HOMOGENIZATION TECHNIQUES FOR THERMOVISCOELASTIC SOLIDS CONTAINING CRACKS

In this paper mathematical techniques are developed for obtaining loca lly averaged (homogenized) constitutive equations for heterogeneous li near thermoviscoelastic solids. Homogenization principles will be deve loped for the cases wherein no internal boundaries are present, and al so where internal boundaries in the form of sharp cracks are present, thus resulting in damage dependent macroscopic constitutive equations. The microthermomechanics problem will first be formulated, followed b y the construction of the locally averaged equations resulting from th e homogenization process. It will be shown that homogenized conservati on laws and constitutive equations rake the same form as do the local equations when locally linear thermoviscoelastic media are considered. However, the resulting homogenized constitutive equations will be non linear in the case wherein time dependent damage occurs. In addition, for materials of convolution type at the local scale, the homogenized equations will be shown to contain a term that depends on the time der ivative of the strain localization tensor. Example problems will be di scussed and the homogenized results will be given for these examples i n order to demonstrate the technique. (C) 1998 Elsevier Science Ltd. A ll rights reserved.