ABSTRACT

Abstract It is shown that the phenomenon of the dependence of material behavior on the specimen's dimensions, commonly known as size effect, can be interpreted by using the gradient approach to deformation as this was developed by the author and his co-workers. In particular, two classes of problems are considered: plastic twisting of copper wires where the strength is observed to increase with decreasing diameter and elastic stressing of an infinite hollow cylinder where it is observed that smaller holes are stiffer and fail at a higher stress. In the first case a gradient-dependent flow stress is direcdy used, while in the second case a simple form of gradient elasticity is employed to solve the relevant boundary value problem. In both cases the gradient approach seems to model sufficientiy well the corresponding size effects. Keywords: gradient effects, size effects, scale effects, gradient elasticity, gradient plasticity

1 Introduction The need for higher order gradients in the theory of deformation for softening solids and heterogeneous microstructures was first pointed out by the author [1-3] in relation to the problems of shear band thickness and persistent slip band spacing. It was further elaborated upon by the author [4-7] and in more detail by the author and co-workers [818] in a series of papers dealing with the localization and stability of deformation in metals and soils. Background material pertaining to these developments of the gradient approach can be found, in particular, in the papers by Aifantis [3,5], Triantafyllidis and Aifantis [8], Zbib and Aifantis [9], Vardoulakis and Aifantis [12], Muhlhaus and Aifantis [15] and Oka/Yashima/Adachi/Aifantis [18]. Additional results with emphasis on numerical aspects can be found in follow-up contributions by de Borst and Muhlhaus [19] and Sluys/de Borst/Muhlhaus [20], as well as by Vardoulakis and Frantziskonis [21] and Vardoulakis/Papamichos/Sulem [22] (see also the author's review [6]).