ON THE LOCALIZATION PROPERTIES OF MULTIPLICATIVE HYPERELASTO-PLASTIC CONTINUA WITH STRONG DISCONTINUITIES

The objective of this work is to examine the large strain localization properties of hyperelasto-plastic materials which are based on the mu ltiplicative decomposition of the deformation gradient. Thereby, the c ase of strong discontinuities is investigated. To this end, first an e xplicit expression for the spatial tangent operator is given, taking i nto account anisotropic as well as nonassociated material behaviour. T hen the structure of a regularized discontinuous velocity gradient is elaborated and discussed in detail. Based on these two results, the lo calization condition is derived with special emphasis on the loading c onditions inside and outside an anticipated localization band. Thereby , the intriguingly simple structure of the tangent operator, which res embles the structure of the geometrically linear theory, is extensivel y exploited. This similarity carries over to the general representatio n for the critical hardening modulus which is exemplified for isotropi c materials. As a result, analytical solutions are available under the assumption of small elastic strains, which is justified for metals. F inally, examples are given for the special case of the associated von Mises dow rule. To this end, the critical localization direction and t he critical hardening modulus are investigated with respect to the amo unt of finite elastic strain within different modes of homogeneous ela sto-plastic deformations. (C) 1997, Elsevier Science Ltd.