Mixture theory for a thermoelasto-plastic porous solid considering fluid flow and internal mass exchange M. Ristinmaa a,⇑ , N.S. Ottosen a , B. Johannesson b a Division of Solid Mechanics, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden b Department of Civil Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark article info Article history: Received 4 March 2011 Accepted 2 July 2011 Available online 27 July 2011 Keywords: Mixture theory Porous material Growth/swelling Mass exchange Large strain abstract A thermoelastic–plastic body consisting of two phases, a solid and a fluid, each comprising two constituents is considered where one constituent in one phase is allowed to exchange mass with another constituent (of the same substance) in the other phase. A large strain setting is adopted and the formulation applies to general anisotropy and the existence of residual stresses. Generalized forms of Fourier’s, Fick’s and Darcy’s laws are derived and also the stresses on the constituent, phase and mixture level are established; in addition, the evolution law for general plasticity is given. Finally, and in particular, a general evolu- tion law for the rate of deformation tensor related to mass exchange is proposed and this leads to general absorption and desorption evolution laws for mass exchange between two constituents (of the same substance), one belonging to the solid phase and the other to the fluid phase. Equilibrium curves for absorption and desorption also emerge from the theory. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Materials consisting of a porous solid with fluid filled pores are of importance in different engineering applications and include the behavior of soil, biotissues, concrete, paper and wood. Common for these kinds of materials is that they swell when subjected to increased moisture contents (or shrink when exposed to drying). For some materials such as soft tissues and paper the deformations induced by drying or wetting are typically large and for this reason large deformation kinematics needs to be considered. Here hybrid mixture theory will be adopted for modeling of these features. The foundation of mixture theory was established by Truesdell and Toupin (1960) and Bowen (1976) and the mixture was assumed to consist of miscible components. To account for immiscible components, the concept of volume fractions can be introduced and this generalization was given by Hassanizadeh and Gray (1979b, 1979a) and later by Bowen (1980, 1982) and then termed hybrid mixture theory. The contribution of Hassanizadeh and Gray (1979b, 1979a) even included averaging pro- cedures by which essential information of the microstructure can be accounted for, but usually hybrid mixture theory is adopted directly without this averaging procedure. In the theory of porous media pursued, for instance, by deBoer (1999) and Ehlers (1993), volume fractions are also included, but, essentially, no distinction is made between phases and constituents. In the present paper, the hybrid mixture theory is adopted and the balance laws are then given by Hassanizadeh and Gray (1979b, 1979a) and Bennethum and Cushman (1996a, 1996b). For simplicity, interfacial effects and electrostatic effects are ignored although the hybrid mixture theory can be extended to account for these features, see Gray and Hassanizadeh (1998) and Bennethum and Cushman (2002a, 2002b). 0020-7225/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijengsci.2011.07.001 ⇑ Corresponding author. Tel.: +46 46 2227987. E-mail address: matti.ristinmaa@solid.lth.se (M. Ristinmaa). URL: http://www.solid.lth.se (M. Ristinmaa). International Journal of Engineering Science 49 (2011) 1185–1203 Contents lists available at ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci