Continuum Mech. Thermodyn. (2007) 18: 455–467 DOI 10.1007/s00161-006-0039-0 ORIGINAL ARTICLE V. L. Berdichevsky · K. C. Le Dislocation nucleation and work hardening in anti-plane constrained shear Received: 8 December 2005 / Accepted: 13 November 2006 / Published online: 10 January 2007 © Springer-Verlag 2006 Abstract The paper aims at studying the dislocation nucleation, the corresponding work hardening and the influence of resistance to the dislocation motion within the framework of continuum theory of dislocations. We consider an anti-plane constrained shear problem which admits an analytical solution. The interesting features of this solution are the energy and dissipation thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effect. Keywords Dislocation nucleation · Work hardening · Size effect · Continuum theory of dislocations PACS 61.72.Bb, 61.72.Lk, 62.20.Fe 1 Introduction Plasticity in crystals and polycrystals is caused by nucleation, multiplication and motion of crystal defects. Defects appear in the crystal lattice to reduce its energy. Motion of defects yields the dissipation of energy, which, in turn, results in a resistance to the defect motion. The general structure of plasticity theory must, therefore, reflect this physical reality: an energy decrease by nucleation of defects and resistance to the defect motion due to dissipation. In classical plasticity theory these features are masked by the use of quite rough characteristics, the plastic strain, for the average description of dislocation network. In continuum theory of dislocations [1–3], these features are pronounced much better; in particular, the dislocation nucleation admits a clear characterization by the variational principle for finite plastic states [2]. This paper aims at studying the dislocation nucleation, the corresponding work hardening and the influence of resistance to the dislocation motion in an anti-plane constrained shear problem within the framework of continuum theory of dislocations suggested in [2,3]. This problem admits an analytical solution and allows one to see clearly all the features mentioned. In particular, the solution obtained exhibits the energy and dissipation thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effect. The paper is organized as follows. In Sect. 2 the setting of the problem is outlined. Sections 3 studies dislocation nucleation at zero resistance by the energy minimization. In Sect. 4 the evolution of the disloca- tion network under the action of external shear and non-zero resistance is determined. Section 5 discusses The financial support by the DFG (German Science Foundation) within the Collaborative Research Center 526 (project D9) for K.C. Le is gratefully acknowledged Communicated by L. Truskinovsky V. L. Berdichevsky (B ) Department of Mechanical Engineering, Wayne State University, Detroit, MI 48202, USA E-mail: vberd@eng.wayne.edu K. C. Le Lehrstuhl für Allgemeine Mechanik, Ruhr-Universität Bochum, 44780 Bochum, Germany