Thermomechanical homogenization analysis of axisymmetric inelastic solids at finite strains based on an incremental minimization principle

The paper presents an attempt to extend homogenization analysis to axisymmetric solids under thermomechanical loading. In axisymmetric solids, under axisymmetric thermomechanical loading and/or torsion, on both scales, macro and micro, the displacement and rotation response is by definition independent of the cylindrical angle co-ordinate. In homogenization analysis the deformation of the micro-structure is driven by the deformation gradient ¯F of the macro-structure and enhanced by a micro-scale fluctuation field ˜u, such that: x= ¯F · X + ˜u and in consequence F= ¯F + ˜F. What is new: on the micro-scale, the fact of independence of the cylindrical angle co-ordinate imposes the homogeneous or Taylor-assumption on the fluctuation field ˜ u of the R(epresentative) V(olume) E(lement) in the radial direction, whereas the other two fluctuation fields, the torsional angle ˜ and the axial displacement ˜w, are not affected. The thermomechanical problem on the macroscale is solved via a split approach: an isentropic mechanical phase, an isogeometrical thermal phase, and—in case of inelasticity—an update phase of the internal micro-variables. The homogenization of inelastic solid materials at finite strains is based on an incremental minimization principle, recently introduced by Miehe et al. (J. Mech. Phys. Solids 2002; 50:2123–2167). Two finite element examples demonstrate the viability of the proposed approach. Copyright q 2006 John Wiley & Sons, Ltd.