On the localization properties of multiplicative hyperelasto-plastic continua with strong discontinuities

Abstract

The objective of this work is to examine the large strain localization properties of hyperelasto-plastic materials which are based on the multiplicative decomposition of the deformation gradient. Thereby, the case of strong discontinuities is investigated. To this end, first an explicit expression for the spatial tangent operator is given, taking into account anisotropic as well as nonassociated material behaviour. Then the structure of a regularized discontinuous velocity gradient is elaborated and discussed in detail. Based on these two results, the localization condition is derived with special emphasis on the loading conditions inside and outside an anticipated localization band. Thereby, the intriguingly simple structure of the tangent operator, which resembles the structure of the geometrically linear theory, is extensively exploited. This similarity carries over to the general representation for the critical hardening modulus which is exemplified for isotropic materials. As a result, analytical solutions are available under the assumption of small elastic strains, which is justified for metals. Finally, examples are given for the special case of the associated von Mises flow rule. To this end, the critical localization direction and the critical hardening modulus are investigated with respect to the amount of finite elastic strain within different modes of homogeneous elasto-plastic deformations.