Multiscale modeling of periodic dissipative composites under thermomechanical loading conditions

Abstract

The modern technological challenges on the engineering industry and the extensive advances in the materials science have caused a tremendous increase in the development of composites. Plenty of engineering and biomechanics applications demand smart materials and structures which combine high strength, multifunctionality and durability. At the same time, a crucial parameter in the choice of the most suitable composite material is the long lifetime during repeated loading cycles, thus fatigue is an essential parameter in design. To achieve the high demands in the modern applications, composite materials often operate under thermomechanical conditions that cause the appearance of dissipative phenomena like plasticity, viscoelasticity-viscoplasticity and damage. The present work deals with periodic composite media subjected to fully coupled thermomechanical loading. The material constituents of these composites are assumed to belong in the general class of generalized standard materials laws. The aim is to provide a proper homogenization framework that describes accurately the basic conservation laws in both microscopic and macroscopic levels. The study is based on the asymptotic expansion homogenization technique, which permits to deduce useful results about the energy potentials that characterize the material response in both scales. Moreover, the numerical implementation is based on an incremental, linearized formulation. This formulation allows to identify proper thermomechanical 3D tangent moduli for the macroscale problem and thus design an implicit computational scheme.