Consequences of dynamic yield surface in viscoplasticity Matti Ristinmaa*, Niels Saabye Ottosen Division of Solid Mechanics, Lund University, Box 118, S-221 00, Lund, Sweden Received 6 February 1999; in revised form 12 May 1999 Abstract A theory of viscoplasticity is formulated within a thermodynamic concept. The key point is the postulate of a dynamic yield surface, which allows us to take advantage of the postulate of maximum dissipation to derive an associated formulation of the evolutions laws for the internal variables without using penalty techniques that only hold in the limit it when viscoplasticity degenerates to inviscid plasticity. Even a non-associated formulation is presented. Within this general formulation, a particular format of the dynamic yield function enables us to derive the static yield function in a consistent manner. Hardening, perfect and softening viscoplasticity is also de®ned in a consistent manner. The approach even includes associated and non-associated viscoplasticity where corners exist on the yield and potential surfaces. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Thermodynamic of solids; Viscoplasticity; Creep; Flow-rule 1. Introduction Today there exist two major concepts when formulating viscoplastic models: the Perzyna or the Duvaut±Lions format. In the Perzyna model, Perzyna (1971), the direction of viscoplastic ¯ow is in general determined by the gradient of a plastic potential function calculated at the current stress point. In the Duvaut±Lions model, Duvaut and Lions (1962), the concept of closest-point projection of the stress onto a static yield surface is introduced and the direction of viscoplastic ¯ow is then determined by the dierence between the current stress and the closest-point projection. Here, we shall concentrate on the Perzyna formulation. A thermodynamic formulation of the Duvaut±Lions model based on the concept of additive split of the conjugated forces has recently been presented by Ristinmaa and Ottosen (1998). The postulate of maximum dissipation plays an important role in the thermodynamic treatment of International Journal of Solids and Structures 37 (2000) 4601±4622 0020-7683/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S0020-7683(99)00158-4 www.elsevier.com/locate/ijsolstr * Corresponding author. Fax: +46-46-2224620. E-mail address: matti.ristinmaa@hallf.lth.se (M. Ristinmaa).