperature and displacement fields is computed. In particular, a new SORH algorithm is proposed for investigating the axisymmetric inelastic structures. Finally, three typical numerical experiments are carried out, and the effectiveness and correctness of our presented algorithms in simulating and predicting the macroscopic behavior of the heterogeneous structures are confirmed.