International Journal of Non-Linear Mechanics 36 (2001) 679 } 686 Lorentz group on Minkowski spacetime for construction of the two basic principles of plasticity Hong-Ki Hong*, Chein-Shan Liu Department of Civil Engineering, National Taiwan University, Taipei 106-17, Taiwan Department of Mechanical and Marine Engineering, National Taiwan Ocean University, Keelung 202-24, Taiwan Received 28 October 1999; accepted 27 March 2000 Abstract We show that a model of plasticity is a necessary consequence of the two basic principles: (1) causality in the truncated future cone of the Minkowski spacetime (or its generalization) of augmented states, and (2) controllability and non-generativity in a reachable, bounded space of states. To consider the symmetry switching between PSO  (n, 1) and SE(n) due to switching on and o! the plasticity mechanism, the model is reconstructed as a dynamical system on a composite space, which results from a surgery on Minkowski spacetime.  2001 Elsevier Science Ltd. All rights reserved. Keywords: Plasticity; Causality; Controllability; Minkowski spacetime; Lorentz group; Two basic principles 1. Introduction Plasticity theory of solid materials and structural members under a complicated mechanical environ- ment is a very important topic for engineering science and practice. However, there remain a few fundamental problems yet to be resolved. We name a few among them. What ideas underlie the behav- ior of plasticity } plastically deformed solids and structures? What attributes should a model of plas- ticity possess? Why do the present-day models of the (conventional) theory of plasticity gather forms of expressions as diverse as yield conditions, plas- tic-#ow rules, loading-unloading criteria, elastic} plastic decompositions, laws of kinematic harden- ing, etc.? Indeed, the ingredients of constitutive * Corresponding author. Tel.: #886-2-2366-1931; fax: #886-2-2362-2975. E-mail address: hkhong@ce.ntu.edu.tw (H.-K. Hong). relations are separately speci"ed and seem to be loosely structured. Curious scholars cannot help asking if there is a backbone idea by which the ingredients become organized. After more than a century of experiments and studies, may we take a step forward to answer these questions? The pres- ent paper is supposed to be one of the attempts to face the di$culties encountered above. It investi- gates internal symmetry, reveals hidden spacetime structure, and derives two basic principles of a plas- ticity model, which we believe underlies the princi- pal behavior of plasticity in general. Concerning the questions posed, we call atten- tion to some occasions in the development of the theory of plasticity, which had paved the way for the research of the present paper. First, the #ow rule which relates (principal) stresses to (principal) strain increments was suggested by Saint Venant (1870) and by Le H vy (1871). Next, the propor- tionality factor between the (deviatoric) stress com- ponents Q and the (plastic) strain increment 0020-7462/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 0 - 7 4 6 2 ( 0 0 ) 0 0 0 3 3 - 0