Journal of the Mechanics and Physics of Solids 54 (2006) 1640–1667 Compressible rigid viscoplastic fluids Oana Cazacu a,Ã , Ioan R. Ionescu b a Department of Mechanical and Aerospace Engineering, REEF, University of Florida, 1350 N. Poquito Road Shalimar, FL 32579, USA b Laboratoire de Mathe´matiques, Universite´de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France Received 30 March 2005; received in revised form 13 February 2006; accepted 14 February 2006 Abstract In this paper, a general methodology for constructing fluid-type constitutive equations for description of the behavior of porous media when subjected to large deformations and high strain rates is proposed. The elastic deformations are neglected and the representation of the dynamic state of stress in the material is obtained from classic yield conditions for plastic solids using the viscoplastic regularization and/or a stress superposition method. Examples of constitutive equations obtained using both procedures are presented. We show that irrespective of the method used, it is not possible to obtain consistent viscoplastic fluid formulations starting from certain yield functions. Comparisons between the response of the proposed models for uniaxial compression conditions is provided. Extensions of these models that include coupling between damage, plastic and viscous effects are proposed. Finally, some results of numerical modeling of penetration into concrete using a compressible rigid-viscoplastic model are presented. r 2006 Elsevier Ltd. All rights reserved. Keywords: Compressible rigid-viscoplastic fluids; Viscoplastic regularization; Stress-superposition method; Dynamic behavior; Porous materials 1. Introduction Tout solide est un fluide qui s’ignore. J. Lemaitre and J.-L. Chaboche (1990) ARTICLE IN PRESS www.elsevier.com/locate/jmps 0022-5096/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jmps.2006.02.001 Ã Corresponding author. Tel.: +1 850 8339350; fax: +1 850 8339366. E-mail address: cazacu@gerc.eng.ufl.edu (O. Cazacu).